# Nitrogen gas (N2) reacts with hydrogen gas (H2) to form ammonia (NH3). At 200°C in a closed container, 1.05 atm of nitrogen gas is mixed with 2.02 atm of hydrogen gas. At equilibrium the total pressure is 2.02 atm. What is the partial pressure of hydrogen gas at equilibrium?

Jun 29, 2014

The partial pressure of hydrogen is 0.44 atm.

#### Explanation:

First, write the balanced chemical equation for the equilibrium and set up an ICE table.

$\textcolor{w h i t e}{X X X X X X} {\text{N"_2 color(white)(X)+color(white)(X)"3H"_2 color(white)(l)⇌ color(white)(l)"2NH}}_{3}$
$\text{I/atm} : \textcolor{w h i t e}{X l l} 1.05 \textcolor{w h i t e}{X X X l} 2.02 \textcolor{w h i t e}{X X X l l} 0$
$\text{C/atm} : \textcolor{w h i t e}{X} - x \textcolor{w h i t e}{X X X} - 3 x \textcolor{w h i t e}{X X} + 2 x$
$\text{E/atm} : \textcolor{w h i t e}{l} 1.05 - x \textcolor{w h i t e}{X} 2.02 - 3 x \textcolor{w h i t e}{X X} 2 x$

${P}_{\text{tot" = P_"N₂" + P_"H₂" + P_"NH₃" = (1.05-x) " atm" + (2.02–3 x) " atm" + 2x " atm" = "2.02 atm}}$

1.05 – x + color(red)(cancel(color(black)(2.02))) – 3x + 2x = color(red)(cancel(color(black)(2.02)))0

$1.05 - 2 x = 0$

$2 x = 1.05$

$x = 0.525$

${P}_{\text{H₂" = (2.02 -3x) " atm" = (2.02 – 3×0.525)" atm" = (2.02 – 1.575) " atm" = "0.44 atm}}$

The partial pressure of hydrogen is 0.44 atm.