Physical Chem
Estimate/Calculate the critical constants (p_c, V_c, and T_c) for a gas molecule whose van der Waals parameters are a = 1.32 atm dm^6 mol^-2 and b = 0.0436 dm^3 mol^-1. The critical volume and critical pressure of a certain gas are 160 cm^3 mol^-1 and 40 atm, respectively. Estimate the critical temperature by assuming the gas obeys the van der Waals equation of state. Starting with the van der Waals equation, substitute in the reduced variables (i.e. you need to substitute in p = p_r/p_c from rearranging p_r = p/p_c, etc.) and replace the critical constants with their analogous van der Waals parameters (i.e. V_c = 3b) to arrive at p_r = 8T_r/3V_r - 1 - 3/V_r^2 All real compression factors are close to a value of 0.3 at the critical point. Using the van der Waals equation of state, we saw in class that Z_c is equal to 3/8 = 0.375 for all gases, which is pretty close, but other equations of state may do better. For instance the Redlich-Kwong equation shows Z_c to be equal to 1/3 = 0.333. Briefly discuss in general why the compression factor would be