A sample of AgCl emits 175Ci/g. A saturated solution prepared from the solid emits$1.25\times {10}^{-2}Bq/mL$ due to radioactive AG ions. What is the molar solubility of AGCL ?

Nuclear reaction: A nuclear reaction occurs when a lighter nucleus fuses together to form new stable nuclei, or when a heavier nucleus splits into stable daughter nuclei, releasing a large amount of energy.

Considering the given information:

Specific activity of AGCL = 175n Ci/g

Activity of $A{g}^{+}=1.25\times {10}^{-2}Bq/mL$

Molar mass of $AgCl=143.4g/mol$

The concentration of can be calculated as follows:

$$\begin{gathered} Concentration=\left(\frac{1.25\times {10}^{-2}Bq}{1mL}\right)\left(\frac{1dps}{1Bq}\right)\left(\frac{1Ci}{3.7\times {10}^{10}dps}\right)\left(\frac{1nCi}{{10}^{-9}Ci}\right)\left(\frac{1gAgCl}{175nCi}\right) \\ =1.9305\times {10}^{-6}g/mLAgCl \end{gathered}$$

The molarity (molar solubility) of AGCL can be calculated using the following equation:

Molarity $=\left(\frac{1.9305\times {10}^{-6}g AgCl}{1mL}\right)\times \frac{1mol AgCl\times \left(\frac{1mL}{{10}^{-3}L}\right)}{143.4 g/mol AgCl}$

$$\begin{gathered} =1.34623\times {10}^{-5}mol/L \\ =1.35\times {10}^{-5}MAgCl \end{gathered}$$

Therefore, the required molar solubility of AGL is$1.35\times {10}^{-5}M$ .