Question

At 3000K, the equilibrium pressures of $C{{O}_{2}}$ , $CO$ and ${{O}_{2}}$ are 0.6, 0.4, and 0.2 atmospheres, respectively. Find the ${{K}_{P}}$ for the reaction: $2CO_{2}\rightleftharpoons 2CO_{2(g)} + O_{2}$
(A) 0.088
(B) 0.0533
(C) 0.133
(D) 0.177

Answer 1

Hint: An equilibrium constant, Kp, is determined by dividing the partial pressure of products by the partial pressure of reactants, and each substance is raised to a power equal to its stoichiometric coefficient.

Formula Used: For a reaction: $2A\rightleftharpoons 2B + C$
The value of ${{K}_{P}}$is given by ${{K}_{P}}=\frac{{{P}_{B}}^{2}\times {{P}_{C}}}{{{P}_{A}}^{2}}$

Complete Step by Step Answer:
The reaction is:
$2CO_{2}\rightleftharpoons 2CO_{2(g)} + O_{2}$
At 3000 K, the equilibrium partial pressures are - $C{{O}_{2}}=0.6$ , $CO=0.4$ , ${{O}_{2}}=0.2$
${{K}_{P}}$ for the given reaction is ${{K}_{P}}=\frac{{{P}_{CO}}^{2}\times {{P}_{{{O}_{2}}}}}{{{P}_{C{{O}_{2}}}}^{2}}$
                                                    ${{K}_{P}}=\frac{{{(0.4)}^{2}}\times (0.2)}{{{(0.6)}^{2}}}$
                                                    ${{K}_{P}}=\frac{0.16\times 0.2}{0.36}$
                                                    ${{K}_{P}}=0.088atm$
Thus, the value of ${{K}_{P}}$ for this reaction is 0.088 atm.
Correct Option: (A) 0.088

Additional Information: Chemical equilibrium is a state in which the rates of both the forward and backward reactions are equal and the concentration of both the reactants and products is constant. At equilibrium, there is no net change in the number of moles, although conversion from reactants to products or products to reactants is still occurring.

Note: The units of equilibrium constant depend upon the number of moles of reactant and product. Its units are given by ${{(atm)}^{\Delta n}}$. Here, $\Delta n={{n}_{P}}-{{n}_{R}}=3-2=1$ . As a result, units of ${{K}_{P}}$ is $atm$. To calculate the equilibrium constant, you must first understand the entire reaction and its stoichiometric coefficients. If$K>1$ , the equilibrium favours products, and if $K<1$ , then the equilibrium favours reactants. But, if $K=1$ , then both reactants and products are present in the mixture in significant amounts.