Question

What is the shape of the curve obtained on plotting log₁₀[A] against t for a first order reaction?

What is the graphical behaviour of a first order reaction on plotting log₁₀[A] against t?

Answer 1

we know that

\[\ce{k = \frac{2.303}{t} log_10 \frac{[A]_0}{[A]}}\]

This equation can be written as

\[\ce{log_10[A] = - \frac{kt}{2.303} + log_10 [A]_0}\]    ...(i)

The equation (i) is of the type y = mx + c and represents a straight line. Therefore, on plotting log₁₀[A] against t, a straight line is obtained. The slope of the line is equal to \[\ce{\frac{- k}{2.303}}\] while the intercept of the line on log₁₀[A] axis is equal to log₁₀[A]₀. Thus,

Slope of the line = \[\ce{\frac{AC}{BC} = - \frac{k}{2.303}}\]

Intercept on log₁₀[A] axis = log₁₀[A]₀

Thus, the value of k can be obtained from the slope of the line.