The equilibrium constant (Kc) for the reaction 2 HCl(g) ⇌H2(g)+Cl2(g) is 4 ×10^-34 at 25^∘ C. Wh

step 1 Answer for the question, the equilibrium constant case for the reaction, we have given reaction

The equilibrium constant (Kc) for the reaction 2 HCl(g)...

The equilibrium constant $\left(K_{c}\right)$ for the reaction $$ 2 \mathrm{HCl}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) $$ is $4 \times 10^{-34}$ at $25^{\circ} \mathrm{C}$. What is the equilibrium constant for the reaction? $$ \frac{1}{2} \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{HCl}(g) $$ (a) $2 \times 10^{-17}$ (b) $2.5 \times 10^{33}$ (c) $5 \times 10^{6}$ (d) None of these

The equilibrium constant $\left(K_{c}\right)$ for the reaction
$$
2 \mathrm{HCl}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g)
$$
is $4 \times 10^{-34}$ at $25^{\circ} \mathrm{C}$. What is the equilibrium constant for the reaction?
$$
\frac{1}{2} \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{HCl}(g)
$$
(a) $2 \times 10^{-17}$
(b) $2.5 \times 10^{33}$
(c) $5 \times 10^{6}$
(d) None of these

Key Concepts

Exponential and Radical Manipulations in Equilibrium Calculations

Understanding exponential rules is essential when adjusting equilibrium constants for changes in reaction coefficients. For instance, raising an equilibrium constant to a fractional exponent (like one-half) is equivalent to taking a square root, which directly applies when the overall reaction is modified by a factor. This manipulation ensures accurate recalculation of the new equilibrium constant for the modified reaction.

Impact of Stoichiometric Coefficients on the Equilibrium Constant

When the stoichiometric coefficients in a balanced chemical equation are altered by a multiplicative factor, the equilibrium constant is raised to a power equal to that factor. This principle is applied when the reaction is scaled, such as halving the coefficients, which mathematically corresponds to taking the square root of the original equilibrium constant or its reciprocal if the reaction is also reversed.

Effect of Reversing a Reaction on the Equilibrium Constant

Reversing a chemical reaction inverts the equilibrium constant. This means that the equilibrium constant for the reverse reaction is the reciprocal of the equilibrium constant for the forward reaction. This concept is crucial for understanding how manipulation of a reaction’s direction affects its equilibrium state.

Chemical Equilibrium

Chemical equilibrium refers to the state in a reversible reaction where the rate of the forward reaction equals the rate of the reverse reaction, resulting in constant concentrations of reactants and products. The equilibrium constant quantifies the ratio of product concentrations to reactant concentrations at equilibrium, providing insight into the reaction’s favorability.

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