Read the passage carefully and answer the Questions.

The concentration dependence of the rate of a reaction is called the differential rate equation. It is not always convenient to determine the instantaneous rate, as it is measured by calculating the slope of the tangent at point 't' in the concentration vs time plot. This makes it difficult to determine the rate and hence the order of the reaction. This difficulty is overcome by integrating the differential rate equation. This integrated rate equation gives a direct relation between concentrations at different times and the rate constant. The integrated rate equations are different for the reactions having different reaction orders.

For an integrated first order reaction, a straight line graph is plotted. The incorrect co-ordinates and resulting slope of the graph are

$ln[R]$ vs $t$; Slope = $k$

The correct answer is Option (2) → $ln[R]$ vs $t$; Slope = $k$ **

Concept Used:

Integrated first order rate law:

ln[R] = ln[R]₀ – kt

Slope of:

ln[R] vs t = –k

Explanation:

For a first order reaction:

Integrated rate law:

ln[R] = ln[R]₀ – kt

This shows:

• Plot of ln[R] vs t → straight line with slope = –k

Now check options:

Option 1: log[R] vs t ; slope = –k/2.303

Correct

Because log form becomes:

log[R] = log[R]₀ – kt/2.303

Option 2: ln([R]₀/[R]) vs t ; slope = k

Correct

Because:

ln([R]₀/[R]) = kt

Option 3: ln[R] vs t ; slope = k

Incorrect

Actual slope should be –k, not +k

Option 4: log([R]₀/[R]) vs t ; slope = k/2.303

Correct

Since:

log([R]₀/[R]) = kt/2.303