CHE 100 - Ch. 2
0.738×0.28 is 0.20664 but is rounded to 0.21. Which rule or rules are applied to this calculation? Select all that apply.
- 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 one of these numbers has 4 sig figs?
4302
Heat capacity depends on __________.
- the composition of the substance - the amount of the substance Heat capacity is an extensive property in that it depends on the composition and amount of a substance. For example, a metal wire tends to have a lower heat capacity than most amounts of water; a wire heats up and cools down much faster than water (i.e., it depends on the substance's composition). Also, a small amount of water has a lower heat capacity than a large amount of water. The ocean has a relatively stable amount of heat, while heat changes dramatically in a puddle (i.e., it depends on the amount of substance). This is different from the specific heat capacity, which is an intensive property and is independent on the amount of substance and depends only on the composition of the substance.
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 qt/32 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 L/1.0567 qt≈0.029573 L Rounding to three significant figures, the result is 0.0296 L.
In regards to temperature, a change of 1 degree Celsius is the same as a change of
1 Kelvin Kelvin and Celsius are related by addition (Tin Kelvin=Tin Celsius+273.15), so if a temperature changes by 1 Kelvin it also changes by 1 degree Celsius.
A liter is equivalent to:
1 dm^3 Use the fact that 1mL=1cm^3 to determine the equivalent volume of 1L. If 1mL=1cm^3, then 1L=1,000mL=1,000cm^3. Now, convert 1,000cm^3 into m^3. 1,000cm^3×(1m100cm)3=1×10−3m^3. Now, use the fact that 1m=10dm to determine the volume of 1dm3 in m^3. 1dm^3×(1m/10dm)3=1×10^−3m^3 Therefore, 1L=1×10^−3m^3=1dm^3.
Which of the following is true about milliliters and cubic centimeters?
1 milliliter is the same volume as 1 centimeter cubed Yes, WRITE THAT DOWN. We use cm^3 and mL interchangeably all the time... Which of the following is true about milliliters and cubic centimeters?
What is the density of a 37.2 mL sample of sulfuric acid weighing 63.8 g, in grams per milliliter?
1.72 g/mL In order to find the density of the sample, we need to use the formula below, where d represents density, m represents mass, and V is the symbol for volume. d=m/V Then we plug in the values for mass and volume and solve for density, rounding to three significant figures. d=63.8g/37.2mL d=1.72 g/mL
How many meters are in a kilometer?
1000 Kilo means one thousand, so one kilometer equals one thousand meters.
A speed limit in a U.S. city is 65.0 miles per hour. Canadian cities express speed limits in kilometers per hour. Express the value in km/hr. (1.609 km=1 mile)
105km/hr To convert the speed from miles per hour to kilometers per hour, we must use the fact that 1mi=1.609km. 65 miles/1 hour×1.609 km/1 mile=104.59km/hr Therefore, the speed limit in a Canadian city would read about 105km/hr.
An object with a heat capacity of 345J∘C experiences a temperature change from 88.0∘C to 45.0∘C. How much heat is released in this process, in joules?
14835J Recall that heat capacity, C, is the ratio of heat to the change in temperature. C=q/ΔT Rewrite the equation to solve for q. q=CΔT In order to solve for q, you must first calculate ΔT ΔT=Tfinal−Tinitial ΔT=45∘C-88∘C=−43∘C Next, Substitute the known values into the equation above and solve for q. q=(345J∘/C)(−43∘C)=−14,835 J Round your answer to the nearest hundred to use correct significant figures. q=−14,800 J The negative sign means that heat is released, or the process is exothermic. Therefore, the amount of heat released is about 14,800 J.
What was the conversion factor used in the problem he just completed?
19.3 g/cm^3 Yes! Density can be used as a conversion factor because of the "slash" (division bar)
The temperature of a substance changes by 1K1K. This is equal to a temperature change of ________?
1∘C Looking at the image above, we can see that the freezing temperature of water on the Kelvin scale is 273.15 K, and its boiling temperature is 373.15 K. Notice that the numerical difference in these two reference temperatures is 100, the same is true for the Celsius scale. Water freezes at 0∘C and boils at 100∘C which is a difference of 100 in magnitude. This means that 1 K is equivalent to 1∘C in magnitude. This makes the conversion between the Celsius and Kelvin quite easy.
