If the half life of a first order reaction is 6.93 minutes then the time required for completion of 99% of the reaction will be _______ minutes. (Given: log 2 = 0.3010)

Step 1: Calculate the rate constant $$(k)$$.

For, first order reaction the rate constant $$(k)$$ is related to $$t_{1/2}$$ by this formula:

$$t_{1/2}=\frac{0.693}{k}$$

since, 

$$t_{1/2}=6.93$$

$$k=\frac{0.693}{6.93}=0.1\ \min^{-1}$$

Step 2: Calculate time for 99% Completion

The integrated rate law for a first-order reaction give us to solve for time $$(t)$$:

$$t=\frac{2.303}{k\ }\log\left(\frac{\left[A_o\right]}{\left[A_t\right]}\right)$$

For 99% completion, 1% of the reactant remains.

Let's assume the initial concentration $$[A]_0 = 100$$, then the final concentration $$[A]_t = 1$$:

$$t=\frac{2.303}{0.1}\log\left(\frac{100}{1}\right)$$

$$t=\frac{2.303}{0.1}\times\ 2$$

$$t=23.03\times\ 2$$

$$t=46.06$$ minutes

Therefore, the time required for completion of 99% of the reaction will be 46.06 minutes.