Chapter 2: Unit Conversions

A piece of Styrofoam has a mass of 88.978 g and a volume of 2.9659 L. What is its density in g/mL?

0.030000 g/mL

Pain signals are transferred through the nervous system at a speed between 12 and 30 meters per second. If a student drops a textbook on her toe, how long will it take for the signal, traveling at a velocity of 18 meters per second, to reach her brain 6.0 feet away?

0.10 s

A piece of balsa wood has a mass of 15.196 g and a volume of 0.1266 L. What is its density in g/mL?

0.1200 g/mL

In chemical reactions that release energy, from 10-8% to 10-7% of the mass of the substances involved is converted into energy. Consider a chemical reaction for which 1.8 X 10^-8% of the mass is converted into energy. What mass in milligrams is converted into energy when 1.0 X 103 kilograms of substance reacts?

0.18 mg to energy

The density of water at 0 C is 0.99987 g/mL. What is the mass in kilograms of 185.0 mL of water?

0.1850 kg

Sound travels at a velocity of 333 m/s. How long does it take for sound to travel the length of a 100-yard football field?

0.275 s

About 6.0 X 10^5 tons of 30% by mass hydrochloric acid, HCl(aq), is used each year to remove metal oxides from metals to prepare them for painting or for the addition of a chrome covering. How many kilograms of pure HCl would be used to make this hydrochloric acid? (Assume that 30% has two significant figures. There are 2000 lb/ton.)

1.6 X 10^8 kg HCl

A first-class stamp allows you to send letters weighing up to 1 oz. (There are 16 ounces per pound.) You weigh a letter and find that it has a mass of 10.5 g. Can you mail this letter with one stamp? The unit analysis setup for converting 10.5 g to ounces follows. Identify whether each value in the setup is exact. Then determine the number of significant figures in each inexact value, calculate the answer, and report it to the correct number of significant figures.

0.370 oz

When one gram of carbon in the graphite form is burned, 32.8 kJ of heat is released. How many kilograms of graphite must be burned to release 1.456 X 10^4 kJ of heat?

0.444 kg C

A tree trunk is found to have a mass of 1.2 x10^4 kg and a volume of 2.4 x 10^4 L. What is the density of the tree trunk in g/mL?

0.50 g/mL

A graduated cylinder is weighed and found to have a mass of 48.737 g. A sample of hexane, C6H14, is added to the graduated cylinder, and the total mass is measured as 57.452 g. The volume of the hexane is 13.2 mL. What is the density of hexane?

0.660 g/mL

The density of a piece of ebony wood is 1.174 g/mL. What is the volume in quarts of a 2.1549-lb piece of this ebony wood?

0.8799 qt

There are 4.070 x 10^6 lb of sulfuric acid used to make Jell-O each year. Convert this to kilograms.

1.846 x 10^6 kg

The mass of the ocean is about 1.8 X 10^21 kg. If the ocean contains 1.076% by mass sodium ions, Na+, what is the mass in kilograms of Na+ in the ocean?

1.9 X 10^19 kg Na+

The re-entry speed of the Apollo 10 space capsule was 11.0 km/s. How many hours would it have taken for the capsule to fall through 25.0 miles of the stratosphere? The unit analysis setup for this calculation follows. Identify whether each value in the setup is exact. Then determine the number of significant figures in each inexact value, calculate the answer, and report it to the correct number of significant figures.

1.02 x 10^-3 hr

meter and centimeter

10^2cm/1m and 1m/10^2cm

meter and kilometer

10^3m/1km and 1km/10^3m

gram and microgram

10^6ug/1g and 1g/10^6ug

liter and gigaliter

10^9L/1GL and 1GL/10^9L

gram and megagram

10^9g/1Mg and 1Mg/10^9g

The diameter of a proton is 2 x 10^-15 meter. What is this diameter in nanometers?

2 x 10^-6 nm

The density of blood plasma is 1.03 g/mL. A typical adult has about 2.5 L of blood plasma. What is the mass in kilograms of the blood plasma in this person?

2.6 kg

The average adult male needs about 58 g of protein in the diet each day. A can of vegetarian refried beans has 6.0 g of protein per serving. Each serving is 128 g of beans. If your only dietary source of protein were vegetarian refried beans, how many pounds of beans would you need to eat each day?

2.7 lb beans per day

We lose between 0.2 and 1 liter of water from our skin and sweat glands each day. For a person who loses an average of 0.89 L H2O per day in this manner, how many quarts of water are lost from the skin and sweat glands in 30 days?

28 qt

A shipment of iron to a steel-making plant has a mass of 242.6 metric tons. What is the volume in liters of this iron?

3.09 x 10^4 L Fe

. An electron takes 6.2 x 10^-9 second to travel across a TV set that is 22 inches wide. What is the velocity of the electron in km/hr?

3.2 x 10^8 km/hr

When one gram of hydrogen gas, H2(g), is burned, 141.8 kJ of heat is released. How much heat is released when 2.3456 kg of hydrogen gas is burned?