In the process of vision, the light-sensitive pigment rhodopsin undergoes cis-trans isomerism in response to light in about 2×10−10ms. How many seconds is this? Write the answer in scientific notation. Enter your answer in scientific notation using the multiplication sign, ×, not the letter x.
2 x 10^-13 s Note that the prefix m stands for "milli." A millisecond equals 1×10−3 second. Use this to write 2×10−10ms in seconds. 2×10−10 ms×10−3 sms=2×10−13 s 2×10−10ms equals 2×10−13 seconds.
Solve the following problem and report answers with appropriate number of significant digits: 1.31 cm×2.3 cm=1.31 cm×2.3 cm= _____
3.0 cm 2.3 cm only has 2 significant figures so the answer can only be as significant as the least significant entry. Therefore the answer should be rounded to 2 significant figures.
35gigatons equals __________.
3.5×10^10tons The prefix "giga" means 109, so it can be written as the following. 35gigaton=35×109tons To write the number in scientific notation, the decimal part must be between 1 and 10. Move the decimal point in 35 to the left one place, and, since this makes the number smaller by a power of 10, add 1 to the exponent on 10 to compensate. 35×109tons=3.5×1010tons.
Saltwater covers approximately 361,900,000 square kilometers of the earth's surface. Write the number of square kilometers of saltwater in scientific notation. When using scientific notation to report your answer use the multiplication sign, ×, not the letter x.
3.619 x 10^8 sq km To convert a number written in standard notation with a value of 10 or greater, move the decimal point to the left until the number has a single digit to the left of the decimal point. Then multiply the result by 10 raised to the power of the number of places that the decimal point was moved. In this case, the unwritten decimal point is to the right of the final zero in the number 361,900,000. It must be moved 8 places to the left to write the number as 3.619, so 3.619 is multiplied by 10^8.
One year consists of 365 days. This is closest to how many seconds? (Remember the following conversion factors: kilo (103), mega (106), giga (109), and tera 1012.)
31.5 megaseconds One year is 365 days and each day has 24 hours. 365 days×24 hoursday×60 minuteshours×60 secondsminute=31,536,000 seconds Writing it in scientific notation gives: 31,536,000 seconds=3.1536×107 seconds. Reviewing the values of the prefixes, the exponential factor, 106, can be replaced by "mega," which is the only prefix that has the correct order of magnitude (maximum place value). 3.1536×107 seconds≈31.5 megaseconds
If the temperature is 90.0∘F, what is this value in Celsius? Report your answer with three significant figures.
32.2 degrees C To convert from Fahrenheit to Celsius, we must use the following equation: C=5/9(F−32) We then plug the temperature given, 90.0∘F , into the correct equation and solve for C C=5/9(90.0−32) C=32.2∘C
If we wish to convert a value in years into days, a conversion factor we could use would be:
365 days/1 year The top and the bottom must be equal to each other, so 365 days and 1 year, as those represent the same length of time. In addition, days must be on top and years on the bottom so that we can appropriately cancel out the existing unit.
How many hours are there in exactly 180 days? Your answer should be exact (do not round).
4320 hours 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 in order to change the way the value is expressed. Take the value of 180 days and multiply by a fraction that is equal to one that we are already aware of: 180 days×24 hours/1 day=4320 hours
Complete the following operation to the correct number of significant figures: 9.693+36.9=
46.6 We must round the result to the same number of decimal places as that of the value with the fewest decimal places. In this case, 9.693 has three decimal places and 36.9 has one, so we will round the result to one decimal place (the tenths place). When we add the numbers together, we get an answer of 46.593. Rounded to the tenths place, we get 46.6; the "9" in the hundredths place indicates that we round the tenths place up from 0.5 to 0.6.
Before you are told, how many sig figs are in 3600.0?
5
How many sig figs are there in 0.000012030?
5
How many sig figs are there in 127.70?
5
If the number 576,000,000 has 4 sig figs, how would you write it in scientific notation?
5.760 x 10^8
The wavelength of yellow light is approximately 0.000000580m. Convert this quantity from meters to nanometers. Write the answer in scientific notation, using the multiplication symbol, × not the letter x.
