Answer : The amount of sodium-24 is left in the sample after 60.0 hours is, 1.408 grams
Explanation :
Half-life of Sodium-24 = 15.0 hr
First we have to calculate the rate constant, we use the formula :
[tex]k=\frac{0.693}{15.0}[/tex]
[tex]k=0.0462hr^{-1}[/tex]
Now we have to calculate the left amount of Sodium-24.
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 = [tex]0.0462hr^{-1}[/tex]
t = age of sample = 60.0 hr
a = let initial amount of the reactant = 22.5 g
a - x = amount left after decay process = ?
Now put all the given values in above equation, we get
[tex]60=\frac{2.303}{0.0462}\log\frac{22.5}{a-x}[/tex]
[tex]a-x=1.408g[/tex]
Therefore, the amount of sodium-24 is left in the sample after 60.0 hours is, 1.408 grams
