Answer: B) about 7.4 hrs
Explanation:
Rate law expression for first order kinetics is given by:
[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
where,
k = rate constant
t = time taken for decay process =6 hours
a = initial amount of the reactant = 5.6 g
a - x = amount left after decay process = 3.2 g
Putting values in above equation, we get:
[tex]k=\frac{2.303}{6}\log\frac{5.6g}{3.2g}[/tex]
[tex]k=0.09hours^{-1}[/tex]
To calculate the half life, we use the formula:
[tex]k=\frac{0.693}{t_{1/2}}[/tex]
[tex]t_{1/2}=\frac{0.693}{0.09}=7.4hours[/tex]
