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Ch.14 - Chemical Kinetics
All textbooksBrown 14th EditionCh.14 - Chemical KineticsProblem 118
Chapter 14, Problem 118

The reaction between ethyl iodide and hydroxide ion in ethanol solution, C2H5I(alc) + OH-(alc) → C2H5OH(l) + I-(alc), has an activation energy of 86.8 kJ/mol and a frequency factor of 2.10 × 10^11 M^-1 s^-1. (b) A solution of KOH in ethanol is made up by dissolving 0.335 g KOH in ethanol to form 250.0 mL of solution. Similarly, 1.453 g of C2H5I is dissolved in ethanol to form 250.0 mL of solution. Equal volumes of the two solutions are mixed. Assuming the reaction is first order in each reactant, what is the initial rate at 35 _x001E_C?

Verified step by step guidance
1
First, calculate the molarity of KOH in the solution. Use the formula: \( \text{Molarity} = \frac{\text{mass of solute (g)}}{\text{molar mass of solute (g/mol)} \times \text{volume of solution (L)}} \). The molar mass of KOH is approximately 56.11 g/mol.
Next, calculate the molarity of C2H5I in its solution using the same molarity formula. The molar mass of C2H5I is approximately 156.02 g/mol.
Since equal volumes of the two solutions are mixed, the concentration of each reactant in the mixed solution will be half of the original concentration. Calculate the new concentrations for both KOH and C2H5I.
Use the Arrhenius equation to find the rate constant \( k \) at 35°C. The Arrhenius equation is \( k = A \cdot e^{-\frac{E_a}{RT}} \), where \( A \) is the frequency factor, \( E_a \) is the activation energy, \( R \) is the gas constant (8.314 J/mol·K), and \( T \) is the temperature in Kelvin. Convert 35°C to Kelvin.
Finally, calculate the initial rate of the reaction using the rate law for a first-order reaction: \( \text{Rate} = k \cdot [\text{C2H5I}] \cdot [\text{OH}^-] \). Use the concentrations calculated in step 3 and the rate constant from step 4.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Activation Energy

Activation energy is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to transform into products. In this reaction, the activation energy of 86.8 kJ/mol indicates how much energy is needed to initiate the reaction between ethyl iodide and hydroxide ion.
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Rate Law and Reaction Order

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. For a first-order reaction in each reactant, the rate is proportional to the concentration of each reactant raised to the power of their respective orders. In this case, the initial rate can be calculated using the concentrations of KOH and C2H5I, reflecting their first-order dependence.
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Concentration and Molarity

Concentration, often expressed in molarity (M), is the amount of solute per unit volume of solution. To find the initial rate of the reaction, it is essential to calculate the molarity of KOH and C2H5I in the mixed solution. This involves converting the mass of each solute into moles and then dividing by the total volume of the solution, which is crucial for determining the reaction rate.
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Related Practice
Textbook Question

Enzymes are often described as following the two-step mechanism:

E + S ⇌ ES (fast)

ES → E + P (slow)

where E = enzyme, S = substrate, ES = enzyme9substrate complex, and P = product.

(a) If an enzyme follows this mechanism, what rate law is expected for the reaction?

Textbook Question

Enzymes are often described as following the two-step mechanism:

E + S  ⇌ ES (fast)

ES → E + P (slow)

where E = enzyme, S = substrate, ES = enzyme9substrate complex, and P = product.

(b) Molecules that can bind to the active site of an enzyme but are not converted into product are called enzyme inhibitors. Write an additional elementary step to add into the preceding mechanism to account for the reaction of E with I, an inhibitor.

Textbook Question

The reaction between ethyl iodide and hydroxide ion in ethanol (C2H5OH) solution, C2H5I(alc) + OH-(alc) → C2H5OH(l) + I-(alc), has an activation energy of 86.8 kJ/mol and a frequency factor of 2.10 × 1011 M-1 s-1. (c) Which reagent in the reaction is limiting, assuming the reaction proceeds to completion?

Textbook Question

The reaction between ethyl iodide and hydroxide ion in ethanol (C2H5OH) solution, C2H5I(alc) + OH-(alc) → C2H5OH(l) + I-(alc), has an activation energy of 86.8 kJ/mol and a frequency factor of 2.10 × 1011 M-1 s-1. (d) Assuming the frequency factor and activation energy do not change as a function of temperature, calculate the rate constant for the reaction at 50 C.

Textbook Question

The gas-phase reaction of NO with F2 to form NOF and F has an activation energy of Ea = 6.3 kJ/mol. and a frequency factor of A = 6.0 × 108 M-1 s-1. The reaction is believed to be bimolecular: NO(g) + F2(g) → NOF(g) + F(g) (b) Draw the Lewis structures for the NO and the NOF molecules, given that the chemical formula for NOF is misleading because the nitrogen atom is actually the central atom in the molecule.