Question

The hydride of an unstable nuclide of a Group IIA metal, MH2(s), decays by a-emission. A 0.025-mol sample of the hydride is placed in an evacuated 1.1 −L container at 298 K. After 64 minutes, the pressure in the container is 0.49 atm.

Find the half-life of the nuclide.

Express your answer to two significant figures and include the appropriate units.

Answer 1

The number of moles of He nuclei

$n = \dfrac {PV}{RT} = \dfrac { \text { 0.49 atm } \times \text { 1.1 L} }{ \text { 0.08206 L atm / mol K} \times \text { 298 K} } = \text { 0.022 mol}$

$a = 0.025, \text { } x = 0.022 \text { and } a-x = 0.025 - 0.022 = 0.003$

$\lambda = \dfrac {2.303}{t} log \dfrac {a}{a-x} = \dfrac {2.303}{ \text {64 min}} log \dfrac {0.025}{0.003} =0.033 \: /min$

$t_{1/2}= \dfrac {0.693}{\lambda }= \dfrac {0.693}{ 0.033 \: /min} = 20.9 \: min$

Hence, the half life period is 21 minutes.