24.101 CP - Chemistry: Molecular Nature Of Matter And Change

Question

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  ?

Step-by-Step Solution

Answer

Molar solubility AGCL of   is  $1.35\times {10}^{-5}M$ .

Step 1: Definition of Concept

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.

Step 2: Find the molar solubility of AGCL

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  $AgCl=143.4 g/mol$

The concentration of   can be calculated as follows:

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

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

 

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

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

                  

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