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

0.0243 atm

Step-by-step explanation:

1. Chemical equation

2PH₃ ⇌ P₂ + 3H₂

E/atm: x 0.417 0.826

2. Kₚ expression

`K_{\text{p}} = \frac{p_{\text{P}_(2)}p_{\text{H}_(2)}^(3)}{p_{\text{PH}_(3)}^(2)} = 398`

Step 3. Calculate the equilibrium concentrations

`\begin{array}{rcl}\\\frac{p_{\text{P}_(2)}p_{\text{H}_(2)}^(3)}{p_{\text{PH}_(3)}^(2)}&=&398\\\\\frac{0.417 * 0.826^(3)}{p_{\text{PH}_(3)}^(2)}&=&398\\\\0.2350&=&398 *{p_{\text{PH}_(3)}^(2)}\\p_{\text{PH}_(3)}^(2)&=& (0.2350)/(398)\\\\&=&5.905 * 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}(0.417 * 0.826^(3))/(0.0243^(2))&=&398\\\\398 & = & 398\\\end{array}`

It checks.