3.326 X 10^5 kJ

A peanut butter sandwich provides about 1.4 103 kJ of energy. A typical adult uses about 95 kcal/hr of energy while sitting. If all of the energy in one peanut butter sandwich were to be burned off by sitting, how many hours would it be before this energy was used? (A kcal is a dietary calorie. There are 4.184 J/cal.)

3.5 hr

In optimum conditions, one molecule of the enzyme carbonic anhydrase can convert 3.6 X 10^5 molecules per minute of carbonic acid, H2CO3, into carbon dioxide, CO2, and water, H2O. How many molecules could be converted by one of these enzyme molecules in 1 week?

3.6 X 10^9 molecules

If an elevator moves 1340 ft to the 103rd floor of the Sears Tower in Chicago in 45 seconds, what is the velocity of the elevator in kilometers per hour?

33 km/hr

The volume of the earth's oceans is estimated to be 1.5 x 10^18 kiloliters. What is this volume in gallons?

4.0 x 10^20 gal

When you are doing heavy work, your muscles get about 75 to 80% by volume of your blood. If your body contains 5.2 liters of blood, how many liters of blood are in your muscles when you are working hard enough to send them 78% by volume of your blood?

4.1 L blood to muscles

Convert 4.352 micrograms to megagrams.

4.352 x 10^-12 Mg

What is the mass in kilograms of 15.6 gallons of gasoline?

41 kg gasoline

The kidneys of a normal adult female filter 115 mL of blood per minute. If this person has 5.345 quarts of blood, how many minutes will it take to filter all of her blood once?

44.0 minutes

When you are at rest, your heart pumps about 5.0 liters of blood per minute. Your brain gets about 15% by volume of your blood. What volume of blood, in liters, is pumped through your brain in 1.0 hour of rest?

45 L

The mass of the ocean is about 1.8 1021 kg. If the ocean contains 0.014% by mass hydrogen carbonate ions, HCO3-, how many pounds of HCO3- are in the ocean?

5. 6 x 10^17 lb HCO3-

A typical nonobese male has about 11 kg of fat. Each gram of fat can provide the body with about 38 kJ of energy. If this person requires 8.0 X 10^3 kJ of energy per day to survive, how many days could he survive on his fat alone?

52 days

In optimum conditions, one molecule of the enzyme amylase can convert 1.0 X 10^5 molecules per minute of starch into the sugar maltose. How many days would it take one of these enzyme molecules to convert a billion (1.0 X 10^9) starch molecules?

6.9 days

The average heart rate is 75 beats/min. How many times does the average person's heart beat in a week?

7.6 X 10^5 beats

The mass of the ocean is about 1.8 x 10^21 kg. If the ocean contains 0.041% by mass calcium ions, Ca2+, how many tons of Ca2+ are in the ocean? (There are 2000 pounds per ton.)

8.1 x 10^14 ton Ca2+

The mass of an electron is 9.1093897 x 10^-31 kg. What is this mass in nanograms?

9.1093897 x 10^-19 ng

While you are doing heavy work, your heart pumps up to 25.0 L of blood per minute. Your brain gets about 3-4% by volume of your blood under these conditions. What volume of blood in liters is pumped through your brain in 125 minutes of work that causes your heart to pump 22.0 L per minute, 3.43% of which goes to your brain?`

94.3 L to brain

When you sneeze, you close your eyes for about 1.00 second. If you are driving 65 miles per hour on the freeway and you sneeze, how many feet do you travel with your eyes closed?

95 ft

During quiet breathing, a person breathes in about 6 L of air per minute. If a person breathes in an average of 6.814 L of air per minute, what volume of air in liters does this person breathe in 1 day?

9812 L air

A saturated salt solution boils at 226 F. What is this temperature in C? in K?

C= 108 K= 381

Benzenethiol, C6H5SH, a mosquito larvicide, melts at 5.4 F. What is benzenethiol's melting point in C and K?

C=(5.4F-32F)/1.8=-14.8C K=-14.8C+273.15=258.4K

The hottest part of the flame on a Bunsen burner is found to be 2.15 X 10^3 K. What is this temperature in C and F?

C=2.15X10^3K-273.15=1.88 X 10^3C F=(1.88 X 10^3C X 1.8+32= 3.42X10^3F

Iron boils at 3023 K. What is this temperature in C? in F?

C=2.750X10^3 F=4982

The surface of the sun is 1.0 X 10^4 F. What is this temperature in C? in K?

C=5.5X10^3 K=5.8X10^3

Butter melts at 31 C. What is this temperature in F? in K?

F= 88 K=304

N,N-dimethylaniline, C6H5N(CH3)2, which is used to make dyes, melts at 2.5 C. What is N,N-dimethylaniline's melting point in F and K?

F=2.5C(1.8F/1C)+32F=36.5F K=2.5C+273.15=275.7

a. 684 - 595.325 = b. 92.771 + 9.3 =

a. 89 b. 102.1