5.80 x 10^2 nm The prefix "nano" means 10−9. To convert meters to nanometers, move the decimal point to the right 9 times, filling in zeros as needed, and then use a prefix symbol, n, to represent 10−9. 0.000000580m=580×10−9m=580nm Now, to write 580nm in scientific notation, move the decimal so that there is only one nonzero digit to the left of the decimal place. Therefore, the decimal should be moved two places to the left. The exponent on 10 will be equal to the number of places the decimal is moved. Therefore, the value written in scientific notation is as follows. 580nm=5.80×102nm Recall that if a trailing zero is on the right side of a decimal point, it is significant and should be included in the scientific notation.
An object has a mass of 0.124kg and a volume of 1893mm^3. What is its density in grams per cubic centimeter? Your answer should have three significant figures (round your answer to one decimal place).
65.5 grams / cubic cm 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=0.124kg1893mm3density=0.124kg1893mm3 To convert from kilograms to grams, use the relationship 1kg=1000g1kg=1000g. The conversion factor 1000g1kg1000g1kg cancels kilograms and leaves grams. In the denominator, use the relationship 1cm=10mm1cm=10mm. Since these are cubic units, use the conversion factor (10mm1cm)3=1000mm31cm3(10mm1cm)3=1000mm31cm3 to cancel cubic millimeters and leave cubic centimeters. Now calculate the density with the converted units. density=0.124kg1893mm3×1000g1kg×1000mm31cm3=65.505gcm3density=0.124kg1893mm3×1000g1kg×1000mm31cm3=65.505gcm3 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 0.124kg0.124kg has the fewest number of significant figures, so the answer has three significant figures. Round the answer to 65.5gcm3.
How many significant figures does the number, 2098.00703 contain?
9 All of the zeroes in the number, 2098.00703, are significant because they are 'captured' between non-zero digits.
Which of the following is not a rule regarding significant figures?
All nonzero digits can be ignored. All of the above are rules: - All trailing zeros to the right of a decimal mark are significant. - All nonzero digits are considered significant. - All zeroes between significant digits are significant. ...except that nonzero digits can be ignored.
Which of the following statements BEST describes the SI system of unit?
An expansion of the metric system. The SI system is used in the scientific and medical fields and is an expanded form of the metric system.
Britta traveled 1250 km on her road trip and used 209 L of gasoline, filling her tank at an average cost of 1.14 euros per liter. Pierce traveled 1405 km on his trip and used 175 L of gasoline, filling his tank at an average cost of 1.23 euros per liter. Who paid more per kilometer driven for their trip?
Britta First calculate Britta's cost per distance: 209 L×1.14€L×11250 km=0.191€km Next calculate Pierce's cost. 175 L×1.23€L×11405 km=0.153€km Therefore, Britta's cost per kilometer traveled was greater.
Which is the largest unit of energy?
Calorie The Calorie, or food calorie, is 1,000 calories, each of which is larger than a joule. Remember that 1 calorie corresponds to 4.184J. Therefore, a calorie (cal) "contains" several joules. Joules is the smallest unit of energy in the list.
The temperature scale we use most frequently in chemistry labs is:
Celsius The Kelvin scale is used most often in equations because it is an absolute temperature scale, but Celsius is most often used in the lab. Fahrenheit is rarely used in the field of chemistry.
The international metric system used in science, medicine, and industry is known as:
International System of Units SI units are the international metric system used in science, medicine, and industry.
Which statement BEST explains why temperature is an intensive property?
It is a property that is independent of the amount of matter in a sample. Temperature is an intensive property because it is independent of the amount of matter for a given sample.
What is significant about the temperature of 0K?
It is the temperature at which atoms stop moving. A temperature of 0K is absolute zero and is the point at which motion of atoms stop.
Which of the following must be true about a precise measurement?
It typically contains many significant figures. A precise measurement has a high degree of certainty, as indicated by having many significant figures.
In which temperature scale is the boiling point of water represented by the largest number?
Kelvin The boiling point of water is 100 Celsius, 212 Fahrenheit, and 373 Kelvin. Therefore the boiling point of water is represented by the largest number on the Kelvin scale.
Should we consider the "1 cm^3" in the numerator of the conversion factor when trying to figure out sig figs of our answer?
No because, in this case, 1 cm^3 is not a measurement; it's an "exact number" so it has infinite number of sig figs and we can therefore ignore it Though he didn't use the term "exact number", that's what he meant by "counting number". It's NOT a measurement so sig fig rules don't apply. Sig fig rules apply to measurements only because that's where the concepts of precision and accuracy apply.
