Critical constants and liquefaction

44 questions on Critical constants and liquefaction from the Real Gases chapter: 9 NEET level, 17 JEE Main, 18 JEE Advanced. Each one opens with its answer and solution.

• The critical temperature of a gas is NEET level
• For a van der Waals gas the critical compressibility factor Z_c = (P_cV_c)/(RT_c) equals NEET level
• Gas P has T_c = 304 K, P_c = 73 atm; gas Q has T_c = 126 K, P_c = 34 atm. Both are treated as van der Waals gases. Which statements are correct? JEE Advanced level
• For methane a = 2.25 L^2 atm mol^-2 and b = 0.0428 L mol^-1. Its critical temperature in K (nearest integer), with R = 0.0821 L atm K^-1 mol^-1, is JEE Main level
• Using the same methane constants (a = 2.25 L^2 atm mol^-2, b = 0.0428 L mol^-1), the critical pressure in atm (one decimal) is JEE Main level
• A gas has T_c = 150 K and P_c = 48 atm. Using the van der Waals relations and R = 0.0821 L atm K^-1 mol^-1, its constant b is closest to JEE Main level
• Which statement about the critical point of a pure substance is correct? JEE Main level
• Carbon dioxide has T_c = 304 K and P_c = 72.8 atm. From the van der Waals relations with R = 0.0821 L atm K^-1 mol^-1, the value of a in L^2 atm mol^-2 (two dec... JEE Advanced level
• For a gas obeying the van der Waals equation, which of the following are correct at the critical point? JEE Advanced level
• The critical density of a van der Waals gas of molar mass M is JEE Advanced level
• Two different gases are at the same reduced temperature T/T_c = 1.5 and the same reduced pressure P/P_c = 2.0. According to the law of corresponding states, whi... JEE Advanced level
• The critical volume V_c of a van der Waals gas is NEET level
• A gas cannot be liquefied at any pressure if NEET level
• The critical pressure of a gas is NEET level
• For CO2 the van der Waals constant b = 0.0427 L mol^-1. The critical volume predicted by the van der Waals equation, in mL mol^-1 (one decimal), is JEE Main level
• A gas has critical pressure 33.5 atm and van der Waals constant b = 0.0391 L mol^-1. Using P_c = a/27b^2 and T_c = 8a/27Rb with R = 0.0821 L atm K^-1 mol^-1, it... JEE Main level
• The critical constants of a gas are T_c = 400 K, P_c = 50 atm and V_c = 0.20 L mol^-1. Its experimental critical compressibility factor (R = 0.0821 L atm K^-1 m... JEE Main level
• Which of the following changes occurs when a liquid in a sealed tube is heated to its critical temperature? JEE Advanced level
• Methane has T_c = 190 K and P_c = 45.8 atm. Using the van der Waals relations and R = 0.0821 L atm K^-1 mol^-1, the predicted critical volume V_c = 3b in mL mol... JEE Advanced level
• The isotherms of a van der Waals gas are plotted as P against V_m. Which statements are correct? JEE Advanced level
• For a van der Waals gas, the ratio (a)/(b) expressed in terms of critical constants is JEE Advanced level
• Which of the following statements about liquefaction of gases are correct? JEE Advanced level
• The temperature, pressure and volume at the critical point are called critical constants. Which of the following is true at the critical point? NEET level
• For a van der Waals gas the critical temperature is JEE Main level
• Which of the following statements about critical temperature is correct? NEET level
• A gas has P_c = 51.0 atm and V_c = 74.8 mL mol^-1. If it behaves as a van der Waals gas (Z_c = 3/8), its critical temperature in K (one decimal, R = 0.0821 L at... JEE Main level
• The critical temperature and critical pressure of a gas are T_c and P_c. In terms of these, the van der Waals constant a is JEE Main level
• Ammonia has T_c = 405 K and P_c = 111.5 atm. Using b = RT_c/8P_c with R = 0.0821 L atm K^-1 mol^-1, the value of b in mL mol^-1 (one decimal) is JEE Main level
• Match the critical constant with its van der Waals expression. (P) V_c, (Q) P_c, (R) T_c. (1) a/27b^2; (2) 3b; (3) 8a/27Rb. The correct matching is JEE Main level
• Using the van der Waals relations, estimate the critical density of methane (molar mass 16 g mol^-1, T_c = 190 K, P_c = 45.8 atm, R = 0.0821 L atm K^-1 mol^-1) ... JEE Advanced level
• A sample of CO2 (T_c = 304 K, P_c = 73 atm) is subjected to the following conditions. In which cases can a distinct liquid phase be obtained by compression at t... JEE Advanced level
• Which of the following is a correct expression for the gas constant R in terms of the van der Waals critical constants of a gas? JEE Advanced level
• In the reduced form of the van der Waals equation, (P_r + (3)/(V_r^2))(3V_r - 1) = 8T_r, where P_r = P/P_c, V_r = V_m/V_c and T_r = T/T_c. Which statements are ... JEE Advanced level
• The critical constants of a gas are NEET level
• The critical temperature of water is 647 K and that of CO2 is 304 K. At 350 K, which of the following is true? JEE Main level
• The gas which has the highest critical temperature among the following is NEET level
• A van der Waals gas has T_c = 304 K and V_c = 0.128 L mol^-1. Using Z_c = 3/8 and R = 0.0821 L atm K^-1 mol^-1, its critical pressure in atm (one decimal) is JEE Main level
• If the critical pressure of a gas is P_c and the critical volume is V_c, the van der Waals constant a equals JEE Main level
• Methane has P_c = 45.8 atm and V_c = 0.0990 L mol^-1. Using a = 3P_cV_c^2, the value of a in L^2 atm mol^-2 (two decimals) is JEE Main level
• Assertion (A): A gas above its critical temperature cannot be liquefied however high the pressure. Reason (R): Above T_c the average kinetic energy of the molec... JEE Main level
• Nitrogen has a = 0.1358 Pa m^6 mol^-2 and b = 3.85 x 10^-5 m^3 mol^-1. Using R = 8.314 J K^-1 mol^-1, the critical temperature in K (one decimal) is JEE Advanced level
• The experimental critical compressibility factor Z_c of most gases lies between 0.27 and 0.30, while the van der Waals equation predicts 0.375. Which statements... JEE Advanced level
• For a van der Waals gas, the ratio (P_c V_c)/(T_c) in terms of R is JEE Advanced level
• Using the van der Waals constants of two gases, M (a = 1.36, b = 0.0318) and N (a = 4.17, b = 0.0371), in L^2 atm mol^-2 and L mol^-1, with R = 0.0821 L atm K^-... JEE Advanced level