CHEM 1001 Study Guide - Midterm Guide: Ideal Gas, Sodium Azide, Airbag

Learning Goal: To be able to predict and calculate properties of real gases. Kinetic molecular theory makes certain assumptions about gases that are, in fact, not true for real gases. Therefore, the measured properties of a gas are often slightly different from the values predicted by the ideal gas law. The van der Waals equation is a more exact way of calculating properties of real gases. The formula includes two constants, a and 6, that are unique for each gas. The van der Waals equation is (p + an^2/V^2) (V - nb) = nRT, where P is the pressure, n the number of moles of gas, V the volume, T the temperature, and R the gas constant. All real gases possess intermolecular forces that can slightly decrease the observed pressure. In the van der Waals equation, the variable P is adjusted to P + an^2/V^2, where a is the attractive force between molecules. The volume of a gas is defined as the space in which the gas molecules can move. When using the ideal gas law we make the assumption that this space is equal to the volume of the container. However, the gas molecules themselves take up some space in the container. So in the van der Waals equation, the variable V is adjusted to be the volume of the container minus the space taken up by the molecules, V - nb, where b is the volume of a mole of molecules. 14.0 moles of gas are in a 5.00 L tank at 20.7 degree C. Calculate the difference in pressure between methane and an ideal gas under these conditions. The van der Waals constants for methane are a = 2.300 L^2 middot atin/mol^2 and b = 0.0430 L/mol Express your answer with the appropriate units.

Testbank, Question 10C.089 The van der Waals equation of state for a real gas is Pn a Frneas + -|(V meas-nb) = nRT At what pressure will 1.00 mole of NH3 be in a 10.00 L container at 298 K assuming NH3 is a real gas (van der Waals constants for NH3 are a = 4.170 L2 atm more b = 0.03707 L mor 1) 2.47 atm 2.41 atm O 2.03 atm 20.3 atm 24.1 atm

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