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Chemistry Question on Stoichiometry and Stoichiometric Calculations

Time required for completion of 90% of a first order reaction is ‘t’. What is the time required for completion of 99.9%of the reaction?

A

t

B

2t

C

3t

D

t/2

Answer

3t

Explanation

Solution

If we want to determine the time required for completion of a certain percentage of the reaction, we can use the equation:
ln([A]₀[A])(\frac { [A]_₀}{ [A]}) = kt
Now, let's consider the given situation where the time required for completion of 90% of the reaction is 't'. This implies that at time 't', the remaining fraction of the reactant is 10% (or 0.1).
ln ([A]₀0.1[A])(\frac { [A]_₀}{0.1 [A]})) = kt
Simplifying,
ln 10.1\frac {1}{0.1} = kt
ln (10) = kt
We can rewrite this equation as:
t = ln(10)k\frac {ln(10)}{k}
Now, let's find the time required for completion of 99.9% of the reaction. At this point, the remaining fraction of the reactant is 0.1% (or 0.001).
ln ([A]₀0.001[A]0)(\frac { [A]_₀}{0.001 [A]_0}) = kt
ln (10.001)(\frac {1}{0.001})= kt
ln (1000) = kt
Again, we can rewrite this equation as:
t' = ln (1000)k\frac {ln\ (1000)}{k}
Comparing t and t', we see that:
t' = ln (1000)k\frac {ln\ (1000)}{k}= 3 * ln(10)k\frac {ln(10)}{k} = 3t
Therefore, the time required for completion of 99.9% of the reaction is 3t.
The correct answer is (C) 3t.