Question

If a sample of C-14 initially contains 1.5 mmol of C-14, how many millimoles will be left after 2255 years?

Answer 1

Answer: $3.2\times 10^{-4}$ millimoles will be left after 2255 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)  $t_{\frac{1}{2}}$ of carbon = 5730 years

$k}=\frac{0.693}{5730}=1.21\times 10^{-4}years^{-1}$

b) millimoles left after 2255 years

$2255=\frac{2.303}{1.21\times 10^{-4}}\log\frac{1.5}{a-x}$

$\log\frac{1.5}{(a-x)}=8.44$

$\frac{1.5}{(a-x)}=4628.5$

$(a-x)=3.2\times 10^{-4}millimoles$