Question

When a mixture of PH3, P2, and H2 comes to equilibrium at 873 K, PP2= 0.422 atm and PH2= 0.832 atm. What is PPH3? Express your answer with the appropriate units.

Answer 1

Answer:

0.0243 atm

Explanation:

1. Chemical equation

           2PH₃ ⇌ P₂  +   3H₂

E/atm:     x      0.417   0.826

2. Kₚ expression

$K_{\text{p}} = \dfrac{p_{\text{P}_{2}}p_{\text{H}_{2}}^{3}}{p_{\text{PH}_{3}}^{2}} = 398$

Step 3. Calculate the equilibrium concentrations

$\begin{array}{rcl}\\\dfrac{p_{\text{P}_{2}}p_{\text{H}_{2}}^{3}}{p_{\text{PH}_{3}}^{2}}&=&398\\\\\dfrac{0.417 \times 0.826^{3}}{p_{\text{PH}_{3}}^{2}}&=&398\\\\0.2350&=&398 \times{p_{\text{PH}_{3}}^{2}}\\p_{\text{PH}_{3}}^{2}&=& \dfrac{0.2350}{398}\\\\&=&5.905 \times 10^{-4}\\p_{\text{PH}_{3}}&=& \textbf{0.0243 atm}\end{array}\\\text{The equilibrium pressure of PH _{3} is \large \boxed{\textbf{0.0243} \textbf{ atm}} }$

Check:

$\begin{array}{rcl}\dfrac{0.417 \times 0.826^{3}}{0.0243^{2}}&=&398\\\\398 & = & 398\\\end{array}$

It checks.