At a certain temperature, the following reactions have the...

At a certain temperature, the following reactions have the equilibrium constants as shown below: $$ \begin{aligned} \mathrm{S}(s)+\mathrm{O}_{2}(g) & \rightleftharpoons \mathrm{SO}_{2}(g) ; \quad K_{c}=5 \times 10^{52} \\ 2 \mathrm{~S}(s)+3 \mathrm{O}_{2}(g) & \rightleftharpoons 2 \mathrm{SO}_{3}(g) ; K_{c}=10^{29} \end{aligned} $$ What is the equilibrium constant $K_{c}$ for the reaction at the same temperature? $$ 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) $$ (a) $2.5 \times 10^{76}$ (b) $4 \times 10^{23}$ (c) $4 \times 10^{-77}$ (d) None of these

At a certain temperature, the following reactions have the equilibrium constants as shown below:
$$
\begin{aligned}
\mathrm{S}(s)+\mathrm{O}_{2}(g) & \rightleftharpoons \mathrm{SO}_{2}(g) ; \quad K_{c}=5 \times 10^{52} \\
2 \mathrm{~S}(s)+3 \mathrm{O}_{2}(g) & \rightleftharpoons 2 \mathrm{SO}_{3}(g) ; K_{c}=10^{29}
\end{aligned}
$$
What is the equilibrium constant $K_{c}$ for the reaction at the same temperature?
$$
2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)
$$
(a) $2.5 \times 10^{76}$
(b) $4 \times 10^{23}$
(c) $4 \times 10^{-77}$
(d) None of these

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Key Concepts

Stoichiometry and Its Effect on Equilibrium Constants

Stoichiometry in a chemical reaction affects the calculation of the equilibrium constant because it alters the exponents in the concentration terms. When a reaction is scaled up or down by a factor, the equilibrium expression is raised to that power. This principle is crucial when combining reactions in order to derive the constant for a overall reaction, ensuring that the correct mathematical relationship is maintained.

Chemical Equilibrium

This concept deals with the state in which the forward and reverse reactions occur at the same rate, resulting in constant concentrations of reactants and products. It provides the foundation for defining the equilibrium constant, which quantifies the ratio of product concentrations to reactant concentrations at equilibrium.

Equilibrium Constant Manipulation

When chemical reactions are algebraically manipulated, their equilibrium constants are also modified according to specific mathematical rules. For instance, if a reaction is multiplied by a factor, the equilibrium constant is raised to the power of that factor. Similarly, if reactions are added or subtracted, the equilibrium constant for the overall reaction is the product or quotient of the constants for the individual reactions.

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