Object A has a density of 2.0 g/ cm^3 and a mass of 100 g. Object B a density of 0.8 g/cm^3 and a mass of 240 g. Object C a density of 5.0 g/cm^3 and a mass of 100 g. Which of the objects above (A, B, or C) has the smallest volume?
Object C volume=massdensityvolume=massdensity For A: 100 g2.0 g cm3=50 cm3100 g2.0 g cm3=50 cm3. For B: 240 g0.8 g cm3=300 cm3240 g0.8 g cm3=300 cm3. And for C: 100 g5.0 g cm3=20 cm3100 g5.0 g cm3=20 cm3. Object C would have the smallest volume.
Which of the following is a rule of significant figures in calculations?
Round down if the digit to be dropped is less than 5. We round down if the digit to be dropped is less than 5. For example, to round the value 2.443 to three significant figures, we round down to 2.44 because the digit to be dropped (3) is less than five.
Why was the answer rounded to three sig figs?
Since the numerator and denominator each had three sig figs, the answer should have three sig figs too Yes, we follow sig fig division rules which says take the least number of sig figs present in the numbers that are being divided. Since they each have three, neither is "lower" in number of sig figs so the answer should have the same number of sig figs.
Why did he flip the density conversion factor in this problem?
To cancel the grams
What is the amount of energy required to raise one gram of water by 1∘ C?
a calorie A calorie is defined as the amount of energy required to raise the temperature of one gram of water by 1∘ C.
In November 2018, the kilogram was redefined in terms of Planck's constant. Directly prior to 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 of platinum-iridium alloy, which is stored in France.
Which is the longest distance?
a terameter A terameter is 1012 meters, whereas a megameter is 106 meters and a kilometer is 103 meters.
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.
Which of the following is NOT a unit used in the SI system?
atomic mass unit Ampere, gram. and meter are all units in the SI system. An atomic mass unit is a commonly used measurement in chemistry, but it is not part of the SI system.
From this new list, what are possible metric units for volume?
cm^3
What is a possible metric unit for volume?
deciliters
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.
What quantities are we given in this problem?
mass and density Yes, and we are solving for volume
What is the formula for density?
mass/volume
What is a possible metric unit for mass?
mg
Which of the following is NOT a base unit used in the SI system of measurement?
milliliter The second, the mole, and the meter are all SI base units. Milliliter is a prefixed unit, with the base unit of "liter."
Which is the shortest length of time?
one nanosecond A nanosecond is 10^−9 seconds, whereas a microsecond is 10^−6 seconds, a millisecond is 10^−3 seconds, and a decisecond is 10^−1 seconds.
Which of the following temperatures are equivalent to absolute zero (0 K)? Select all that apply.
−273.15∘C−273.15∘C −459.67∘F−459.67∘F We can convert from Kelvin to Celsius using the following equation: ∘C=K−273.15∘C=K−273.15 Therefore, 0K−273.15=−273.15∘C0K−273.15=−273.15∘C We can convert from Celsius to Fahrenheit using the following equation: ∘F=9/5×∘C+32 ∘F=9/5×−273.15∘C+32=−459.67∘F Therefore, −273.15∘C and −459.67∘F show absolute zero on the Celsius and Fahrenheit scales.
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.
In dimensional analysis, what is a conversion factor?
ratios of physical quantities used to compare desired units Conversion units are ratios of physical quantities used to compare between two desired units. They are not experimental or theoretical.
The digits in a measurement, including the uncertain last digit, are known as:
significant figures The digits in a measurement, including the uncertain last digit, are known as significant figures.
Today, the meter is based on:
the distance light travels in a particular fraction of a second
For a number written in scientific notation, 1.02×10−7, what does the exponent represent?
the power of ten the digit term is multiplied by In scientific notation, the digit term (also known as the mantissa) is the number before the times symbol, and it gives the precise value of the number. The exponent (b) gives the order of magnitude of the number (power of 10) and can be used to count the number of decimal shifts from the mantissa to write the number in standard notation.
Which of the following is the name of the measurement (quantity) that describes how much space an object takes up in three dimensions?
volume Volume is the amount of space that an object takes up. For a rectangular prism (like the shipping box in the video), volume can be calculated with the formula v=length× width ×height, but volume is used to describe the amount of space occupied by any three-dimensional object.
