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The half life of a first order reaction is 12.6 h. The time at which the concentration of reactants becomes 0.001 M from 1.0 M is _____ h.
Correct answer is '126'. Can you explain this answer?
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The half life of a first order reaction is 12.6 h. The time at which t...
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Given Data:
- Half-life of first order reaction = 12.6 h
- Initial concentration of reactants = 1.0 M
- Final concentration of reactants = 0.001 M
Calculation:
Step 1: Determine the Rate Constant (k) of the Reaction
- We know that the half-life of a first-order reaction is related to the rate constant (k) by the equation:
t1/2 = (0.693) / k
- Substituting the given half-life value, we can solve for the rate constant:
12.6 h = 0.693 / k
k = 0.693 / 12.6
k ≈ 0.055 h^-1
Step 2: Use the Integrated Rate Law for First-Order Reactions
- The integrated rate law for a first-order reaction is given by the equation:
ln([A]t/[A]0) = -kt
- We can rearrange this equation to solve for time (t) when the concentration of reactants ([A]t) reaches 0.001 M:
ln(0.001/1.0) = -0.055t
ln(0.001) = -0.055t
-6.9078 = -0.055t
t ≈ 126 h
Therefore, the time at which the concentration of reactants becomes 0.001 M from 1.0 M is approximately 126 hours.
- Half-life of first order reaction = 12.6 h
- Initial concentration of reactants = 1.0 M
- Final concentration of reactants = 0.001 M
Calculation:
Step 1: Determine the Rate Constant (k) of the Reaction
- We know that the half-life of a first-order reaction is related to the rate constant (k) by the equation:
t1/2 = (0.693) / k
- Substituting the given half-life value, we can solve for the rate constant:
12.6 h = 0.693 / k
k = 0.693 / 12.6
k ≈ 0.055 h^-1
Step 2: Use the Integrated Rate Law for First-Order Reactions
- The integrated rate law for a first-order reaction is given by the equation:
ln([A]t/[A]0) = -kt
- We can rearrange this equation to solve for time (t) when the concentration of reactants ([A]t) reaches 0.001 M:
ln(0.001/1.0) = -0.055t
ln(0.001) = -0.055t
-6.9078 = -0.055t
t ≈ 126 h
Therefore, the time at which the concentration of reactants becomes 0.001 M from 1.0 M is approximately 126 hours.
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The half life of a first order reaction is 12.6 h. The time at which the concentration of reactants becomes 0.001 M from 1.0 M is _____h.Correct answer is '126'. Can you explain this answer?
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