Question

write the mass-action expression of \\(k_c\\) for the following chemical reaction.

\\(\text{no}(g) + 1/2\text{br}_2(g) \longleftrightarrow \text{nobr}(g)\\)

\\(\bigcirc \frac{\text{no}\text{br}_2^{0.5}}{\text{nobr}}\\)

\\(\bigcirc \frac{\text{nobr}}{\text{no}^{0.5}\text{br}_2}\\)

\\(\bigcirc \frac{\text{nobr}}{\text{no}\text{br}_2^{0.5}}\\)

\\(\bigcirc \frac{\text{nobr}^2}{\text{no}^2\text{br}_2}\\)

\\(\bigcirc \frac{\text{no}^2\text{br}_2}{\text{nobr}^2}\\)

Explanation:

Identify the chemical equation

We are given the following reversible gas-phase chemical reaction:

$$\text{NO}(g) + \frac{1}{2}\text{Br}_2(g) ightleftharpoons \text{NOBr}(g)$$

Define the equilibrium constant expression

The equilibrium constant \(K_c\) is defined by the law of mass action. For a general reaction:

$$a\text{A} + b\text{B} ightleftharpoons c\text{C} + d\text{D}$$

The expression for \(K_c\) is:

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

where the concentrations of the products are in the numerator and the reactants are in the denominator, each raised to the power of their stoichiometric coefficients.

Apply the coefficients to the expression

For our specific reaction:

• The product is \(\text{NOBr}\) with a stoichiometric coefficient of \(1\).
• The reactants are \(\text{NO}\) with a coefficient of \(1\), and \(\text{Br}_2\) with a coefficient of \(\frac{1}{2}\) (or \(0.5\)).

Substituting these into the \(K_c\) formula gives:

$$K_c = \frac{[\text{NOBr}]^1}{[\text{NO}]^1 [\text{Br}_2]^{0.5}} = \frac{[\text{NOBr}]}{[\text{NO}][\text{Br}_2]^{0.5}}$$

Match with the given options

Let's analyze the provided choices:

• Option 1: \(\frac{[\text{NO}][\text{Br}_2]^{0.5}}{[\text{NOBr}]}\) (Inverted)
• Option 2: \(\frac{[\text{NOBr}]}{[\text{NO}]^{0.5}[\text{Br}_2]}\) (Incorrect exponents)
• Option 3: \(\frac{[\text{NOBr}]}{[\text{NO}][\text{Br}_2]^{0.5}}\) (Correct)
• Option 4: \(\frac{[\text{NOBr}]^2}{[\text{NO}]^2[\text{Br}_2]}\) (This represents the squared reaction, not the given one)
• Option 5: \(\frac{[\text{NO}]^2[\text{Br}_2]}{[\text{NOBr}]^2}\) (Inverted and squared)

Answer:

• (A) \(\frac{[\text{NO}][\text{Br}_2]^{0.5}}{[\text{NOBr}]}\)
• (B) \(\frac{[\text{NOBr}]}{[\text{NO}]^{0.5}[\text{Br}_2]}\)
• (C) \(\frac{[\text{NOBr}]}{[\text{NO}][\text{Br}_2]^{0.5}}\) (Correct answer)
• (D) \(\frac{[\text{NOBr}]^2}{[\text{NO}]^2[\text{Br}_2]}\)
• (E) \(\frac{[\text{NO}]^2[\text{Br}_2]}{[\text{NOBr}]^2}\)