A sample of nitrogen gas occupies a volume of 7.38 L at 57.0°C and 1.24 atm.
If it is desired to increase the volume of the gas sample to 9.25 L, while increasing its pressure to 1.71 atm, the temperature of the gas sample at the new volume and pressure must be
°C.
To calculate the final temperature of the gas sample, we can use the combined gas law formula:
(P1)(V1) / (T1) = (P2)(V2) / (T2)
Given:
P1 = 1.24 atm
V1 = 7.38 L
T1 = 57.0°C + 273 = 330 K
P2 = 1.71 atm
V2 = 9.25 L
T2 = ?
Substitute the values into the combined gas law formula and solve for T2:
(1.24 atm)(7.38 L) / 330 K = (1.71 atm)(9.25 L) / T2
(9.1512 atm*L) / 330 K = (15.8175 atm*L) / T2
T2 = (15.8175 atm*L * 330 K) / 9.1512 atm*L
T2 = 570 K
Therefore, the temperature of the gas sample at the new volume and pressure must be 570 K.