Question

A mixture of water and graphite is heated to 600 K in a 1 L container. When the system comes to equilibrium it contains 0.17 mol of H2, 0.17 mol of CO, 0.74 mol of H2O, and some graphite. Some O2 is added to the system and a spark is applied so that the H2 reacts completely with the O2.
Find the amount of CO in the flask when the system returns to equilibrium.
Express your answer to two significant figures and include the appropriate units.

Answer 1

Answer:

0.44 moles

Explanation:

Given that :

A mixture of water and graphite is heated to 600 K in a 1 L container. When the system comes to equilibrium it contains 0.17 mol of H2, 0.17 mol of CO, 0.74 mol of H2O, and some graphite.

The equilibrium constant $K_c= \dfrac{[CO][H_2]}{[H_2O]}$

The equilibrium constant  $K_c= \dfrac{(0.17 )(0.17)}{0.74}$

The equilibrium constant $K_c= 0.03905$

Some O2 is added to the system and a spark is applied so that the H2 reacts completely with the O2.

The equation for the reaction is :

$H_2 + \dfrac{1}{2}O_2 \to H_2O \\ \\ 0.17 \ \ \ \ \ \ \ \ \ \to0.17$

Total mole of water now = 0.74+0.17

Total mole of water now = 0.91 moles

Again:

$K_c= \dfrac{[CO][H_2]}{[H_2O]}$

$0.03905 = \dfrac{[0.17+x][x]}{[0.91 -x]}$

0.03905(0.91 -x) = (0.17 +x)(x)

0.0355355 - 0.03905x = 0.17x + x²

0.0355355 +0.13095 x -x²

x² - 0.13095 x - 0.0355355 = 0

By using quadratic formula

x = 0.265  or   x = -0.134

Going by the value with the positive integer; x = 0.265 moles

Total moles of CO in the flask when the system returns to equilibrium is :

= 0.17 + x

= 0.17 + 0.265

= 0.435 moles

=0.44 moles (to two significant figures)