Explain how the volume of the bubbles exhausted by a scuba diver) change as they rise to the surface, assuming that they remain intact.

## Solution

As the bubbles rise, the ambient pressure decreases, so their volume increases.

A spray can is used until it is empty except for the propellant gas, which has a pressure of 1344 torr at 23 °C. If the can is thrown into a fire (T = 475 °C), what will be the pressure (in torr) in the hot can?

## Solution

3.40 x 10^{3} torr

A 2.50-L volume of hydrogen measured at –196 °C is warmed to 100 °C. Calculate the volume of the gas at the higher temperature, assuming no change in pressure.

## Solution

12.1 L

A weather balloon contains 8.80 moles of helium at a pressure of 0.992 atm and a temperature of 25 °C at ground level. What is the volume of the balloon under these conditions?

## Solution

217 L

The volume of an automobile air bag was 66.8 L when inflated at 25.0 °C with 77.8 g of nitrogen gas. What was the pressure in the bag in kPa?

## Solution

103 kPa

How many moles of gaseous boron trifluoride, BF_{3}, are contained in a 4.3410-L bulb at 788.0 K if the pressure is 1.220 atm? How many grams of BF_{3}?

## Solution

8.190 x 10^{–2} mol

5.553 g

Iodine, I_{2}, is a solid at room temperature but sublimes (converts from a solid into a gas) when warmed. What is the temperature in a 73.3-mL bulb that contains 0.292 g of I_{2} vapor at a pressure of 0.462 bar?

## Solution

354 K

How many grams of gas are present in each of the following cases?

(a) 0.100 L of CO_{2} at 307 torr and 26 °C

(b) 8.75 L of C_{2}H_{4}, at 378.3 kPa and 483 K

(c) 221 mL of Ar at 0.23 torr and –54 °C

## Solution

(a) 7.24 $\times $ 10^{–2} g; (b) 23.1 g; (c) 1.5 $\times $ 10^{–4} g

A high altitude balloon is filled with 1.41 × 10^{4} L of hydrogen at a temperature of 21 °C and a pressure of 745 torr. What is the volume of the balloon at a height of 20 km, where the temperature is –48 °C and the pressure is 63.1 torr?

## Solution

4.27 x 10^{5} L

A cylinder of medical oxygen has a volume of 35.4 L, and contains O_{2} at a pressure of 151 atm and a temperature of 25 °C. What volume of O_{2} does this correspond to at normal body conditions, that is, 1 atm and 37 °C?

## Solution

5561 L

A large scuba tank with a volume of 18 L is rated for a pressure of 220 bar. The tank is filled at 20 °C and contains enough air to supply 1860 L of air to a diver at a pressure of 2.37 atm (a depth of 45 feet). Was the tank filled to capacity at 20 °C?

## Solution

The pressure when the tank was filled is 248 bar, which exceeds the rated pressure of 220 bar, so the tank was actually overfilled.

A 20.0-L cylinder containing 11.34 kg of butane, C_{4}H_{10}, was opened to the atmosphere. Calculate the mass of the gas remaining in the cylinder if it were opened and the gas escaped until the pressure in the cylinder was equal to the atmospheric pressure, 0.983 atm, and a temperature of 27 °C.

## Solution

46.4 g

For a given amount of gas showing ideal behavior, draw labeled graphs of:

(a) the variation of *P* with *V*

(b) the variation of *V* with *T*

(c) the variation of *P* with *T*

(d) the variation of $\frac{1}{P}$ with *V*

## Solution

For a gas exhibiting ideal behavior:

A balloon with a volume of 100.21 L at 21 °C and 0.981 atm is released and just barely clears the top of Mount Crumpit in British Columbia. If the final volume of the balloon is 144.53 L at a temperature of 5.24 °C, what is the pressure experienced by the balloon as it clears Mount Crumpet?

## Solution

0.644 atm

If the volume of a fixed amount of a gas is tripled at constant temperature, what happens to the pressure?

