Excess solid carbon, \text{C}(s), is allowed to react with 1.0\text{ mol} of carbon dioxid… — JAMB UTME

Excess solid carbon,

\text{C}(s)

, is allowed to react with

1.0\text{ mol}

of carbon dioxide gas,

\text{CO}_2(g)

, in a sealed

2.0\text{ dm}^3

reaction vessel at a constant high temperature according to the equation:

\text{C}(s) + \text{CO}_2(g) \rightleftharpoons 2\text{CO}(g)

1.0\text{ mol}

of carbon monoxide gas,

\text{CO}(g)

, is present at equilibrium, calculate the numerical value of the equilibrium constant,

K_c

, in

\text{mol dm}^{-3}

Cevap: 1 mol dm^-3

1.0

To find

K_c

, convert initial and equilibrium amounts to molar concentrations by dividing by the volume (

2.0\text{ dm}^3

). Initial concentration of

\text{CO}_2

0.50\text{ mol dm}^{-3}

. At equilibrium,

[\text{CO}] = \frac{1.0}{2.0} = 0.50\text{ mol dm}^{-3}

. From the

1:2

stoichiometry,

0.25\text{ mol dm}^{-3}

\text{CO}_2

reacted, leaving

[\text{CO}_2] = 0.25\text{ mol dm}^{-3}

. For a heterogeneous system, solid carbon is excluded from the equilibrium constant expression. Thus,

K_c = \frac{[\text{CO}]^2}{[\text{CO}_2]} = \frac{(0.50)^2}{0.25} = 1.0\text{ mol dm}^{-3}

Calculate initial concentrations from the given moles and volume

Initial

[\text{CO}_2] = 0.50\text{ mol dm}^{-3}

, initial

[\text{CO}] = 0.0\text{ mol dm}^{-3}

Concentration is calculated using

C = \frac{n}{V}

where

V = 2.0\text{ dm}^3

Determine equilibrium concentrations using stoichiometric mole ratios

Equilibrium

[\text{CO}] = 0.50\text{ mol dm}^{-3}

and

[\text{CO}_2] = 0.25\text{ mol dm}^{-3}

Producing

1.0\text{ mol}

\text{CO}

consumes

0.50\text{ mol}

\text{CO}_2

. Remaining moles of

\text{CO}_2 = 1.0 - 0.50 = 0.50\text{ mol}

Write the equilibrium constant expression for the heterogeneous system

K_c = \frac{[\text{CO}]^2}{[\text{CO}_2]}

Pure solids like

\text{C}(s)

have constant activity and are omitted from the

K_c

expression.

Substitute concentrations into the

K_c

expression and solve

K_c = \frac{(0.50)^2}{0.25} = 1.0\text{ mol dm}^{-3}

Calculates the numerical value of the equilibrium constant.

Heterogeneous equilibrium constant expression and ICE calculations

Soru