Consider the following reaction: $$\mathrm{CH}_{3} \mathrm{Br}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(a q)+\mathrm{Br}^{-}(a q)$$ The rate law for this reaction is first order in \(\mathrm{CH}_{3} \mathrm{Br}\) and first order in \(\mathrm{OH}^{-} .\) When \(\left[\mathrm{CH}_{3} \mathrm{Br}\right]\) is \(5.0 \times 10^{-3} \mathrm{M}\) and \(\left[\mathrm{OH}^{-}\right]\) is \(0.050 \mathrm{M},\) the reaction rate at 298 \(\mathrm{K}\) is 0.0432 \(\mathrm{M} / \mathrm{s}\) . (a) What is the value of the rate constant? (\mathbf{b} )What are the units of the rate constant? (c) What would happen to the rate if the concentration of OH \(^{-}\) were tripled? (d) What would happen to the rate if the concentration of both reactants were tripled?

Step by step solution

01

Find the rate constant (k) value

To find the rate constant, we can use the given rate law and the reaction rate at specific concentrations of the reactants. The rate law is given as: Rate = k [CH3Br] [OH⁻] We can plug in the given values: 0.0432 M/s = k (5.0 × 10⁻³ M)(0.050 M) Now, we can solve for k: k = 0.0432 M/s / [(5.0 × 10⁻³ M)(0.050 M)] k = 17.28 s⁻¹ Therefore, the rate constant value (k) is 17.28 s⁻¹.

02

Find the units of the rate constant (k)

The units of the rate constant can be derived from the rate law equation: Rate = k [CH3Br] [OH⁻] Since the rate itself has units of M/s: k = Rate / ([CH3Br] [OH⁻]) k will have the units of (M/s) / (M²), which simplifies to: Units of k = s⁻¹ (M⁻¹) The units of the rate constant (k) are s⁻¹ (M⁻¹).

03

Effect on the rate when the concentration of OH⁻ is tripled

If the concentration of OH⁻ is tripled, the new reaction rate can be calculated using the rate law: New Rate = k [CH3Br] [3 × OH⁻] New Rate = k [CH3Br] (3 [OH⁻]) Since the reaction is first order in OH⁻, the new rate will be three times the initial rate: New Rate = 3 × (k [CH3Br] [OH⁻]) Therefore, the rate will triple when the concentration of OH⁻ is tripled.

04

Effect on the rate when the concentrations of both reactants are tripled

If both reactant concentrations are tripled, the new reaction rate can be calculated using the rate law: New Rate = k [3 × CH3Br] [3 × OH⁻] New Rate = k (3 [CH3Br])(3 [OH⁻]) Since the reaction is first order in both CH3Br and OH⁻, the new rate will be nine times the initial rate: New Rate = 9 × (k [CH3Br] [OH⁻]) Therefore, the rate will be nine times faster when the concentrations of both reactants are tripled.

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