Use the van der Waals equation for real gases to calculate the pressure exerted by 1.00 mole of ammonia at 27°C in a 750-mL container. (a = 4.17 L²·atm/mol², b = 0.0371 L/mol) A)23.2 atm B)27.1 atm C)32.8 atm D)42.0 atm E)32.8 torr

Question

Quizplus · Accepted Answer

The van der Waals equation is:
$\left(P + \frac{a}{V_m^2}\right)(V_m - b) = RT$
where $P$ is the pressure, $V_m$ is the molar volume, $a$ is a measure of the attractive forces between the gas molecules, $b$ is the volume excluded by the gas molecules themselves, $R$ is the gas constant and $T$ is the temperature.

Rearranging the equation yields:
$P = \frac{RT}{V_m-b} - \frac{a}{V_m^2}$

Substituting the values given for ammonia:
$a = 4.17\ L^2\ atm/mol^2$
$b = 0.0371\ L/mol$
$T = 27\ °C = 300\ K$
$V_m = \frac{0.75\ L}{1.00\ mol} = 0.75\ L/mol$

Plugging these values into the equation and converting the temperature to Kelvin:
$P = \frac{(0.08206\ L\ atm/(mol\ K))(300\ K)}{(0.75\ L/mol - 0.0371\ L/mol)} - \frac{(4.17\ L^2\ atm/mol^2)}{(0.75\ L/mol)^2}$
$P = 27.1\ atm$

Therefore, the pressure exerted by 1.00 mole of ammonia at 27°C in a 750-mL container is 27.1 atm (answer choice B).

Use the Van Der Waals Equation for Real Gases to Calculate