Can the speed of a given molecule in a gas double at constant temperature? Explain your answer.

## Solution

Yes. At any given instant, there are a range of values of molecular speeds in a sample of gas. Any single molecule can speed up or slow down as it collides with other molecules. The average velocity of all the molecules is constant at constant temperature.

A 36.0–L cylinder of a gas used for calibration of blood gas analyzers in medical laboratories contains 350 g CO_{2}, 805 g O_{2}, and 4,880 g N_{2}. At 25 degrees C, what is the pressure in the cylinder in atmospheres?

## Solution

141 atm, 107,000 torr, 14,300 kPa

A sample of gas isolated from unrefined petroleum contains 90.0% CH_{4}, 8.9% C_{2}H_{6}, and 1.1% C_{3}H_{8} at a total pressure of 307.2 kPa. What is the partial pressure of each component of this gas? (The percentages given indicate the percent of the total pressure that is due to each component.)

## Solution

CH_{4}: 276 kPa; C_{2}H_{6}: 27 kPa; C_{3}H_{8}: 3.4 kPa

A 1-L sample of CO initially at STP is heated to 546 K, and its volume is increased to 2 L.

(a) What effect do these changes have on the number of collisions of the molecules of the gas per unit area of the container wall?

(b) What is the effect on the average kinetic energy of the molecules?

(c) What is the effect on the average speed of the molecules?

## Solution

(a) The number of collisions per unit area of the container wall is constant.

(b) The average kinetic energy doubles.

(c) The root average speed will increase (specifically, it will increase to $\sqrt{2}$ times its initial value).

Answer the following questions:

(a) Is the pressure of the gas in the hot-air balloon shown at the opening of this chapter greater than, less than, or equal to that of the atmosphere outside the balloon?

(b) Is the density of the gas in the hot-air balloon shown at the opening of this chapter greater than, less than, or equal to that of the atmosphere outside the balloon?

(c) At a pressure of 1 atm and a temperature of 20 °C, dry air has a density of 1.2256 g/L. What is the (average) molar mass of dry air?

(d) The average temperature of the gas in a hot-air balloon is 54.44 °C. Calculate its density, assuming the molar mass equals that of dry air.

(e) The lifting capacity of a hot-air balloon is equal to the difference in the mass of the cool air displaced by the balloon and the mass of the gas in the balloon. What is the difference in the mass of 1.00 L of the cool air in part (c) and the hot air in part (d)?

(f) A balloon carries 40.0 gallons of liquid propane (density 0.5005 g/L). What volume of CO_{2} and H_{2}O gas is produced by the combustion of this propane?

## Solution

(a) equal; (b) less than; (c) 29.48 g mol^{−1}; (d) 1.0966 g L^{−1}; (e) 0.129 g/L; (f) 270 L;