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kondor19780726 [428]
2 years ago
15

A first-order reaction is 45% complete at the end of 43 minutes. What is the length of the half-life of this reaction

Chemistry
1 answer:
shtirl [24]2 years ago
4 0

The half-life of the reaction is 50 minutes

Data;

  • Time = 43 minutes
  • Type of reaction = first order
  • Amount of Completion = 45%

<h3>Reaction Constant</h3>

Let the initial concentration of the reaction be X_0

The reactant left = (1 - 0.45) X_0 = 0.55 X_0 = X

For a first order reaction

\ln(\frac{x}{x_o}) = -kt\\ k = \frac{1}{t}\ln (\frac{x_o}{x}) \\ k = \frac{1}{43}\ln (\frac{x_o}{0.55_o})\\ k = 0.013903 min^-^1

<h3>Half Life </h3>

The half-life of a reaction is said to be the time required for the initial amount of the reactant to reach half it's original size.

x = \frac{x_o}{2} \\t = t_\frac{1}{2} \\t_\frac{1}{2} = \frac{1}{k}\ln(\frac{x_o}{x_o/2})\\

Substitute the values

t_\frac{1}{2} = \frac{1}{k}\ln(2)=\frac{0.6931}{0.013903}\\t_\frac{1}{2}= 49.85 min = 50 min

The half-life of the reaction is 50 minutes

Learn more on half-life of a first order reaction here;

brainly.com/question/14936355

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