The equilibrium constant, $K,$ of a reaction at a particular temperature is determined by the concentrations or pressures of the reactants and products at equilibrium.

For a gaseous reaction with the general form

$aA+bBcC+dD$

the $K_c$ and $K_p$ expressions are given by

$K_c=\frac{[C{]}^c[D{]}^d}{[(A){]}^a[(B){]}^b}$

$K_p=\frac{(P_C{)}^c(P_D{)}^d}{(P_A{)}^a(P_B{)}^b}$

The subscript $c$ or $p$ indicates whether $K$ is expressed in terms of concentrations or pressures. Equilibrium$-$constant expressions do not include a term for any pure solids or liquids that may be involved since their composition does not change throughout the reaction. The standard state of a pure substance is the pure substance itself, and although the quantity may change the sample remain pure. The constant value is incorporated into the value of $K,$ and does not need to be accounted for separately.

Part A

Phosgene $($carbonyl chloride$),COC{l}_2,$ is an extremely toxic gas that is used in manufacturing certain dyes and plastics. Phosgene can be produced by reacting carbon monoxide and chlorine gas at high temperatures:

$CO(g)+C{l}_2(g)COC{l}_2(g)$

Carbon monoxide and chlorine gas are allowed to react in a sealed vessel at $478C.$ At equilibrium, the concentrations were measured and the following results obtained:

$\backslash$table$[[$Gas$,\backslash$table$[[$Partial Pressure$],[($atm$)]]],[CO,0\mathrm{.}760],[C{l}_2,1\mathrm{.}18],[COC{l}_2,0\mathrm{.}150]]$

What is the equilibrium constant, $K_p,$ of this reaction?

Express your answer numerically.

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Previous Answers

Correct

Deriving concentrations from data

In Part A$,$ you were given the equilibrium pressures, which could be plugged directly into the formula for $K.$ In Part B however, you will be given initial concentrations and only one equilibrium concentration. You must use this data to find all three equilibrium concentrations before you can apply the formula for $K.$

Part B

The following reaction was performed in a sealed vessel at $785C$ :

$H_2(g)+I_2(g)2HI(g)$

Initially, only $H_2$ and $I_2$ were present at concentrations of $[H_2]=3\mathrm{.}55M$ and $[I_2]=3\mathrm{.}00M.$ The equilibrium concentration of $I_2$ is $0\mathrm{.}0200M.$ What is the equilibrium constant, $K_c,$ for the reaction at this temperature?

Express your answer numerically.

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