van der Waals equation and its constants

44 questions on van der Waals equation and its constants from the Real Gases chapter: 8 NEET level, 17 JEE Main, 19 JEE Advanced. Each one opens with its answer and solution.

• In the van der Waals equation (P + (an^2)/(V^2))(V - nb) = nRT, the term (an^2)/(V^2) corrects for NEET level
• The SI unit of the van der Waals constant b is NEET level
• The van der Waals constants of four gases are: W (a = 0.034, b = 0.0237), X (a = 1.39, b = 0.0391), Y (a = 3.59, b = 0.0427), Z (a = 4.17, b = 0.0371), with a i... JEE Advanced level
• Two moles of CO2 (a = 3.59 L^2 atm mol^-2, b = 0.0427 L mol^-1) are kept in a 5.0 L vessel at 300 K. Using the van der Waals equation and R = 0.0821 L atm K^-1 ... JEE Main level
• The van der Waals constant b is related to the radius r of a spherical molecule by JEE Main level
• The van der Waals constant b of a gas is 0.0400 L mol^-1. Treating molecules as hard spheres with b = 4N_A((4)/(3)pi r^3) and N_A = 6.022 x 10^23 mol^-1, the mo... JEE Main level
• The van der Waals constant a for a gas is 1.39 L^2 atm mol^-2. Its value in SI units (Pa m^6 mol^-2) is approximately (1 atm = 1.013 x 10^5 Pa, 1 L = 10^-3 m^3) JEE Main level
• One mole of a gas with b = 0.0427 L mol^-1 occupies 1.00 L at 273 K and exerts a pressure of 20.4 atm. Assuming the gas obeys the van der Waals equation (R = 0.... JEE Advanced level
• For a van der Waals gas, which of the following statements are correct? JEE Advanced level
• At high pressure a van der Waals gas has Z = 1 + (Pb)/(RT). For a gas at 300 K the plot of Z against P in this region has slope 1.60 x 10^-3 atm^-1. The value o... JEE Advanced level
• One mole of oxygen (a = 1.36 L^2 atm mol^-2, b = 0.0318 L mol^-1) is confined to 0.500 L at 350 K. By what percentage is the van der Waals pressure lower than t... JEE Advanced level
• In the van der Waals equation the quantity (V - nb) represents NEET level
• The pressure of a real gas is less than that calculated from the ideal gas equation at the same V and T (at moderate pressure) because NEET level
• The dimensions of the ratio a/b of the van der Waals constants are the same as those of JEE Main level
• One mole of methane (a = 2.25 L^2 atm mol^-2, b = 0.0428 L mol^-1) occupies 0.500 L at a pressure of 40.0 atm. Using the van der Waals equation and R = 0.0821 L... JEE Main level
• For a van der Waals gas at low pressure (neglecting b), the compressibility factor is JEE Main level
• Three moles of ammonia (a = 4.17 L^2 atm mol^-2, b = 0.0371 L mol^-1) are contained in a 2.0 L vessel at 400 K (R = 0.0821 L atm K^-1 mol^-1). Which statements ... JEE Advanced level
• Two gases have the following van der Waals constants: gas X, a = 5.5, b = 0.030; gas Y, a = 1.4, b = 0.065 (usual units). Which statement is correct? JEE Main level
• One mole of hydrogen (a = 0.244 L^2 atm mol^-2, b = 0.0266 L mol^-1) is compressed to 0.100 L at 600 K. The difference P_vdW - P_ideal in atm (nearest integer),... JEE Advanced level
• A van der Waals gas is described by (P + (a)/(V_m^2))(V_m - b) = RT. Which of the following are correct? JEE Advanced level
• The van der Waals constants of a gas are a = 6.49 L^2 atm mol^-2 and b = 0.0562 L mol^-1. If 1 mol of this gas at 400 K occupies 0.800 L, the ratio P_vdW/P_idea... JEE Advanced level
• The excluded volume b in the van der Waals equation is related to the molecular diameter d by b = (2)/(3)pi N_A d^3. Which statements are correct? JEE Advanced level
