# Ideal Gases

## Problems

Problem : Molly admires her red balloon, which has a volume of 2.0 liters at sea level (1.0 atm). A clown catches her eye, and she lets go of the balloon. The red balloon goes up and up until the pressure around it is 0.80 atm. Assuming isothermal conditions, what is the new volume of Molly's red balloon?

This problem is a straightforward application of Boyle's law. P1V1 = P2V2 rearranges to = V2. After plugging in values, we find that the balloon's volume V2 = 2.5 liters.

Problem : Graph the pressure vs. volume relationship dictated by Boyle's law. If Boyle's law stated that P = aV, where a < 0, what would the graph of P vs. V look like?

A graph of P vs. V according to Boyle's law is shown below:
Boyle's Law
When P = aV, the graph of P vs. V will look like this:
P = aV
Note that P = aV cannot be true. The equation predicts negative volumes as P increases.

Problem : Initially the volume and pressure of a sample of gas are 1 dm3 and 10 smoots, respectively. The volume is raised isothermally to 10 dm3. What is the pressure of the gas in smoots under these conditions?

Don't let the unfamiliar units of dm3 and smoots confuse you. Your first reaction may to be convert to SI units. In this case you can't; smoots are completely imaginary. Instead realize that the equation P1V1 = P2V2 works as long as the units of P1P2 and V1V2 are the same. The actual units of pressure or volume don't matter. So rearrange the equation to = P2. Plugging in values, we find that P2 = 1 smoot.

Problem : One end of a mercury filled manometer is open to the atmosphere, while the other is closed and contains a vacuum. What does the height difference h of the Hg columns measure?

h measures the difference in pressure between the two ends of the manometer. Since the pressures at the two ends are 0 and Patm, the height h will measure the atmospheric pressure.

Problem : The pressure of gas A (PA) is 3.0 atm. The height of the mercury column h is 1140 mm. What is the pressure of gas B (PB) in atmospheres? Assume that 1 mm Hg = 1/760 atm.

From the diagram we can see that PA must be greater than PB by 1140 mm of Hg. 1140 mm Hg converts to 1.5 atm, so PB = 3.0 - 1.5 = 1.5 atm.