## Solution

The pressure decreases by a factor of 3.

Calculate the density of Freon 12, CF_{2}Cl_{2}, at 30.0 °C and 0.954 atm.

## Solution

4.64 g L^{−1}

How could you show experimentally that the molecular formula of propene is $C_3H_6$, not $CH_2$?

## Solution

Since the gas volume will be proportional to the number of moles of gas at a given temperature, you could measure the volume of a known mass of the gas and determine the number of moles of gas present. knowing the number of moles and total mass, you can calculate the approximate molar mass, and match it with either is $CH_2$ or $C_3H_6$.

The density of a certain gaseous fluoride of phosphorus is 3.93 g/L at STP. Calculate the molar mass of this fluoride and determine its molecular formula.

## Solution

88.1 g mol^{−1}; PF_{3}

Joseph Priestley first prepared pure oxygen by heating mercuric oxide, HgO:

$$2HgO(s)⟶2Hg(l)+O_2(g)$$

(a) Outline the steps necessary to answer the following question: What volume of O_{2} at 23 °C and 0.975 atm is produced by the decomposition of 5.36 g of HgO?

(b) Answer the question.

## Solution

(a) Determine the moles of HgO that decompose; using the chemical equation, determine the moles of O_{2} produced by decomposition of this amount of HgO; and determine the volume of O_{2} from the moles of O_{2}, temperature, and pressure. (b) 0.308 L

The chlorofluorocarbon CCl_{2}F_{2} can be recycled into a different compound by reaction with hydrogen to produce CH_{2}F_{2}(*g*), a compound useful in chemical manufacturing:

(a) Outline the steps necessary to answer the following question: What volume of hydrogen at 225 atm and 35.5 °C would be required to react with 1 ton ($1.000×10^3$ kg) of CCl_{2}F_{2}?

(b) Answer the question.

## Solution

(a) Determine the molar mass of CCl_{2}F_{2}. From the balanced equation, calculate the moles of H_{2} needed for the complete reaction. From the ideal gas law, convert moles of H_{2} into volume. (b) $3.72×10^3$ L

Lime, CaO, is produced by heating calcium carbonate, CaCO_{3}; carbon dioxide is the other product.

(a) Outline the steps necessary to answer the following question: What volume of carbon dioxide at 875 K and 0.966 atm is produced by the decomposition of 1 ton ($1.000×10^3$ kg) of calcium carbonate?

(b) Answer the question.

## Solution

(a) Balance the equation. Determine the grams of CO_{2} produced and the number of moles. From the ideal gas law, determine the volume of gas. (b) $7.43×10^5$ L

Calculate the volume of oxygen required to burn 12.00 L of ethane gas, C_{2}H_{6}, to produce carbon dioxide and water, if the volumes of C_{2}H_{6} and O_{2} are measured under the same conditions of temperature and pressure.

## Solution

42.00 L

What volume of oxygen at 423.0 K and a pressure of 127.4 kPa is produced by the decomposition of 129.7 g of BaO_{2} to BaO and O_{2}?

## Solution

10.57 L O_{2}

Ethanol, C_{2}H_{5}OH, is produced industrially from ethylene, C_{2}H_{4}, by the following sequence of reactions:

What volume of ethylene at STP is required to produce 1.000 metric ton (1000 kg) of ethanol if the overall yield of ethanol is 90.1%?

## Solution

$5.40×10^5$ L

A sample of a compound of xenon and fluorine was confined in a bulb with a pressure of 18 torr. Hydrogen was added to the bulb until the pressure was 72 torr. Passage of an electric spark through the mixture produced Xe and HF. After the HF was removed by reaction with solid KOH, the final pressure of xenon and unreacted hydrogen in the bulb was 36 torr. What is the empirical formula of the xenon fluoride in the original sample? (Note: Xenon fluorides contain only one xenon atom per molecule.)

## Solution

XeF_{4}