Knewton assessment:
Chemical symbols on the periodic table will have a maximum of how many letters? Report your answer as a whole number with one significant figure.
0.074 mol - To calculate the number of moles in 2.3g of phosphorus, divide this mass by the molar mass as follows. 2.3g×1mol30.974g=0.0743mol Therefore, after rounding to two significant figures, we find that there are about 0.074mol of phosphorus in a 2.3g sample.
How many molecules are in 3 moles of benzene?
1.807×1024 - Since a mole is a fixed amount, simply multiply the number of molecules in a mole, 6.022×1023, by the number of moles, 3, in order to determine the number of molecules in 3 moles.
What is the molar mass of methane (CH4)?
16.043 g/mol - The molar mass also known as the formula mass is found using the atomic masses on the periodic table. The image above shows you where to find the atomic mass on a single element block on the periodic table. Follow the steps below to find the molar mass. Step 1: Find the quantity of each element using the molecular formula. Number of C atoms=1Number of H atoms=4 Step 2: Find the the average atomic mass (amu) from the periodic table of elements. Although the units typically associated with atomic masses are called amu (short for "atomic mass unit"), these are equivalent to grams per mole, and unit that is more frequently associated with "molar mass." C=12.011 g/molH=1.008 g/mol Step 3: Multiply the quantity of each element by its atomic mass to get the subtotal. C=12.011×1=12.011 g/molH=1.008×4=4.032 g/mol Step 4: Add the subtotals together to get the total molecular mass CH4=12.011 g/mol+4.032 g/mol=16.043 g/mol
When 5.0 grams of calcium are burned in oxygen, 7.0 grams of calcium oxide result. What mass of oxygen reacted?
2.0 grams
Using the periodic table provided, identify the atomic mass of sodium (Na) . Your answer should have 5 significant figures.
22.990 amu - Sodium (Na) is the 11th element on the periodic table. The atomic mass of sodium is 22.990 amu.
A 430 g sample of N2I6 would contain how many molecules?
3.3×1023 molecules - 430 g×1 mol N2I6789.44 g N2I6×6.022×1023 molecules1 mol=3.3×1023 molecules
110 grams of baking soda (NaHCO3) is equal to how many moles?
3.8 x 10^25 molecules - First, convert the mass of SO3 into moles of SO3 by dividing by the molar mass: 5100 g×1 mol SO380.063 g SO3=63.70 mol Recall that Avogadro's number describes the number of atoms or molecules in a mole. By dimensional analysis, we see that we can convert the moles of SO3 into molecules by multiplying the moles of SO3 by Avogadro's number: 63.70 mol×6.022×1023 molecules1 mol=3.836×1025 molecules The answer should have two significant figures, so round to 3.8×1025 molecules.
What is the mass in grams of 1.00×106 sodium atoms?
3.82 x 10 ^-17 g - To determine the mass of 1.00×106 sodium atoms, divide by Avogadro's number and multiply by the molar mass of sodium. 1.00×106 atoms×1 mol6.022×1023 atoms×22.990 g1 mol=3.818×10−17 g Therefore, after rounding to three significant figures, we find that the mass of 1.00×106 sodium atoms is about 3.82×10−17g.
What is the average mass in grams of one uranium atom (U)? Use 6.022×1023mol−1 for Avogadro's number.
3.953×10−22g 1 atom×1 mole6.022×1023×238.029 g1 mole=3.953×10−22 g
Which measurement of the length of an object is the most precise?
4.3084 cm - The more significant figures there are in a value, the more precise of a measurement it represents.
What is the formula mass in atomic mass units for NaF?
41.998 amu - Use the periodic table to get the atomic mass of each element. Multiply the atomic mass of the element by the number of atoms of that element in the compound. mass of Na: 22.990×1=22.990 mass of F: 18.998×1=18.998 Add the mass of each element to find the total. 22.990+18.998=41.988 Notice that subscripts in formulas (indicating numbers of atoms) are exact, so they do not constrain the number of significant figures.
What is the mass of a sample of barium carbonate (BaCO3) that contains 21.30mol?
4203 g - To calculate the mass of barium carbonate given the number of moles in the sample, multiply the number of moles by the molar mass as follows. 21.30mol×197.336gmol=4,203.3g Therefore, after rounding to four significant figures, we find that the mass of 21.30mol of barium carbonate is about 4,203g.
The mass of 1 mole of CO2 is:
44 grams - If one molecule of CO2 has a mass of 44 atomic mass units, by definition a mole of CO2 will have a mass of 44 grams. This is the difference in the molar mass versus the atomic mass. Molar mass will always be grams/mole. The atomic mass will always be the amu of 1 atom.
The formula mass of SO is:
48.065 amu - 1(32.066)+1(15.999) is 48.065 amu. Notice that subscripts in formulas (indicating numbers of atoms) are exact, so they do not constrain the number of significant figures.
