Question

The half-life period for the decomposition of a substance is 2.5 hours. If the initial weight of the substance is 160 g, how much of the substance will be left after 10 hours?

Answer 1

Given: t_1/2 = 2.5 hours

N₀ = 160 g

t = 10 hours

We have to use the formula for first-order reactions involving half-life:

N_t = `N_0 xx (1/2)^(t//t_(1//2))`    ...(i)

Where:

N₀ = initial amount of the substance

N_t = amount left after time ttt

t = total time

t_1/2 = half-life

Putting the values in equation (i), we get

N_t = `160 xx (1/2)^(10//2.5)`

= `160 xx (1/2)^4`

= `160 xx 1/16`

= 10 g

∴ The 10 grams of substance will be left after 10 hours.