Respuesta :
Answer : The initial mass of the sample is, 31.9 mg
Explanation :
Half-life = 4 days
First we have to calculate the rate constant, we use the formula :
[tex]k=\frac{0.693}{t_{1/2}}[/tex]
[tex]k=\frac{0.693}{4\text{ days}}[/tex]
[tex]k=0.173\text{ days}^{-1}[/tex]
Now we have to calculate the initial mass of sample.
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]0.173\text{ days}^{-1}[/tex]
t = time passed by the sample = 12 days
a = initial amount of the reactant = ?
a - x = amount left after decay process = 4 mg
Now put all the given values in above equation, we get
[tex]12=\frac{2.303}{0.173}\log\frac{a}{4}[/tex]
[tex]a=31.9mg[/tex]
Therefore, the initial mass of the sample is, 31.9 mg
