Chemistry - Real Gas Question with Solution | TestHub
N2 gas behaves ideally at its Boyle temperature in the pressure range from 0 to 50 atm. The critical temperature of N2 gas is -177°C. Assume that the gas obeys van der Waal's equation in the entire range of pressure and temperature. Which of the following statement(s) must be incorrect regarding the molar volume of the gas at the given conditions?
Options:(select one or more)
Answer:
Solution:
Boyle temperature TB = 27Tc/8 = 27 × 96/8 = 324 K = 51°C, so the gas is ideal only at 51°C (for 0-50 atm). (a) At 96 K (= Tc < TB), Z < 1, so V < RT/P = 9.6 l: statement incorrect. (b) At 400 K (> TB), Z > 1, so V > RT/P = 40 l: statement incorrect. (c) At 51°C the ideal value is 0.0821 × 324/82.1 = 324 ml, but 82.1 atm lies beyond the 0-50 atm ideal range; the higher-order terms give Z > 1, so V > 324 ml, not 310 ml: incorrect. (d) At 51°C and 0.821 atm the gas is ideal, V = 324 ml, not 32.4 ml: incorrect. All four must be incorrect. Hence (a), (b), (c), (d).