There are ________ atoms of calcium in a 40.08 gram sample.
6.022×1023 - 40.08 grams×1 mol Ca40.08 g×6.022×1023atoms1 mole=6.022×1023 atoms
How many water molecules are in 1 mole of water?
6.022×1023 - A mole is a fixed amount equal to 6.022×1023, and this is Avogadro's number. Just as there are always 12 to a dozen, there are always 6.022×1023 to a mole.
Which of the following is equivalent to a mole of oxygen atoms?
6.022×1023 oxygen atoms - A mole of oxygen atoms is 6.022×1023 oxygen atoms. In fact, 1 mole of any substance will contain 6.022×1023 items because that is the definition of a mole.
A 1.00 m long beam of stainless steel with a square 2.00 cm×2.00 cm cross section has a mass of 3.02 kg. What is its density in grams per cubic centimeter?
7.55 grams per cubic centimeter
How many moles are in 2141 grams of magnesium?
88.09 moles - Grams2141 gx=moles×molar mass=x moles×24.305gmol≈88.09 moles
A compound is a chemical substance composed of two or more kinds of elements in a fixed ratio. By what means can the components of a compound be separated?
Chemical means - A compound cannot be separated into its component elements by physical means, but it can be separated into its component elements by chemical means.
Who determined the structure of the atomic nucleus?
Ernest Rutherford - Rutherford elucidated the structure of the atomic nucleus in his gold foil experiment.
If a compound's formula mass was experimentally determined to be 34, the chemical formula could be:
H3P - Use the periodic table to get the atomic masses of each element. Then you can calculate the formula mass as such: H=1.008×3=3.024 P=30.974×1=30.974 Adding these together we get 33.998, which is approximately 34.
Which of the following events fail to follow the law of conservation of matter? Select the correct answer below: Burning wood for a fire Freezing water into ice cubes The decomposition of MgCl2 into Mg and Cl2 None of these
None of these
The ampere is the base unit for electric current in what metric system?
SI - The ampere is the base unit for electric current in the SI system.
The ______ of an object changes by location, while the ______ of an object does not change by location.
Weight, mass - The weight of an object can change by location with respect to a gravitational field, while the mass of an object does not change based on location.
Which of the following CANNOT be classified as a compound?a. carbon dioxideb. sodium chloridec. lithiumd. sugar
c. lithiumLithium is an element. The rest are made of multiple elements.
A mole is defined as the number of atoms in an exact mass of which isotope?
carbon-12 - The mole is defined to be the number of atoms in exactly 12 grams of carbon-12. This means that 12 g C=1 mol C atoms≈6.022×1023C atoms. The mass of a single atom of carbon-12 is defined as exactly 12amu. All other isotopes have masses with measurement uncertainty.
The mole is the way to convert between atomic mass units and:
grams - The mole is a way of converting directly between atomic mass units and grams, as an atom's atomic mass is equal to its molar mass in grams.
Density is a(n):
intensive property - Density is an intensive property, because a substance will have the same density no matter how much of it we are examining.
For a given atom, which of the following is typically the largest in value?
mass number - The mass number is equal to the number of protons and neutrons in the nucleus. This is typically larger than the atomic number, which is equal to the number of protons. The only exception would be hydrogen, which will typically have an atomic number and mass number both equal to one.
A _________ is defined as the amount of substance containing the same number of discrete particles as the number of atoms in a 12.00-gram sample of pure carbon-12.
mole - The mole is defined as the specific amount of a substance containing the same number of items as the number of atoms in a sample of carbon weighing precisely 12 grams.
All of the atoms in the same element have the same:
number of protons - All atoms of the same element have the same number of protons.
If we compare a mole of carbon atoms to a mole of oxygen atoms, which sample will contain more atoms?
they will contain the same number of atoms - If they both contain a mole of atoms, they will both contain precisely avogadro's number of atoms.
The unit cubic meters is associated with:
volume - The unit of cubic meters is associated with volume.
Using the image provided, identify the atomic mass of the element.
1401 amu - The atomic mass of the element (in amu) is shown by the number 14.01.
A car's fuel efficiency is 39.0 miles per gallon. What is its fuel efficiency in kilometers per liter? (1.6094 km=1 mile)(1 gallon=3.79 L) Report your answer with three significant figures.
16.6 km/L - 39.0 miles1 gallon×1.6094 km1 mile×1 gallon3.79 L=16.6 kmL
Give the result of the following expression with the correct number of significant figures: 84ms×32.533 s=?
2700 m - The answer 2732.772 m is rounded to 2 significant figures so the answer is 2700 m. Remember, when we multiply or divide numbers, we should round the result to the same number of digits as the number with the least number of significant figures (the least relatively precise value in terms of multiplication and division). Thus the correct answer will have 2 significant figures.
