Question

32P has a half life of 14.0 days. If you order 60.0 grams of 32P and it took 46.7hrs from the time it was made to the time it was delivered, how much radioactive 32P (in grams) did you actually receive?

Answer 1

Answer:

$[A_t]=54.5\ g$

Explanation:

Given that:

Half life = 14.0 days

$t_{1/2}=\frac{\ln2}{k}$

Where, k is rate constant

So,  

$k=\frac{\ln2}{t_{1/2}}$

$k=\frac{\ln2}{14.0}\ days^{-1}$

The rate constant, k = 0.04951 days⁻¹

Initial concentration [A₀] = 60.0 g

Time = 46.7 hrs

Considering, 1 hr = 0.041667 days

So, time = 1.9458 days

Using integrated rate law for first order kinetics as:

$[A_t]=[A_0]e^{-kt}$

Where,  

$[A_t]$ is the concentration at time t

So,  

$[A_t]=60.0\times e^{-0.04951\times 1.9458}\ g$

$[A_t]=54.5\ g$