Math Problem Statement

The reaction butyl chloride, C4H9Cl, with water was studied by dissolving butyl chloride in water and measuring time dependence of the concentration of butyl chloride. A solution of C4H9Cl in water was prepared; the concentration of butyl chloride was 0.1087 M after 51.94 seconds and 0.07953 M after 205.8 seconds. What was the average rate of reaction (M/s) over that time period? C4H9Cl(aq) + H2O(l) →C4H9OH(aq) + HCl(aq)

Key concept: Average rate of reaction is defined as the overall change in concentration of a reactant over some reaction period, i.e. average rate of A = −Δ[A]/Δt

Solution

To find the average rate of reaction, we use the formula:

Average rate of reaction=−Δ[C4H9Cl]Δt\text{Average rate of reaction} = - \frac{\Delta [\text{C}_4\text{H}_9\text{Cl}]}{\Delta t}

where:

  • Δ[C4H9Cl]\Delta [\text{C}_4\text{H}_9\text{Cl}] is the change in concentration of butyl chloride, and
  • Δt\Delta t is the change in time.

Given dataTo find the average rate of reaction, we use the formula:

Average rate of reaction=−Δ[C4H9Cl]Δt\text{Average rate of reaction} = - \frac{\Delta [\text{C}_4\text{H}_9\text{Cl}]}{\Delta t}

where:

  • Δ[C4H9Cl]\Delta [\text{C}_4\text{H}_9\text{Cl}] is the change in concentration of butyl chloride, and
  • Δt\Delta t is the change in time.

Given

  • Initial concentration of butyl chloride at t1=51.94 secondst_1 = 51.94 \, \text{seconds} is [C4H9Cl]1=0.1087 M[\text{C}_4\text{H}_9\text{Cl}]_1 = 0.1087 \, \text{M}.
  • Concentration of butyl chloride at t2=205.8 secondst_2 = 205.8 \, \text{seconds} is [C4H9Cl]2=0.07953 M[\text{C}_4\text{H}_9\text{Cl}]_2 = 0.07953 \, \text{M}.

  1. Calculate the change in concentration: [ \Delta [\text{C}_4\text{H}_9\text{Cl}] = [\text{C}_4\text{H}_9\text{Cl}]_2 - [\text{C}_4\text{H}_9\text{Cl}]_1 = 0.07953 , \text{M} - 0.1087 , \text{M} = -0.02917 , \text{M} ]

  2. Calculate the change in time: Δt=t2−t1=205.8 seconds−51.94 seconds=153.86 seconds\Delta t = t_2 - t_1 = 205.8 \, \text{seconds} - 51.94 \, \text{seconds} = 153.86 \, \text{seconds}

  3. Calculate the average rate of reaction: Average rate of reaction=−Δ[C4H9Cl]Δt=−−0.02917 M153.86 seconds=1.896×10−4 M/s\text{Average rate of reaction} = - \frac{\Delta [\text{C}_4\text{H}_9\text{Cl}]}{\Delta t} = - \frac{-0.02917 \, \text{M}}{153.86 \, \text{seconds}} = 1.896 \times 10^{-4} \, \text{M/s}

Thus, the average rate of reaction is 1.90×10−4 M/s1.90 \times 10^{-4} \, \text{M/s} (rounded to 3 significant figures).

Would you like further details or have any questions?

Here are some related questions to explore further:

  1. How does the concentration of reactants typically affect the rate of reaction?
  2. What is the difference between average rate and instantaneous rate of reaction?
  3. How would the rate of reaction change if the temperature was increased?
  4. What is the significance of the negative sign in the rate expression?
  5. How would a catalyst affect the reaction rate in this scenario?

Tip: When calculating reaction rates, ensure you use consistent units for time and concentration to avoid conversion errors.

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Math Problem Analysis

Mathematical Concepts

Average Rate of Reaction
Concentration Change
Time Interval

Formulas

Average rate of reaction = - (Δ[C4H9Cl] / Δt)

Theorems

Rate Law
Stoichiometry in Reaction Rates

Suitable Grade Level

Undergraduate Chemistry (Introductory Level)

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