Virial equation of state

44 questions on Virial equation of state from the Real Gases chapter: 9 NEET level, 17 JEE Main, 18 JEE Advanced. Each one opens with its answer and solution.

• The virial equation of state for one mole of a real gas is written as Z = 1 + (B)/(V_m) + (C)/(V_m^2) + dots. The coefficient B is called the NEET level
• The second virial coefficient B of a gas is negative at low temperature and positive at high temperature. The temperature at which B = 0 is the NEET level
• The second virial coefficient of a gas is measured as B = -160 mL mol^-1 at 250 K and B = 0 at 425 K. Assuming van der Waals behaviour, B = b - a/RT, and R = 0.... JEE Advanced level
• For a van der Waals gas, the second virial coefficient in the expansion Z = 1 + B/V_m + dots is JEE Main level
• For nitrogen (a = 1.39 L^2 atm mol^-2, b = 0.0391 L mol^-1) the second virial coefficient B = b - a/RT at 300 K, in mL mol^-1 (one decimal, R = 0.0821 L atm K^-... JEE Main level
• A gas has second virial coefficient B = -0.120 L mol^-1 at a certain temperature. Neglecting higher virial terms, which statements are correct? JEE Main level
• The virial equation can also be written in pressure form, Z = 1 + B'P + C'P^2 + dots. To first order the coefficients are related by JEE Main level
• At 273 K the second virial coefficient of a gas is B = -24.0 mL mol^-1. Using Z = 1 + (BP)/(RT) and R = 0.0821 L atm K^-1 mol^-1, the pressure in atm (one decim... JEE Advanced level
• For a van der Waals gas expanded as Z = 1 + B/V_m + C/V_m^2 + dots, which statements are correct? JEE Advanced level
• The compressibility factor of a gas at 300 K is found to be 0.9850 at 5.00 atm and 0.9700 at 10.0 atm. Assuming Z = 1 + B'P holds, the value of B' and the secon... JEE Advanced level
• A gas is at its Boyle temperature. Which of the following is the best approximation for Z at molar volume V_m, retaining the lowest non-vanishing correction, fo... JEE Advanced level
• The virial equation of state expresses Z as a power series in NEET level
• At the Boyle temperature of a gas, the second virial coefficient B is NEET level
• For a gas at a given temperature the second virial coefficient is B = +25 mL mol^-1. Which conclusion is correct? JEE Main level
• For a gas at 300 K the second virial coefficient is B = -45.0 mL mol^-1. Using Z = 1 + (BP)/(RT) and R = 0.0821 L atm K^-1 mol^-1, the compressibility factor at... JEE Main level
• The virial coefficients B and B' of the two forms Z = 1 + B/V_m and Z = 1 + B'P have the units respectively JEE Main level
• A gas has Z = 0.9880 at a molar volume of 5.00 L mol^-1. Neglecting the third and higher virial terms, its second virial coefficient B in mL mol^-1 (nearest int... JEE Main level
• As the temperature of a gas is raised from well below to well above its Boyle temperature, the second virial coefficient B JEE Main level
• A gas obeys PV_m = RT(1 + (B)/(V_m)) with B = -0.0700 L mol^-1 at 300 K. Its molar volume at 10.0 atm, in L mol^-1 (three decimals, R = 0.0821 L atm K^-1 mol^-1... JEE Advanced level
• Comparing the two forms of the virial equation, Z = 1 + B/V_m + C/V_m^2 and Z = 1 + B'P + C'P^2, which of the following are correct? JEE Advanced level
• For a van der Waals gas the virial coefficients are B = b - a/RT and C = b^2. A gas has b = 0.0400 L mol^-1 and a = 1.60 L^2 atm mol^-2. At 487 K and molar volu... JEE Advanced level
• The second virial coefficient of nitrogen is -160 mL mol^-1 at 100 K, -10 mL mol^-1 at 300 K and +21 mL mol^-1 at 700 K. Which statements are correct? JEE Advanced level
• The virial equation PV_m = RT(1 + (B)/(V_m) + (C)/(V_m^2) + dots) reduces to the ideal gas equation when NEET level
• The second virial coefficient B of a gas depends on JEE Main level
• Assertion (A): The second virial coefficient of a gas is negative at low temperature. Reason (R): At low temperature intermolecular attraction dominates over re... NEET level
• At 273 K the second virial coefficient of a gas is B = -21.5 mL mol^-1. The pressure-series coefficient B' = B/RT, in units of 10^-4 atm^-1 (one decimal, R = 0.... JEE Main level
• Which of the following gives the second virial coefficient of a gas that obeys P(V_m - b) = RT exactly? JEE Main level
• For a gas B = -0.050 L mol^-1 and C = 0.0016 L^2 mol^-2 at a certain temperature. Its compressibility factor at a molar volume of 0.400 L mol^-1, keeping terms ... JEE Main level
• The virial equation is considered more general than the van der Waals equation because JEE Advanced level
• For oxygen (a = 1.36 L^2 atm mol^-2, b = 0.0318 L mol^-1) the second virial coefficient is B = b - a/RT. At what temperature in K (nearest integer, R = 0.0821 L... JEE Advanced level
• For a gas with Z = 1 + B'P at low pressure, where B' is negative at T_1 and positive at T_2, which statements are correct? JEE Advanced level
• Expanding the van der Waals equation in powers of P gives Z = 1 + B'P + C'P^2 + dots. Using B = b - a/RT and C = b^2 together with C' = (C - B^2)/(RT)^2, the th... JEE Advanced level
• A gas has second virial coefficient B = -80 mL mol^-1 at 300 K (R = 0.0821 L atm K^-1 mol^-1). Neglecting higher terms, which statements are correct? JEE Advanced level
• In the virial equation Z = 1 + B'P + C'P^2 + dots, at low pressure the most important correction term is NEET level
• For a gas, B is negative at 200 K and positive at 600 K. The Boyle temperature lies NEET level
• Assertion (A): The virial equation reduces to the ideal gas law at the limit of zero pressure. Reason (R): All correction terms in the virial series are multipl... NEET level
• A gas has B' = -1.80 x 10^-3 atm^-1 at a certain temperature. Using Z = 1 + B'P, its compressibility factor at 15.0 atm (three decimals) is JEE Main level
• The second virial coefficient of a gas at T_1 is -150 mL mol^-1 and at T_2 is -30 mL mol^-1. Which statement is correct? JEE Main level
• At 300 K and 12.5 atm a gas has Z = 0.9625. Assuming Z = 1 + BP/RT and R = 0.0821 L atm K^-1 mol^-1, the second virial coefficient B in mL mol^-1 (nearest integ... JEE Main level
• Match the virial coefficient with its sign for a van der Waals gas. (P) B at T less than T_B; (Q) B at T greater than T_B; (R) C = b^2 at any T. (1) positive; (... JEE Main level
• A gas has B = -0.0400 L mol^-1 and C = 0.0016 L^2 mol^-2 at a certain temperature. Keeping terms up to C in Z = 1 + B/V_m + C/V_m^2, the molar volume in L mol^-... JEE Advanced level
• For nitrogen at 300 K, B = -4.5 mL mol^-1 and C = 1100 mL^2 mol^-2. At a molar volume of 0.100 L mol^-1 (i.e. 100 mL mol^-1), which statements are correct? JEE Advanced level
• The second virial coefficient of a certain gas obeys B = b - a/RT with b = 0.0400 L mol^-1 and a = 1.60 L^2 atm mol^-2 (R = 0.0821 L atm K^-1 mol^-1). The tempe... JEE Advanced level
• Which of the following statements about the virial equation of state are correct? JEE Advanced level