• The van der Waals equation for n moles of a gas is NEET level
• For which of the following gases is the van der Waals constant b the largest? JEE Main level
• Assertion (A): The van der Waals constant a for NH3 is greater than that for N2. Reason (R): NH3 molecules are held by hydrogen bonds in addition to dispersion ... NEET level
• One mole of oxygen (a = 0.138 Pa m^6 mol^-2, b = 3.19 x 10^-5 m^3 mol^-1) occupies 2.00 x 10^-3 m^3 at 300 K. Using the van der Waals equation and R = 8.314 J K... JEE Main level
• For a van der Waals gas at very high pressure (where a/V_m^2 is negligible compared with P), the compressibility factor is JEE Main level
• At 300 K and 200 atm a gas has Z = 1.125. Assuming the high-pressure form Z = 1 + (Pb)/(RT) and R = 0.0821 L atm K^-1 mol^-1, the value of b in mL mol^-1 (one d... JEE Main level
• Match the van der Waals constants with their physical meaning. (P) a, (Q) b. (1) excluded volume per mole; (2) measure of intermolecular attraction; (3) measure... JEE Main level
• Using the van der Waals equation, find the molar volume of CO2 (a = 3.59 L^2 atm mol^-2, b = 0.0427 L mol^-1) at 350 K and 40.0 atm by iteration: start from the... JEE Advanced level
• One mole each of two gases X (a = 2.0, b = 0.040) and Y (a = 2.0, b = 0.020), in the usual units, are kept at the same temperature in identical 0.500 L vessels.... JEE Advanced level
• A gas obeys P(V_m - b) = RT (van der Waals equation with a = 0). Which statement about this gas is correct? JEE Advanced level
• A van der Waals gas has a = 1.39 L^2 atm mol^-2 and b = 0.0391 L mol^-1. Two moles are placed in a 1.00 L vessel at 300 K (R = 0.0821 L atm K^-1 mol^-1). Which ... JEE Advanced level
• Which of the following is the correct form of the van der Waals equation for one mole of gas? NEET level
• The van der Waals constant a for a gas is high. This indicates that the gas NEET level
• If the volume of the container is very large compared with nb and P is low, the van der Waals equation becomes JEE Main level
• Four moles of chlorine (a = 6.49 L^2 atm mol^-2, b = 0.0562 L mol^-1) are stored in a 3.00 L cylinder at 400 K (R = 0.0821 L atm K^-1 mol^-1). Which statements ... JEE Advanced level
• Rearranging the van der Waals equation, the pressure of n moles of a real gas is given by JEE Main level
• 0.500 mol of a gas with a = 5.46 L^2 atm mol^-2 and b = 0.0305 L mol^-1 is confined to 0.400 L at 350 K. The van der Waals pressure in atm (two decimals, R = 0.... JEE Main level
• Among the following, the gas expected to have the smallest value of the van der Waals constant a is JEE Main level
• A 1.00 L vessel contains nitrogen (a = 1.39 L^2 atm mol^-2, b = 0.0391 L mol^-1) at 300 K and 30.0 atm. Solve the van der Waals equation for the amount of gas b... JEE Advanced level
• Consider two gases: X with a = 0.03 L^2 atm mol^-2, b = 0.024 L mol^-1, and Y with a = 5.5 L^2 atm mol^-2, b = 0.030 L mol^-1. Which statements are correct? JEE Advanced level
• For a van der Waals gas, the term (a)/(V_m^2) is sometimes called the internal pressure. For CO2 (a = 3.59 L^2 atm mol^-2) at a molar volume of 0.500 L mol^-1 t... JEE Advanced level
• The van der Waals equation written as a cubic in V_m is V_m^3 - (b + (RT)/(P))V_m^2 + (a)/(P)V_m - (ab)/(P) = 0. Which statements are correct? JEE Advanced level