Question

75% of a first order reaction was completed in 32 minutes; when was 50% of the reaction completed?

Options

• 4 min

• 8 min

• 24 min

• 16 min

Answer 1

16 min

Explanation:

Given: It’s a first-order reaction

Time for 75% completion = 32 min

Time for 50% completion = ?

In first-order reactions, the time for completion of a fraction is given by:

t = `2.303/k log_10 ([R]_0/[R])`

Let

t_75% = 32 min → 75% reacted, 25% remains → [R]_t = `1/4` [R]₀

t_50% → 50% reacted, 50% remains → [R]_t = `1/2` [R]₀

⇒ `t_(75%)/t_(50%) = (log (4))/(log (2))`

= `0.602/0.301`

= 2

⇒ `t_(75%)/t_(50%) = 2`

⇒ `t_(50%) = t_(75%)/2`

= `32/2`

= 16 min