If a car gets 45.00 miles per gallon, and gas costs $2.95 per gallon, about how far can you get with $200? Report your answer with four significant figures.
3051 miles - To determine the number of gallons that can be purchased with 200 dollars, we must divide 200 dollars by the cost per gallon. 200 dollars2.95 dollarsgal=67.8 gallons We can then multiply the number of gallons that can be purchased by the gas mileage of the car to determine the number of miles that can be driven. 67.8 gallons×45.00 miles gallon=3,051 miles that can be driven on $200
If a compound has a formula mass of 35, the chemical formula could be:
NH4OH - Use the periodic table to get the atomic masses of each element. Then you can calculate the formula mass as such: N=14.007×1=14.007H=1.008×5=5.040O=15.999×1=15.999 Adding these together we get 35.046, which is approximately 35 amu.
In November 2018, the kilogram was redefined in terms of Planck's constant. Before this, the kilogram was based on:
a cylinder of platinum-iridium alloy - The kilogram was originally defined to be the mass of one liter of water; however, there is some variance in this quantity with temperature and pressure. A more rigid definition for the kilogram was adopted In the late 19th century, which defined the mass of one kilogram as the mass of a metal cylinder, which is stored in France. *NOTE: It should be noted that in November of 2018, the kilogram was redefined in terms of Planck's constant, which is a fundamental constant of nature.
If something is a compound, it is also
a pure substance - Pure substances are either elements or compounds. A compound is a pure substance composed of more than one element.
Dimensional analysis can be used to compute:
all of the above - Dimensional analysis can help us in a great number of every-day situations by simplifying seemingly complicated mathematical problems.
What element is used as the standard for the atomic mass unit?
carbon - Carbon is used as the standard for the atomic mass unit (amu).
Which prefix means one one-hundredth?
centi - Deci is one tenth, milli is one one-thousandth, and kilo is one thousand.
The charges on the proton and electron are typically measured in:
coulombs - These fundamental particles bear the fundamental unit of charge, which is either positive or negative 1.602×10−19 coulombs.
Atoms of the same element that have different mass numbers are called:
isotopes - Atoms of the same element with differing numbers of neutrons are called isotopes.
Which SI unit do we use to measure mass?
kilograms - We measure mass in kilograms. Volume is measured in liters, length is measured in meters, and time is measured in seconds.
Leading zeros are only significant if they are:
leading zeros are - - never significant Leading zeros serve to display the magnitude of a value, but they never imply precision, so they are never significant.
In some cases, volume can be found by cubing which of the following quantities?
length - Volume can be considered length times width times height, or a length in each of three spatial dimensions.
To find the number of neutrons in an atom, simply calculate:
mass number - atomic number - The mass number gives the sum of the protons and neutrons, so if we subtract from that the atomic number, which is the number of protons, we will get the number of neutrons in an atom. Your answer:
The nucleus of an atom can be split into smaller components by what kind of process?
none of the above: a physical or chemical process or melting - The nucleus of an atom cannot be split into its components by either a physical or chemical change. Splitting an atom is a nuclear process.
Which element is NOT abbreviated based on an ancient name?
radium - Radium is simply Ra.
Volume is the:
space occupied by any sample of matter - Volume is the space occupied by any sample of matter.
The prefix in subatomic tells us that subatomic particles are:
the basic building blocks of atoms - The prefix "sub" can mean below, under, or imply that some smaller things are used to define a larger system. All of these contexts can apply here, to state that subatomic particles are less massive than atoms, take up less space than atoms, or more generally that they comprise atoms.
Which of the following is used to abbreviate an element or an atom of a given element?
the chemical symbol - The chemical symbol is used to abbreviate an element or an atom of a given element.
Today, the meter is based on:
the distance light travels in a particular fraction of a second - The meter was once defined as a particular fraction of the distance from the equator to the north pole, but it was eventually revised to be more universal.
If you boil an entire sample of water, the steam that results will have:
the same mass as the water
A hybrid car holds 32 gallons of gas in its tank. If it travels from San Diego to Seattle in three tanks of gas, and gas costs $3.29 per gallon, about how much did the trip cost? Report your answer with three significant figures.
$316 - Three tanks of gas times 32 gallons per tank times $3.29 per gallon gives approximately $316 as the total cost for the trip.
What is the volume in liters of 1.00 oz, given that 1 L=1.0567 qt and 1 qt=32 oz (exactly)?
0.0296 L - First you have to convert ounces to quarts using the conversion factor 1 qt=32 oz. This yields the answer 0.03125 qt, the volume in quarts. 1.00 oz×1 qt32 oz=0.03125 qt Then you need to convert this volume to liters using the unit conversion 1 L=1.0567 qt. 0.03125 qt×1 L1.0567 qt≈0.029573 L Rounding to three significant figures, the result is 0.0296 L.
