Question

Suppose 10.00 mol of Kr gas are pumped into a 1.700 L container at 298.150 K.

Calculate the expected pressure based on the ideal gas law, Pideal.
Calculate an estimate of the gas pressure one might observe based on the van der Waals equation, Pobs. a = 2.349 L2 · atm/mol2, b = 0.03978 L/mol
Which factor, a or b, is the primary reason for the difference in the calculated pressures?
What does this factor reflect?

Answer 1

The expected pressure of 10.00 mol of Kr gas in a 1.700 L container at 298.150 K can be calculated using the ideal gas law. An estimate based on the van der Waals equation accounts for intermolecular forces and the volume of particles. The differences in pressures from these calculations are primarily due to these two factors.

Step-by-step explanation:

To calculate the expected pressure of 10.00 mol of Kr gas in a 1.700 L container at 298.150 K using the ideal gas law. The ideal gas law is given by PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant (0.08206 L·atm·K⁻¹·mol⁻¹), and T is the temperature in Kelvin.

First, convert the temperature to Kelvin, which it already is, and use the provided mole and volume in the formula:

Pideal = (nRT) / V
= (10.00 mol × 0.08206 L·atm·K⁻¹·mol⁻¹ × 298.150 K) / 1.700 L

Next, we can calculate an estimate of the gas pressure using the van der Waals equation, which is (P + (a(n²/V²)))(V - nb) = nRT. Using the constants a and b specific for Kr, pump the values into the formula to estimate Pobs.

Comparing the factors a and b, the primary reason for the difference in calculated pressures will be identified as either factor. Factor a represents the intermolecular forces, while factor b represents the volume occupied by the gas particles themselves.