Concept:
The Solvay process is used for the manufacture of sodium carbonate. The raw materials are brine (\(\mathrm{NaCl}\)), ammonia, limestone (\(\mathrm{CaCO_3}\)) and water.
Step 1: Identify the raw materials.
• \(\mathrm{NaCl}\) -- Raw material.
• \(\mathrm{NH_3}\) -- Used in the process and regenerated.
• \(\mathrm{Ca(OH)_2}\) -- Obtained during the process and used for ammonia recovery.
• \(\mathrm{CaCl_2}\) -- By-product of the process.
Step 2: Final conclusion.
Since \(\mathrm{CaCl_2}\) is formed as a by-product and not used as a raw material,
\[
\boxed{\mathrm{CaCl_2}}
\]
is the correct answer.
Hence, the correct option is \(\boxed{(C)}\).