A sample of nitrogen occupies 10.0 liters at 25°C and 98.7 kPa. What would be the volume at 20°C and 102.7 kPa?

To solve the problem, we assume the sample to be ideal. Then, we use the ideal gas equation which is expressed as PV = nRT. From the first condition of the nitrogen gas sample, we calculate the number of moles.

n = PV / RT

n = (98.7x 10^3 Pa x 0.01 m^3) / (8.314 Pa m^3 / mol K) x 298.15 K

n = 0.40 mol N2

At the second condition, the number of moles stays the same however pressure and temperature was changed. So, the new volume is calculated as follows:

V = nRT / P

V = 0.40 x 8.314 x 293.15 / 102.7 x 10^3

V = 9.49 x 10^-3 m^3 or 9.49 L