Answer: [tex]3.2\times 10^{-4}[/tex] millimoles will be left after 2255 years.
Explanation:
Expression for rate law for first order kinetics is given by:
[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
where,
k = rate constant
t = age of sample
a = let initial amount of the reactant
a - x = amount left after decay process
a) [tex]t_{\frac{1}{2}}[/tex] of carbon = 5730 years
[tex]k}=\frac{0.693}{5730}=1.21\times 10^{-4}years^{-1}[/tex]
b) millimoles left after 2255 years
[tex]2255=\frac{2.303}{1.21\times 10^{-4}}\log\frac{1.5}{a-x}[/tex]
[tex]\log\frac{1.5}{(a-x)}=8.44[/tex]
[tex]\frac{1.5}{(a-x)}=4628.5[/tex]
[tex](a-x)=3.2\times 10^{-4}millimoles[/tex]