What would 0.038851 be rounded to if it needed to retain 3 significant figures?
0.0389 - The dropped digit is 5 so the number is rounded up to 0.0389 to have 3 significant digits.
If hydrogen atoms contain 1 proton, what is the atomic number of hydrogen?
1 - If hydrogen contains 1 proton then the atomic number is 1.
When considering precise mass, which particle has the greatest mass?
neutron - The neutron has slightly more mass than the proton, and much more mass than the electron.
Which of the following units is a derived SI unit (not one of the SI base units)?
newton - Newtons are defined to be kg ms2. The other three units are base SI units.
Light travels at roughly 3.00×108ms. What is this speed in miles per minute? Use 1mi=1609.344m and 60s=1min. Report your answer in scientific notation with three significant figures. Use the multiplication symbol, ×, rather than the letter x in your answer.
1.12 x 10^7 miles per min - First, use the fact 1mi=1609.344m to convert the speed from meters per second to miles per second. 3×108ms×1mi1609.344m=1.8641×105mis Now, use the fact that 1min=60s to convert the speed from miles per second to miles per minute. 1.864×105ms×60s1min=1.1185×107mimin Therefore, after rounding to three significant figures, we find that the speed of light in miles per minute is about1.12×107mimin.
What is the mass number of an isotope of rhodium with 58 neutrons?
103 - The mass number is equal to the total number of protons and neutrons in the nucleus. Rhodium has an atomic number of 45, so it must have 45 protons. It is given that there are 58 neutrons, so the mass number is 45+58=103.
A speed limit in a U.S. city is 65 miles per hour. What would the equivalent of this speed limit be in a Canadian city (in kmhr)? (1.609 km=1 mile)
105 km/hr - 65 miles1 hour×1.609 km1 mile=104.61kmhr≈105kmhr
Which of the following has 3 significant figures? Select all that apply.
123 12.3 1.23 x 10^4 - All of the answer choices have 3 significant figures except for 123000. The decimal point at the end of the number means that the trailing zeros are also significant, so it has 6 total.
Through the complete electrolysis of a sample of pure water, a student collects 14.0 grams of hydrogen gas and 112.0 grams of oxygen gas. What mass of water (in grams), if it reacted completely, was initially present? (The electrolysis of water is the use of an electric current to decompose it into its component elements.)
126.0 g
The density of water is 1.0gcm3 at 4∘C. What is the mass of 15mL of water at this temperature? Use the fact that 1cm3=1mL.
15 g - The density of water is 1.0gcm3 at 4∘C. This is water's maximum density. Use the conversion factors to determine how much 15 mL of water will weigh. 15 mL×1 cm31 mL×1 g1 cm3=15 g Therefore, 15mL of water at 4∘C will have a mass of 15g.
The water in a garden hose flows at a rate of 10.0 liters per minute. What is the flow rate in gallons per hour? (1gal=3.79L)
158 gallons per hour - Use conversion factors that cancel the given units, Lmin, and leave the desired units, galhr. To convert from liters to gallons, use the relationship 1gal=3.79L. The conversion factor 1gal3.79L cancels liters and leaves gallons. To convert from minutes to hours, use the relationship 1hr=60min. The conversion factor 60min1hr cancels minutes in the denominator and leaves hours in the denominator. Now multiply to find the answer. 10.0Lmin×1gal3.79L×60min1hr=158.3galhr Finally, round to the correct number of significant figures (in this case, three): 158galhr.
How many kilograms does a 40.0 lb-bag of cat food weigh? (1 lb=454 g)
18.2 kg - We use dimensional analysis to convert between different units of measurement by multiplying a value by one or more fractions that are equal to one to change the way the value is expressed. Begin by starting with the value of 40.0 lb and multiply by a fraction that is equal to one that we are already aware of: 40.0 lb×454 g1 lb When we multiply this value of 40.0 lb by this fraction, we can see that the units cancel, just like an algebraic variable: 40.0 lb×454 g1 lb We repeat this process with a different conversion until we end up with the desired unit of kg: 40.0 lb×454 g1 lb×1 kg1000 g=18.16 kg The answer should have three significant figures, so round to 18.2 kg.
How many neutrons are in 188O, or oxygen-18?
2 - There can be one or two letters in a chemical symbol. Looking at the periodic table, we see that most symbols have two letters.
The label on a soft drink bottle gives the volume in two units: 2.0 L and 67.6 fl oz. Use this information to derive a conversion factor between the English and metric units.
