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Identify the INCORRECT statement among the following: (A) A gas can be liquefied at 320 K and 42 atm if its critical temperature is 340 K and critical pressure is 42 atm. (B) At Boyle's temperature, a real gas behaves ideally under low-pressure conditions. (C) When the temperature of an ideal gas is increased at constant pressure, its molecular collision frequency increases. (D) The ratio of the root-mean-square speed of H2(g) at 50 K to that of O2(g) at 800 K equals 1.

1. A gas can be liquefied at 320 K and 42 atm if its critical temperature is 340 K and critical pressure is 42 atm.
2. At Boyle's temperature, a real gas behaves ideally under low-pressure conditions.
3. When the temperature of an ideal gas is increased at constant pressure, its molecular collision frequency increases.
4. The ratio of the root-mean-square speed of H2(g) at 50 K to that of O2(g) at 800 K equals 1.

Correct answer: When the temperature of an ideal gas is increased at constant pressure, its molecular collision frequency increases.

Solution

Statement (A): Correct. Since T = 320 K < Tc = 340 K and P = 42 atm = Pc, liquefaction is possible (below critical temperature). Statement (B): Correct. Boyle's temperature is defined as the temperature at which real gas behavior approaches ideal at low pressures. Statement (C): INCORRECT. Collision frequency Z = sqrt(2)*pi*d²*(N/V)*v_avg. At constant P, N/V = P/(kT) proportional to 1/T, while v_avg proportional to sqrt(T). So Z proportional to (1/T)*sqrt(T) = T^(-1/2). As T increases, Z decreases. Statement (D): v_rms = sqrt(3RT/M). For H2 at 50 K: sqrt(3R*50/2). For O2 at 800 K: sqrt(3R*800/32). Ratio = sqrt(50/2) / sqrt(800/32) = sqrt(25) / sqrt(25) = 5/5 = 1. Correct.

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