By Sunil Bhardwaj

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A reaction is said to be of the first order if the rate of the reaction depends upon one concentration term only. E.g. $$N_2O_2(g) \longrightarrow N_2O_4(g) + \frac12{ O }_{ 2 }(g) \text{ (First Order reaction) }$$

Equation for rate constant for first order reaction is $$\boxed { k = \frac { 2.303 }{ t } \log { \frac { a }{ a-x } } }$$ $$\therefore \frac { kt }{ 2.303 } = \log { \frac { a }{ a-x } }$$ or $$\frac { kt }{ 2.303 } = \log { \left( a \right) } - \log { \left( a-x \right) }$$ $$\therefore \boxed { \log { \left( a-x \right) } = -\frac { kt }{ 2.303 } + \log { \left( a \right) } }$$ which is similar to straight line graph, $$\boxed { y = mx + c }$$ where slope $$\boxed { m = -\frac { k }{ 2.303 } }$$ and intercept $$\boxed { c = \log { \left( a \right) } }$$

Thus from the plot of $$\log { \left( a-x \right) }$$ Vs $$t$$ we can calculate the value of rate constant k, as $$\boxed { k = 2.303 \times \left( -slope \right) }$$ -ve sign indicates that the concentration of reactants decreases with time.

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