Question

In the case of a zero-order reaction, the ratio of time required for $75\%$completion to $50\%$ completion is?

Answer 1

Step 1: formula of time for Zero order Reaction:

Zero-order reaction is known as a chemical reaction wherein the rate does not change with the increase or decrease in the concentration of the reactants.

For Zero order reaction, time is given by;

Here $\mathrm{x}$= concentration of product after time $\mathrm{t}$;and$\mathrm{k}$ = zero-order rate constant

Step 2: Calculating the time required for $75\%$ completion of the reaction:

Let the initial concentration, =$100$

Hence after $75\%$completion of time, the concentration of the product =$100-25$

The time for this will be calculated as:

Step 3: Calculating the time required for $50\%$ completion of the reaction:

After $50\%$completion of time, the concentration of the product = $100-50$

The time for this will be calculated as:

$\mathrm{t}=\frac{100-50}{2\mathrm{k}}$

Step 4: Calculating the ratio of time required for $75\%$completion to $50\%$ completion is:-

The ratio is calculated as:

$$\begin{gathered} {\mathrm{t}}_{75}:{\mathrm{t}}_{80}=\frac{{\displaystyle \frac{(100-25)}{2\mathrm{k}}}}{{\displaystyle \frac{(100-50)}{2\mathrm{k}}}} \\ \Rightarrow {\mathrm{t}}_{75}:{\mathrm{t}}_{80}=3:2 \end{gathered}$$

Hence, In the case of a zero-order reaction, the ratio of time required for $75\%$completion to $50\%$ completion is $3:2.$