A reaction takes \(30\, \ minutes\) to complete \(50\%\) of the reaction and takes \(45\, \ minutes\) to complete \(75\%\) of the reaction. The order of the reaction is:

Zero

The correct answer is option 4. Zero.

The problem provides two data points:

30 minutes for \(50\%\) completion \((t_1)\)

45 minutes for \(75\%\) completion \((t_2)\)

The key point for a zero-order reaction is that the time difference (Δt) between reaching different percentages of completion should be constant.

\(Δt\)= \(t_2 – t_1 = 45\, \ min – 30\, \ min = 15\, \ min\)

In this case, the observed time difference is 15 minutes, it is a constant value for reaching every 25% completion (from 50% to 75%). This observation aligns with the characteristic behavior of a zero-order reaction.

While the increasing percentage of completion does lead to a time difference, the constant time difference (15 minutes for every 25% increase) suggests that the reaction rate is independent of the concentration throughout the process. This points towards a zero-order reaction.

Therefore, the correct answer is indeed 4. Zero.