Question

The penicillin in a mixture was determined by adding $0.981mg$ of the ¹⁴C-labeled compound having a specific activity of $5.42\times {10}^3$cpm/mg. After equilibration, $0.406mg$of pure crystalline penicillin was isolated. This material had a net activity of $343cpm$. Calculate the mass in milligrams of penicillin in the

sample.

Short answer

The mass of the penicillin in the given sample is$5.31mg$.

Step-by-step solution

Given information

$$\begin{gathered} m_t=0.981mg \\ {R}_t=5.42\times {10}^{3}cpm/mg \\ {m}_m=0.406mg \\ {R}_m=343cpm \end{gathered}$$

Calculation

The activity of tracer in can be calculated as:

$$\begin{gathered} R_t=0.981\times 5.42\times {10}^3 \\ {R}_t=5317cpm \end{gathered}$$

Now, The mass of the penicillin can be calculated by the following formula:

$m_x=\frac{R_t}{R_m}\times m_m-m_t$

By substituting the given and calculated values in the above equation, we get,
$$\begin{gathered} m_x=\frac{5317}{343}\times 0.406-0.981 \\ {m}_x=5.31mg \end{gathered}$$

Final answer

The mass of penicillin is$5.31mg$in the given sample.