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

Step-by-step explanation:

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

`t=(2.303)/(k)\log(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_{(1)/(2)}=(0.693)/(k)`

`k=(0.693)/(5730)=0.00012years^(-1)`

b) Amount left after 2250 years

`2250=(2.303)/(k)\log(1.6)/(a-x)`

`2250=(2.303)/(0.00012)\log(1.6)/(a-x)`

`\log(1.6)/(a-x)=0.117`

`(1.6)/(a-x)=1.31`

`{a-x}=(1.6)/(1.31)=1.2`

Thus 1.2 millimoles will be left after 2250 years