Question

A first order reaction takes 100 minutes for completion of 60% of the reaction find the time when 90% of the reaction will be completed

Answer 1

for completion of 60 percent of reaction.
time taken =100
for 90 percent of completion reaction it take.
time =130 minutes

Answer 2

At 253.07 min 90% of the reaction will be completed.

Given:

Time taken to complete 60% of the reaction = 100 minutes

To find:

Time taken to complete 90% of the reaction = ?

Calculation:

The rate law for first order reaction is mathematically expressed as

t = $\frac{2.303}{k}log\frac{C_0}{C_t}$

Let initial concentration be 100%

∴ $C_t$ = 100-60 = 40%

Substituting the values in formula, it gives

t = $\frac{2.303}{k}log\frac{C_0}{C_t}$

100 = $\frac{2.303}{k}log\frac{100}{40}$

100 = $\frac{2.303}{k}log\frac{5}{2}$

On simplification of the above equation, it gives

k = 0.0091

To calculate time taken for completion of 90% of reaction

t = $\frac{2.303}{k}log\frac{C_0}{C_t}$

t = $\frac{2.303}{0.0091}log\frac{100}{100-90}$

t = 253.07

Conclusion

At 253.07 min 90% of the reaction will be completed.

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