2.0 L/67.6 fl oz= 0.030 L/1 fl oz - For this question, we must set up a ratio to figure out the number of liters in one fluid ounce. We do this by noting that there are 2.0 L in 67.6 fl. oz: we set this up as 2.0 L67.6 fl. oz. To figure out the number of liters in one fluid ounce, we simply divide 2.0 L by 67.6 fl. oz This gives us 0.030 L1 fl. oz. Completing the ratio, we obtain 2.0 L67.6 fl. oz=0.030 L1 fl. oz.
A cube with a mass of 250.0 g has sides measuring 5.00 cm each. What is the density of this cube in grams per cubic centimeter?
2.00 grams per cubic centimeter
Tyson Gay's best time to run 100.0 meters was 9.69 seconds. What was his average speed during this run, in miles per hour? (3.281ft=1 m)(1 mile=5280 ft)
23.1 mph - To find the average speed, divide the distance traveled by the time and use conversion factors to cancel the given units, ms, and leave the desired units, mihr. speed=100.0m9.69s To convert from meters to miles, use the relationships 3.281ft=1m and 5280ft=1mi. The conversion factor 3.281ft1m cancels meters and leaves feet, and the conversion factor 1mi5280ft cancels feet and leaves miles. In the denominator, use the relationships 1min=60s and 1hr=60min. The conversion factor 60s1min cancels seconds and leaves minutes, and the conversion factor 60min1hr cancels minutes and leaves hours. Now multiply to find the answer. speed=100.0m9.69s×3.281ft1m×1mi5280ft×60s1min×60min1hr=23.08mihr When we multiply or divide, our answer should have the same number of significant figures as the number with the fewest significant figures, which in this case is the 9.69 seconds. Therefore, after rounding to three significant figures, we find that the speed in miles per hour is 23.1mihr.
A train is traveling across the country at 65.0 m/s. How would this be represented in km/hr? Report your answer with three significant figures.
234 km/hr
Which conversion factor would NOT be used in converting ms into kmhr?
24hr / 1 day - The other three are needed to convert m into km, s into min, and then min into hr. Days will not be involved in this calculation.
The density of an unknown crystal is 2.65gmL. If a 4.46 g sample of the crystal is added to a graduated cylinder containing 25.0 mL of water, what will the volume read?
26.7 mL - Use a systematic approach to solve the problem.1. Read the problem carefully: Note that the crystal is added to the water and the total volume will represent the volume of the water and the volume of the crystal.2. Identify the given information: The given density is 2.65gmL, the mass is 4.46 g, and the volume of the water (Vw) is 25.0 mL.3. Identify what is being asked for: The question is asking for the total volume in milliliters (Vtot).4. Identify intermediate steps: The total volume (Vtot) will be the volume of the water (Vw) plus the volume of the crystal Vc. Vtot=Vw+Vc So the volume of the crystal is needed. To find the volume of the crystal, use the definition of density, d=mV, and isolate V. Vc=md 5. Find the answer: Find the volume of the crystal. Vc=4.46 g2.65gmL=1.683 mL Add it to the volume of water. Vtot=25.0 mL+1.683 mL=26.683 mL Round the answer to one decimal place. The answer is 26.7 mL.6. Check answer reasonableness: A 4.46 g crystal is not particularly large, so it makes sense that it could be measured in a milliliter scale. The change in the water volume is a reasonable amount of displacement.
Jacob takes 7 classes, each 50.00 minutes long, every day of the 5 day school week. How many hours per week does he spend in class?
29.17 hours per week - The question is asking to convert the quantity 7classesschool day to the units hours of classweek. Use conversion factors that cancel the given units and leave the desired units. To convert from classes to hours of class, multiply by the conversion factor 50.00minutes of class1class to cancel classes and leave minutes of class, and then multiply by the conversion factor 1hour of class60minutes of class. To convert from school days to weeks, use the relationship 1week=5school days to write the conversion factors 5school days1week. This conversion factor cancels school days in the denominator and leaves weeks in the denominator. Now multiply to find the answer. 7classesschool day×50.00minutes of class1class×1hour of class60minutes of class×5school days1week=29.1667hours of classweek When we multiply or divide, our answer should have the same number of significant figures as the fewest significant figures. In this calculation, all of conversions are exact numbers except for the 50.00 minutes per class, so the final answer has four significant figures. Round to the correct number of significant figures: 29.17hours of classweek.
What is 0.29 km in mm? Report your answer with two significant figures.
2900000 mm - There are 1000 meters in 1 kilometer and 1000 millimeters in 1 meter, so there are 1,000,000 millimeters in a kilometer. Dimensional analysis can involve 103 m1 km×103 mm1 m or can simply be 106 mm1 km. 0.29 km×103 m1 km×103 mm1 m=290,000 mm
Write the formula for an isotope of hydrogen with two neutrons, including the mass number and the atomic number.
