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. ( a
= 0.211 L2-atm/mol2, b
= 0.0171 L/mol)

Answer 1

To calculate the pressure using the van der Waals equation, we first need to rearrange the equation to solve for pressure. The van der Waals equation is:

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

Where:
P is the pressure
a and b are van der Waals constants
n is the number of moles
V is the volume
R is the ideal gas constant
T is the temperature

Plugging in the values given:
a = 0.211 L^2-atm/mol^2
b = 0.0171 L/mol
n = 1.00 mol
V = 22.4 L
R = 0.0821 L-atm/mol-K
T = 100°C = 373 K

Now we can substitute the values into the van der Waals equation and solve for pressure:

(P + (0.211 (1.00/22.4)^2)) (22.4 - 0.0171(1.00)) = 1.00 * 0.0821 * 373
(P + 0.00437)(22.3829) = 30.6233
P + 0.0973 = 30.6233
P = 30.6233 - 0.0973
P = 30.526 atm

Therefore, the pressure in the vessel containing 1.00 mol of neon gas at 100 °C is 30.526 atm.