A sample of nitrogen (N2) has a volume of 53.0 L at a pressure of 750. mmHg .

Question

A sample of nitrogen (N2) has a volume of 53.0 L at a pressure of 750. mmHg . What is the final volume, in liters, of the gas at each of the following pressures, if there is no change in temperature and amount of gas?

721 mmHg

Express your answer using three significant figures

1.8 atm

Express your answer using two significant figures.

0.440 atm

Express your answer using three significant figures.

830 torr

Express your answer using two significant figures.

Answer 1

Hello, Anya,

When comparing the same moles of a gas under different conditions of volume, temperature and pressure, use the following relationship:

P1V1/T1 = P2V2/T2 where P, V and T are the pressures, volumes and temperatures of the two states (1 is initial and 2 is final). You can deduce this simplified formula by taking the full equation PV=nRT and place one condition on top and the second state on bottom: (P1V1 = nRT1)/(P2V2 = nRT2) Since no matter is added or removed from the system, the value for moles, n, cancels, as does the gas constant R. This leaves the simpler formula P1V1/T1 = P2V2/T2.

Enter the data in a table:

The top three rows show the known values, including a line for expressing pressure in atm. To convert mmHg to atm, just remember that 760 mmHg = 1 atm.

Use the simplified equation and note that the temperature does not change, so T1 = T2 and they cancel out to leave P1V1 = P2V2. We want V2, so V2 = P1V1/P2. Substitute the different pressures for P2 and you'll get the last line, the new volume in liters. I did not modify the Excel format to the correct number of sig figs.

I hope this is helpful,

Bob