3 1 H - Hydrogen has an atomic number of 1, so there is one proton. The mass number is equal to the total number of protons and neutrons in the nucleus, so an isotope of hydrogen with two neutrons has a mass number of 2+1=3. The chemical formula for a specific isotope of an element is written as AZX, where A is the mass number, Z is the atomic number, and X is the chemical symbol. Therefore, the chemical formula for this isotope of hydrogen is H13.
The volume of a 12.4 g metal pellet is measured by water displacement. It is added to a graduated cylinder filled with water, and the level rises from 10.00 mL to 13.65 mL. What is the density of the metal?
3.4 g per mL - Use a systematic approach to solve the problem.1. Read the problem carefully: Note that the pellet's volume is being found by the change in total volume when it is added to a sample of water.2. Identify the given information: The given mass is 12.4 g. The starting volume (the volume of the water) is 10.00 mL. The final volume (total) is 13.65 mL.3. Identify what is being asked for: The question is asking for the density in grams per milliliter.4. Identify intermediate steps: Density is mass per volume, or d=mV. Since the mass is known, the volume of the pellet is needed, and it can be found from the change in volume read from the graduated cylinder. Vpellet=Vfinal−Vinitial .5. Find the answer: Find the volume of the pellet. Vpellet=13.65 mL−10.00 mL=3.65 mL Next, substitute the mass and volume of the pellet into the formula for density. d=mV=12.4 g3.65 mL=3.3973gmL The answer should be rounded to one decimal place, so round to 3.4gmL.6. Check answer reasonableness: A density of 3.4gmL is reasonable for metal.
Convert a volume of 3.5 m3 to cubic centimeters.
3.52+6 cubic centimeters - 3,500,000 cubic centimeters 1. Read the problem carefully: This is a volume conversion problem. Note that the units are cubic lengths.2. Identify the given information: The given volume is 3.5 m3.3. Identify what is being asked for: The question is asking for the volume in cubic centimeters (cm3).4. Identify intermediate steps: Use the equivalent measure 100 cm=1 m to write a conversion factor 100 cm1 m. Since the units are cubed, the conversion factor needs to be cubed as well: (100 cm1 m)3.5. Find the answer: Multiply. 3.5 m3×(100 cm1 m)3=3,500,000 cm3 6. Check answer reasonableness: Centimeters are smaller than meters, so it makes sense that the number of cubic centimeters is larger than the number of cubic meters.
Johnny's bakery has 30,900 grams of sugar. A recipe calls for 32 pounds of sugar to be used. How many pounds of sugar will be left over? (1 lb=453.59 g). Report your answer with two significant figures.
36 lbs - First convert grams to pounds using the relationship 1lb=453.59g. The conversion factor 1lb453.59g cancels grams and leaves pounds. 30,900g×1lb453.59g=68.1lb Next, subtract the 32lb of sugar used. 68.1lb−32lb=36.1lb When we add or subtract, our answer should have the same number of decimal places as the number with the least number of decimal places. In this case, the number of with the least number of decimal places is 32, so our answer should be rounded to the nearest whole number. Rounding to the nearest whole number gives 36lb.
The density of a cube is 2.0gcm3. If the mass is 128 g, what is the length of each side of the cube?
4.0 cm To calculate the length of each side of the cube we must first calculate the volume of the cube. We can use the equation d=mV, where d is the density, m is the mass and V is the volume. Rearrange the equation to solve for V and substitute the given values into the equation to calculate the volume. V=md=128g2.0gcm3=64cm3 Since the volume of a cube is equal to the length of a side cubed, take the cube root of the volume to find the side length. length=64 cm3−−−−−−√3=4.0 cm
A substance has a density of 4.5gmL. What is this in kgL? Report your answer with two significant figures.
4.5 kg/L - Use dimensional analysis to convert grams to kilograms in the numerator and to convert milliliters to liters in the denominator. Since we want grams to cancel, leaving kilograms in the numerator, use the conversion factor 1 kg1000 g. Since we want milliliters to cancel, leaving liters in the denominator, use the conversion factor 1000mL1L. Now multiply. 4.5gmL×1kg1000g×1000mL1L=4.5kgL
A Toyota Prius Hybrid uses 59.7 L gasoline to drive from San Francisco to Seattle, a distance of 1300 km (two significant digits). What (average) fuel economy, in miles per gallon (mpg), did the Prius get during this trip?
51 mpg - First, you convert the distance from kilometers to miles using the conversion factor, 1 km=0.62137 mi. Second, you convert volume from liters to gallons using the following conversion factors: 1 L=1.0567 qt and 4 qt=1 gallon. Third, you divide the miles that you calculated by the gallons that you calculated to get the average miles per gallon.
A train is traveling at 200.kmhr. What is that in ms? Report your answer with the correct number of significant figures.
55.56 meters per sec - 200kmhr×1000 mkm ×1 hr60 min×1 min60 s gives us 55.6 ms.
