To calculate the percentage mass of impurity present in the oyster shell, we first need to determine how much hydrochloric acid (HCl) reacted with the calcium carbonate (CaCO₃) present in the oyster shell. The chemical reaction between HCl and CaCO₃ is as follows:
\[ \text{CaCO}_3 (s) + 2\text{HCl} (aq) \rightarrow \text{CaCl}_2 (aq) + \text{H}_2\text{O} (l) + \text{CO}_2 (g) \]
Step 1: Calculate the moles of HCl
The concentration of the HCl solution is given as \(2 , \text{mol/dm}^3\), and the volume of the solution is \(400 , \text{cm}^3\).
First, convert the volume to \( \text{dm}^3\):
\[ 400 , \text{cm}^3 = \frac{400}{1000} , \text{dm}^3 = 0.4 , \text{dm}^3 \]
Now, calculate the moles of HCl:
\[ \text{moles of HCl} = \text{concentration} \times \text{volume} = 2 , \text{mol/dm}^3 \times 0.4 , \text{dm}^3 = 0.8 , \text{mol} \]
Step 2: Determine moles of CaCO₃ that reacted
From the balanced chemical equation, we can see that 2 moles of HCl react with 1 mole of CaCO₃. Therefore, 0.8 moles of HCl will react with:
\[ \text{moles of CaCO}_3 = \frac{0.8}{2} = 0.4 , \text{mol} \]
Step 3: Calculate the mass of CaCO₃
The molar mass of CaCO₃ is approximately:
\[ \text{Ca} = 40 , \text{g/mol}, , \text{C} = 12 , \text{g/mol}, , \text{O} = 16 , \text{g/mol} \times 3 = 48 , \text{g/mol} \] \[ \text{Molar mass of CaCO}_3 = 40 + 12 + 48 = 100 , \text{g/mol} \]
Now, we can calculate the mass of CaCO₃ that reacted:
\[ \text{mass of CaCO}_3 = \text{moles} \times \text{molar mass} = 0.4 , \text{mol} \times 100 , \text{g/mol} = 40 , \text{g} \]
Step 4: Calculate the percentage mass of impurity
The mass of the impure oyster shell is given as 50 g. The mass of the pure CaCO₃ is 40 g. Therefore, the mass of the impurity in the oyster shell is:
\[ \text{mass of impurity} = \text{total mass} - \text{mass of CaCO}_3 = 50 , \text{g} - 40 , \text{g} = 10 , \text{g} \]
Now, we can calculate the percentage of impurity:
\[ \text{Percentage mass of impurity} = \left( \frac{\text{mass of impurity}}{\text{total mass}} \right) \times 100 = \left( \frac{10 , \text{g}}{50 , \text{g}} \right) \times 100 = 20% \]
Final Answer
The percentage mass of impurity present in the oyster shell is 20%.