For a reaction $A \xrightarrow{\mathrm{K}_1} \mathrm{~B} \xrightarrow{\mathrm{K}_2} \mathrm{C}$ If the rate of formation of B is set to be zero then the concentration of B is given by :

<p>To determine the concentration of $ \mathrm{B} $ when the rate of formation of $ \mathrm{B} $ is set to zero, let's consider the reaction sequence:</p> <p>$$ \mathrm{A} \xrightarrow{\mathrm{K}_1} \mathrm{B} \xrightarrow{\mathrm{K}_2} \mathrm{C} $$</p> <p>The rate of formation of $ \mathrm{B} $ from $ \mathrm{A} $ is given by:</p> <p>$\text{Rate of formation of } \mathrm{B} = \mathrm{K}_1[\mathrm{A}]$</p> <p>The rate of consumption of $ \mathrm{B} $ to form $ \mathrm{C} $ is given by:</p> <p>$\text{Rate of consumption of } \mathrm{B} = \mathrm{K}_2[\mathrm{B}]$</p> <p>At steady state, where the rate of formation of $ \mathrm{B} $ is set to zero, the rate of formation of $ \mathrm{B} $ is equal to the rate of its consumption. Therefore, we have:</p> <p>$\mathrm{K}_1[\mathrm{A}] = \mathrm{K}_2[\mathrm{B}]$</p> <p>Solving for $ [\mathrm{B}] $, we get:</p> <p>$[\mathrm{B}] = \frac{\mathrm{K}_1}{\mathrm{K}_2} [\mathrm{A}]$</p> <p>Therefore, the correct concentration of $ \mathrm{B} $ is:</p> <p><strong>Option D:</strong> $\left(\frac{\mathrm{K}_1}{\mathrm{K}_2}\right)[\mathrm{A}]$</p>