The half-life of a sample A (t½ = 100 days) did not change with concentration of A. The half-life of4another sample B (t½ = 120 days) decreases with decrease in concentration of B. If the initialconcentration of both the samples were 1M, what will be their rate constants
Question
The half-life of a sample A (t½ = 100 days) did not change with concentration of A. The half-life of4another sample B (t½ = 120 days) decreases with decrease in concentration of B. If the initialconcentration of both the samples were 1M, what will be their rate constants
Solution
To determine the rate constants for samples A and B, we can use the formula for the half-life of a first-order reaction:
t½ = (0.693 / k)
For sample A, the half-life is given as 100 days. Plugging this value into the formula, we have:
100 = (0.693 / kA)
Solving for kA, we find:
kA = 0.693 / 100 kA = 0.00693
Therefore, the rate constant for sample A is 0.00693.
For sample B, the half-life is given as 120 days. We are told that the half-life decreases with a decrease in concentration. This indicates that the reaction is concentration-dependent, suggesting a second-order reaction.
In a second-order reaction, the rate constant can be determined using the following equation:
k = (1 / t½) * (1 / [A]₀)
Where [A]₀ is the initial concentration of the reactant.
For sample B, the initial concentration is 1M and the half-life is 120 days. Plugging these values into the equation, we have:
kB = (1 / 120) * (1 / 1) kB = 0.00833
Therefore, the rate constant for sample B is 0.00833.
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