Question

The specific rate constant, k, for radioactive beryllium–11 is 0.049 s–1. What mass of a 0.500 mg sample of beryllium–11 remains after 28 seconds? This reaction was found to be first order.

Answer 1

Answer: The mass of sample that remained is 0.127 mg

Explanation:

The integrated rate law equation for first-order kinetics:

$k=\frac{2.303}{t}\log \frac{a}{a-x}$ ......(1)

Given values:

a = initial concentration of reactant = 0.500 mg

a - x = concentration of reactant left after time 't' = ?mg

t = time period = 28 s

k = rate constant = $0.049s^{-1}$

Putting values in equation 1:

$0.049s^{-1}=\frac{2.303}{28s}\log (\frac{0.500}{(a-x)})\\\\\log (\frac{0.500}{(a-x)})=\frac{0.049\times 28}{2.303}\\\\\frac{0.500}{a-x}=10^{0.5957}\\\\frac{0.500}{a-x}=3.94\\\\a-x=\frac{0.500}{3.942}=0.127mg$

Hence, the mass of sample that remained is 0.127 mg