Question

Observe the graph in the given figure and answer the following questions:

(a) Predict the order of reaction.
(b) What is the slope of the curve?

Hint:

For a first-order reaction, the plot of \( \log |R_0| \) versus time yields a straight line with a slope of \( -k \).

Answer 1

(a) Predict the Order of Reaction

The graph shows a linear relationship between log |R₀| and time. This suggests a first-order reaction.

In a first-order reaction, the concentration of the reactant decreases exponentially over time. This means:

\[ \ln [R] = \ln [R_0] - kt \]

Taking the logarithm (base 10) of both sides also gives a linear equation, which justifies that a plot of \(\log [R]\) versus time is a straight line.

(b) What is the Slope of the Curve?

For a first-order reaction, the slope of the \(\log [R]\) vs time graph is equal to \(-k\), where \(k\) is the rate constant.

So, the slope \(m\) of the graph is:

\[ \text{slope} = -k \]