An object has a mass of 0.0124kg and a volume of 1893mm3. What is its density in grams per cubic centimeter?
6.55 - Divide the mass by the volume in order to find the density, and then use conversion factors to cancel the given units and leave the desired units. density=0.0124kg1893mm3 To convert from kilograms to grams, use the relationship 1kg=1000g. The conversion factor 1000g1kg cancels kilograms and leaves grams. In the denominator, use the relationship 1cm=10mm. Since these are cubic units, use the conversion factor (10mm1cm)3=1000mm31cm3 to cancel cubic millimeters and leave cubic centimeters. Now calculate the density with the converted units. density=0.0124kg1893mm3×1000g1kg×1000mm31cm3=6.5505gcm3 When we multiply or divide, our answer should have the same number of significant figures as the number with the fewest significant figures. In this calculation, the numbers in the unit conversions are exact numbers. The mass of 0.0124kg has the fewest number of significant figures, so the answer has three significant figures. Round the answer to 6.55gcm3.
What is the mass number of an isotope of copper with 34 neutrons?
63 - The mass number is equal to the number of protons and neutrons in the nucleus. Copper has an atomic number of 29, so it must have 29 protons. It is given that there are 34 neutrons, so the mass number is 29+34=63.
Lithium occurs naturally as 6Li and 7Li. Given that lithium's average atomic mass is 6.94 amu, determine which isotope is more abundant.
7Li - The atomic mass of each isotope is close to the mass number (a whole number by definition) because each proton and neutron in a nucleus adds about 1 amu to the mass. For elements with many stable isotopes, there is not enough information to determine the most abundant isotope from just the average atomic mass, but if we know that there are only two naturally occurring isotopes that contribute to the average atomic mass, then the more abundant isotope must be the one closer in mass to the average. This is because the average atomic mass is a weighted average. If the isotopes were present in equal amounts, the average atomic mass would be the simple average of each isotope's mass, or about 6.5 amu. Because the weighted average is actually about 6.94 amu, which is much closer to 7 than to 6, there must be more lithium-7 than lithium-6.
Which of the following factors used in a dimensional analysis calculation have a finite number of significant figures (in other words, they are not exact numbers) that might limit the precision of the calculated value?
A measurement of speed equaling (27.7 km/hour) - Unit conversion factors are almost always exact numbers. For example, there are exactly 1000 m in 1 km because that is how the kilometer is defined. There is no uncertainty involved in the conversion factor, so it will not affect the number of significant figures in our answer. But when using actual measurements, the number of significant figures will have an impact on our calculation.
Choose the best explanation below for why dimensional analysis is also sometimes referred to as the factor label approach.
It is sometimes called the factor label approach because units are treated as a factor (along with a numeric factor) in a quantity like 25g, allowing us to subject the unit to algebraic operations as if they were variables. - It is sometimes called the factor label approach because we can treat a quantity like 25g as a product of a numerical factor and a unit factor, allowing us to subject the unit to arithmetic operations as if they were variables. Dimensional analysis can be most helpful when helping to set up a problem involving multiplication or division, but it is not limited to multiplication and division: Adding or subtracting quantities, for example, requires they have the same unit, just like adding algebraic terms 5x and 6x, and this rule can be used to help set up or check a calculation.
When reading a measurement from an analog instrument like a ruler or a mercury thermometer, how should you determine the number of significant figures to record?
The least significant figure should be estimated by reading between the smallest markings on the instrument. - It is only feasible to estimate one digit further than the precision inherent in the instrument, so if a ruler has centimeters, we can estimate tenths of a centimeter, but no more than that. The last digit should be estimated in this fashion, because the least significant digit in a measured number is treated as uncertain.
Which subatomic particle has no electric charge?
neutron - The proton is positively charged and the electron is negatively charged, while the neutron, as its name would suggest, has neutral charge, or no charge.
If a compound's formula mass was experimentally determined to be 76 amu, the chemical formula could be:
N2O3 - The formula mass of N2O3 is calculated by 2(14.007)+3(15.999)=76.011 amu which is approximately 76 amu.
0.738×0.28 is 0.20664 but is rounded to 0.21. Which rule or rules are applied to this calculation?
Round the result to the same number of significant figures as the value with the least number of significant figures. Round up if the digit to be dropped is 5 or greater. - For multiplication and division, we round the result to the same number of significant figures as the value with the least number of significant figures. In this calculation, this means rounding to two significant figures by dropping all of the digits after and including the 6 in the thousandths place and rounding up to 0.21.
Which of the following defines mass?
The amount of matter in an object - Mass is the amount of matter in an object.
