To calculate the percent difference between the pressure calculated using the van der Waals' equation and the ideal pressure, we need to compute the pressure using both equations and then find the difference.
The ideal gas law is given by:
PV = nRT
Where:
P = Pressure (in atm)
V = Volume (in L)
n = Number of moles
R = Ideal gas constant (0.0821 L*atm/(mol*K))
T = Temperature (in K)
Rearranging the equation, we can solve for P:
P = (nRT) / V
Substituting the given values into the formula, we get:
P_ideal = (1.005 mol * 0.0821 L*atm/(mol*K) * 269.2 K) / 1.609 L
P_ideal = 14.0283 atm
The van der Waals' equation is given by:
[P + a(n/V)^2] [V - nb] = nRT
Where:
P = Pressure (in atm)
V = Volume (in L)
n = Number of moles
R = Ideal gas constant (0.0821 L*atm/(mol*K))
T = Temperature (in K)
a = van der Waals' constant for the gas (0.084 L^2*atm/(mol^2) for oxygen)
b = van der Waals' constant for the gas (0.0318 L/mol for oxygen)
Rearranging the equation, we can solve for P:
P = [nRT/V - a(n/V)^2] / (V - nb)
Substituting the given values into the formula, we get:
P_vanderwaals = [1.005 mol * 0.0821 L*atm/(mol*K) * 269.2 K / 1.609 L - 0.084 L^2*atm/(mol^2) (1.005 mol / 1.609 L)^2] / (1.609 L - 0.0318 L/mol * 1.005 mol)
P_vanderwaals = 13.034 atm
To find the percent difference, we can use the formula:
Percent difference = |(P_ideal - P_vanderwaals) / P_ideal| * 100
Substituting the values, we get:
Percent difference = |(14.0283 atm - 13.034 atm) / 14.0283 atm| * 100
Percent difference = |0.9943 atm / 14.0283 atm| * 100
Percent difference = 0.0709 * 100
Percent difference = 7.09%
Therefore, the percent difference between the pressure calculated using the van der Waals' equation and the ideal pressure is 7.09%.
According to the ideal gas law, a 1.005 mol sample of oxygen gas in a 1.609 L container at 269.2 K should exert a pressure of 13.80 atm. What is the percent difference between the pressure calculated using the van der Waals' equation and the ideal pressure?
1 answer
2 answers