Question

1. consider two separate gas containers at the following conditions:

container a
contents: so₂(g)
pressure = pₐ
moles of gas = 1.0 mol
volume = 1.0 l
temperature = 7°c

container b
contents: unknown gas
pressure = pᵦ
moles of gas = 2.0 mol
volume = 2.0 l
temperature = 287°c

how is the pressure in container b related to the pressure in container a?

Explanation:

Step1: Convert temperatures to Kelvin

$T_A=7 + 273=280K$, $T_B=287+ 273 = 560K$

Step2: Use the ideal - gas law $PV = nRT$

For container A: $P_A=\frac{n_ART_A}{V_A}$, substituting $n_A = 1.0mol$, $V_A=1.0L$, $T_A = 280K$ and $R$ (the ideal - gas constant).
For container B: $P_B=\frac{n_BRT_B}{V_B}$, substituting $n_B = 2.0mol$, $V_B=2.0L$, $T_B = 560K$ and $R$.

Step3: Calculate the ratio $\frac{P_B}{P_A}$

$P_A=\frac{1.0mol\times R\times280K}{1.0L}=280R$
$P_B=\frac{2.0mol\times R\times560K}{2.0L}=560R$
$\frac{P_B}{P_A}=\frac{560R}{280R}=2$

Answer:

$P_B = 2P_A$