Question

1.366×10-1 mol of ammonia (NH3) gas is isolated in a chamber of volume 20.00 mL at 299.1 °C.
Calculate the predicted pressure in the chamber using first the ideal gas law and then the Van der Waals equation.
(For NH3, the Van der Waals constants are: a = 4.17 atm L2 mol-2; b = 0.0371 L mol-1.)
Enter the numerical value (in either decimal or scientific notation) for the ratio, PvdW/Pideal.

Answer 1

Number of moles of ammonia $(n)=1.366\times 10^{-1}$

Volume of chamber$(V)=20 ml=20\times10^{-3} L$

Temperature$(T)=299.1\degree C=299.1+273=572.1K$

Predicted pressure using ideal gas equation:

$P_{id}V=nRT\ (R=0.0821)$

$P_{id}\times20\times 10^{-3}=1.366\times 10^{-1}\times 0.0821\times 572.1$ $\implies P_{id}=313.75\ atm$

Predicted pressure using Van der Wall gas equation:

$(P +\frac{an^2}{V^2})(V-nb)=nRT$

$(P+\frac{4.17\times 0.1366^2}{(20 \times 10^{-3})^2})(20\times 10^{-3}-0.1366\times 0.0371)=$ $0.1366 \times 0.0821 \times 572.1$

$P_{van}=235.14\ atm$