Step 1: Moles of starting material.
Moles of starting material = \( \frac{137 \times 10^{-3}}{137} = 0.001 \) mole.
Step 2: Moles of the product.
Moles of product = 0.001 mole (since the reaction is 1:1).
Step 3: Mass of the product.
Mass of product = \( 0.001 \times 228 \, \text{g} = 0.228 \, \text{g} = 228 \, \text{mg} \).
Step 4: Conclusion.
Thus, the mass of the final product is 228 mg.