Read the passage carefully and answer the Questions.

The decomposition of $N_2O_5 (g)$ is given as

$N_2Os (g) → 2NO_2(g) +\frac{1}{2}O_2(g)$

The above reaction is found to be of first order.

Predict the intercept for the plot of $\log\frac{[N_2O_5]_o}{[N_2O_5]}$ versus time

zero

The correct answer is Option (3) → zero

The intercept for the plot of log([N₂O₅]₀ / [N₂O₅]) versus time is zero.

For a first-order reaction:

log([A]₀ / [A]) = (k / 2.303) t

Comparing with the straight-line equation:

y = mx + c

So,
y = log([N₂O₅]₀ / [N₂O₅])
x = t
m = k / 2.303
c = intercept

At time t = 0:

[N₂O₅] = [N₂O₅]₀

Substituting:

log([N₂O₅]₀ / [N₂O₅]₀) = log(1) = 0

When t = 0, y = 0

Therefore,
Intercept (c) = 0

Hence, zero is the answer