The compression factor (compressibility factor) for one mole of a Van der Waals gas at 00 C and 100 atmosphere pressure is found to be 0.5. Assuming that the volume of the gas molecule is negligible, calculate the Van der Waals constant ‘a’.
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Based on the information provided, using the van der Waals equation: Z = PV/RT = 0.5 where P = 100 atm, V = 1 mol, R = 0.08206 L.atm/mol.K, and T = 273 K.
The formula for the van der Waals constant “a” is rearranged as follows: a = (27/64) * (RTc)^2 / Pc, where Tc and Pc stand for the gas’s critical temperature and pressure, respectively.
The critical compressibility factor Zc for non-polar gases is roughly 0.3, assuming that the gas in question is one of those gases. This allows us to calculate the critical pressure:
Zc = 3/8 * (Pc/RTc) 0.3 = 3/8 * (Pc/RTc) Pc/RTc = 0.8
To find a, use the formula a = (27/64) * (RTc)^2 / (0.8Pc).
Assuming Tc = 190 K and Pc = 56 atm (typical values for non-polar gases), we get: a = (27/64) * (0.08206 L.atm/mol.K * 190 K)^2 / (0.8 * 56 atm) = 1.254 L^2.atm/mol^2
Based on the information provided, using the van der Waals equation: Z = PV/RT = 0.5 where P = 100 atm, V = 1 mol, R = 0.08206 L.atm/mol.K, and T = 273 K.
The formula for the van der Waals constant “a” is rearranged as follows: a = (27/64) * (RTc)^2 / Pc, where Tc and Pc stand for the gas’s critical temperature and pressure, respectively.
The critical compressibility factor Zc for non-polar gases is roughly 0.3, assuming that the gas in question is one of those gases. This allows us to calculate the critical pressure:
Zc = 3/8 * (Pc/RTc) 0.3 = 3/8 * (Pc/RTc) Pc/RTc = 0.8
To find a, use the formula a = (27/64) * (RTc)^2 / (0.8Pc).
Assuming Tc = 190 K and Pc = 56 atm (typical values for non-polar gases), we get: a = (27/64) * (0.08206 L.atm/mol.K * 190 K)^2 / (0.8 * 56 atm) = 1.254 L^2.atm/mol^2