Step 1: Understanding the Concept:
This is a stoichiometry problem based on the precipitation reaction between calcium chloride and silver nitrate.
Step 2: Detailed Explanation:
The balanced chemical equation is:
\[ CaCl_2 + 2AgNO_3 \rightarrow 2AgCl + Ca(NO_3)_2 \]
Molar mass of \(AgCl\) = \(108 + 35.5 = 143.5\) g/mol.
Moles of \(AgCl\) formed = \(\frac{14.35}{143.5} = 0.1\) mol.
From the equation, 2 moles of \(AgCl\) are produced from 1 mole of \(CaCl_2\).
So, moles of \(CaCl_2\) required = \(\frac{0.1}{2} = 0.05\) mol.
Molar mass of \(CaCl_2\) = \(40 + (2 \times 35.5) = 40 + 71 = 111\) g/mol.
Mass of \(CaCl_2\) required = \(0.05 \times 111 = 5.55\) g.
Step 3: Final Answer:
The required mass of calcium chloride is 5.55 g, option (A).