Question

For a first order reaction, intercept of the graph between \(\log \frac{[A]_0}{[A]_t}\) (Y-axis) and conc. (X-axis) is equal to

• A. \(-\frac{k}{2.303 \, K}\)
• B. \(-\log[A]_0\)
• C. zero
• D. \(\frac{2.303}{K}\)

Hint:

For a first order reaction, the graph of log([A]0/[A]) vs time is a straight line passing through origin (intercept zero).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
For a first order reaction, we plot \(\log \frac{[A]_0}{[A]_t}\) (Y-axis) versus concentration (X-axis). We need the intercept.

Step 2: Key Formula or Approach:
Integrated rate law for first order: \(\log \frac{[A]_0}{[A]_t} = \frac{k}{2.303} t\). This is a straight line when Y = \(\log([A]_0/[A]_t)\) vs X = time (t), not vs concentration. The question says "conc." on X-axis – that might be a trick. If X-axis is concentration, then at zero concentration, the value of \(\log([A]_0/[A]_t)\) is not defined. However, if they mean X-axis = time, then intercept = 0. Possibly misprint: X-axis should be time. Standard first order plot: Y = log([A]0/[A]) vs t gives intercept = 0.

Step 3: Detailed Explanation:
For first order: \(\log\frac{[A]_0}{[A]_t} = \frac{k}{2.303}t\). Comparing with y = mx + c, intercept c = 0. Thus intercept is zero.

Step 4: Final Answer:
Intercept = zero, option (C).