Units of measurement provide which of the following?
a standard comparison of measurements - It is only with agreed upon units of measure that measurements can be compared. For example, it is not possible to pick up a football field and place it next to another football field to ensure they have the same length, but with an an agreed upon definition of the length of a "yard" or a "foot" they can each be measured in yards or feet and the lengths compared. The magnitude of a measurement is determined by both the units and the numerical portion (120 yds is longer than 50 yds because 120>50, and units do not convey any information about measurement uncertainty.
If object A and object B have the same density, but object A has greater mass, then object A must have:
greater volume - If these objects have the same density, that means they have the same ratio of mass to volume, so a greater mass must also mean a greater volume.
Atoms of the same element can differ in which of the following?
mass numbers - Atoms of a specific element have a particular atomic number (which is the same as the number of protons), but may have different mass numbers, which correspond to different numbers of neutrons.
Atoms of the same element can have different:
mass numbers - Atoms of the same element must have the same number of protons, as this defines their atomic number which is characteristic of that element. But they may have differing numbers of neutrons which would generate a different mass number.
Which is the SI unit for length?
meters - Meters are the SI unit for length, and can be used to describe any length, large or small.
Every element on the periodic table has isotopes that contain:
all of the above - All elements contain all of these particles, which is why it is so important to understand them. Although one of hydrogen's isotopes does not have a neutron, hydrogen does have other neutron-containing isotopes.
The symbol Fe could refer to which of the following? Select the best answer below.
all of the above - Fe means "iron" and it can be used to represent an individual iron atom in a molecular formula, or a ratio of iron atoms to other elements or compounds in a reaction, or just to represent the element itself without reference to any specific sample of iron.
Which has the smallest mass?
an electron - Electrons have much less mass than protons and neutrons, and all of these are much smaller than an atom.
When adding numbers, the sum will have:
as many decimal places as the number with fewest decimal places - The rules state that for addition and subtraction we round to the same number of decimal places as the value with the fewest number of decimal places. This is how we adequately propagate the uncertainty of the most uncertain value through the operation.
The mass of an individual atom is most often described in:
atomic mass units - The mass of an atom is most readily described in atomic mass units, because this unit was created specifically to discuss mass on the order of individual atoms. Grams and kilograms would require tedious scientific notation.
Which particle contributes neither to the atomic number nor the mass number of an atom?
electron - The electron does not have sufficient mass to be included in the mass number, and only the proton contributes to atomic number.
Which two subatomic particles would have a combined unit charge of 0?
electron, proton - Two subatomic particles that when combined have a 0 net charge are the electron (−1) and the proton (+1).
Despite the units frequently seen on laboratory scales, the most appropriate unit below for quantifying weight is _______.
newtons - Newtons measure force, and weight is the force exerted by an object because of its position in a gravitational field. Kelvin measures temperature, grams measure mass, and amperes measure electrical current. Most laboratory scales purport to measure mass and display grams (or kilograms or milligrams) rather than newtons, because it is assumed that they will be used on Earth and most chemists would need to convert the weight to a mass anyway.
Which of the following is NOT a base unit of SI?
ounce - The second, the mole, and the meter are all SI units.
The number of significant figures in a value is a display of the _________ of a measurement.
precision - Accuracy is a measure of how close a measurement is to a true or accepted value, whereas precision is a measure of how well consecutive measures of the same quantity agree with one another. The number of significant figures in a value will provide information regarding the precision of the value. For example, 15.000mL is a more precise value than 15mL. Significant figures alone will not provide evidence to suggest that a measured value is close to the true or accepted value.
What subatomic particle determines the element that an atom belongs to?
proton - The number of protons in an atom determines its atomic number, which corresponds to a specific element.
An element's atomic number refers to the number of __________ in an atom of that element.
protons - Atomic number describes the number of protons in an atom of a particular element. Every element has a different atomic number that determines its place in the Periodic Table of the Elements.
Mass depends on:
the amount of material - Mass is an extensive property, which means it depends on how much of a substance there is.
The sum of the average atomic masses of all the atoms present in a substance's formula is known as:
the formula mass (molecular mass) - The sum of the average atomic masses of all the atoms present in a substance's formula is known as the formula mass or the molecular mass.
What is the standard SI unit of mass?
the kilogram
What is exactly equal to the total number of protons and neutrons in an atom?
the mass number - The number of protons and neutrons in an atom is equal to the atom's mass number. Atomic mass is the average mass of all the isotopes of a certain kind of atom.
Which has a greater mass, 1 kg of rocks or 1 kg of feathers?
they will be equivalent - 1 kg is a particular mass, it does not depend on the substance. Two objects that each have a mass of 1 kg will necessarily have the same mass regardless of their identity.
When computing using dimensional analysis:
unit conversions can be done either simultaneously or separately - We can perform unit conversions one at a time or many at a time, just be sure to keep in mind that this could create a discrepancy in the number of significant figures in your result, depending on when you decide to round your value.