Question

Using the van der Waals equation, the pressure in a 22.4 L vessel containing 1.00 mol of neon gas at 100 °C is ________ atm

Answer 1

To calculate the pressure using the van der Waals equation, we first need to know the values of the van der Waals constants for neon gas:

a = 0.2136 L^2 atm/mol^2
b = 0.01718 L/mol

Now we can use the van der Waals equation:

(P + a(n/V)^2)(V - nb) = nRT

Where:
P = pressure
a = van der Waals constant
n = number of moles
V = volume
b = van der Waals constant
R = ideal gas constant (0.08206 L atm/mol K)
T = temperature in Kelvin

Given:
V = 22.4 L
n = 1 mol
R = 0.08206 L atm/mol K
T = 100 °C = 373 K

Substitute the values into the van der Waals equation:

(P + 0.2136(1/22.4)^2)(22.4 - 0.01718) = 1 * 0.08206 * 373

(P + 0.2136(0.04464)^2)(22.38282) = 30.42638

(P + 0.2136(0.002104)*22.38282) = 30.42638

(P + 0.2136(0.04710562)) = 30.42638

P + 0.01005 = 30.42638

P = 30.42638 - 0.01005
P = 30.41633 atm

Therefore, the pressure in the 22.4 L vessel containing 1.00 mol of neon gas at 100 °C is approximately 30.42 atm.