Step-by-step explanation:
The van der Waals equation is:
(P + (n^2 a / V^2))(V - n b) = n R T
where P is the observed pressure of the gas, n is the number of moles of the gas, V is the volume of the container, T is the temperature, R is the gas constant, a is the van der Waals constant for the gas, and b is another van der Waals constant for the gas.
To solve for the ideal pressure (P_ideal), we need to use the ideal gas law, which is:
P_ideal = n R T / V
where P_ideal is the pressure that the gas would have if it behaved ideally.
To use this equation, we need to solve for T in the van der Waals equation. Rearranging the equation, we get:
T = (P + (n^2 a / V^2))(V - n b) / (n R)
Substituting the given values, we get:
T = (2.867 atm + ((3^2)(2.32 L^2 atm/mol^2) / (7.812 L)^2))(7.812 L - (3 mol)(0.0391 L/mol)) / (3 mol)(0.0821 L atm/mol K)
T = 88.5 K
Now we can use the ideal gas law to solve for P_ideal:
P_ideal = (3 mol)(0.0821 L atm/mol K)(88.5 K) / 7.812 L
P_ideal = 2.44 atm
Therefore, the pressure that the gas would have if it behaved ideally is 2.44 atm.