Question

A first order reaction has a rate constant $1.15\times {10}^{-3}{\mathrm{s}}^{-1}$. How long will 5 g of this reactant take to reduce to 3 g?

Answer 1

Step 1: Given data

Rate constant(k)$=1.15\times {10}^{-3}{\mathrm{s}}^{-1}$

Initial mass$=\mathrm{a}=5\mathrm{g}$

Final mass$=(\mathrm{a}-\mathrm{x})=3\mathrm{g}$

Step 2: Finding the time required

According to the rate law,

$$\begin{gathered} \mathrm{t}=\frac{2.303}{\mathrm{k}}\log \left(\frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}\right) \\ \Rightarrow \mathrm{t}=\frac{2.303}{1.15\times {10}^{-3}}\log \left(\frac{5}{3}\right) \\ \Rightarrow \mathrm{t}=2.00\times {10}^{-3}\log (1.667) \\ \Rightarrow \mathrm{t}=2.00\times {10}^{-3}\times 0.2219 \\ \Rightarrow \mathrm{t}=443.85\approx 444\sec \end{gathered}$$

Therefore, the time taken is $444\sec$