Question

If a sample of C-14 initially contains 1.6 mmol of C-14, how many millimoles will be left after 2250 years

Answer 1

Answer: 1.2 millimoles will be left after 2250 years

Explanation:

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process  

a) for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

$t_{\frac{1}{2}}=\frac{0.693}{k}$

$k=\frac{0.693}{5730}=0.00012years^{-1}$

b) Amount left after 2250 years

$2250=\frac{2.303}{k}\log\frac{1.6}{a-x}$

$2250=\frac{2.303}{0.00012}\log\frac{1.6}{a-x}$

$\log\frac{1.6}{a-x}=0.117$

$\frac{1.6}{a-x}=1.31$

${a-x}=\frac{1.6}{1.31}=1.2$

Thus 1.2 millimoles will be left after 2250 years