The solubility product of silver bromide $(AgBr)$ is $5.0 \times 10^{-13}$. Calculate the mass of potassium bromide $(KBr)$ (molar mass = $120 \, g \, mol^{-1}$) that must be added to $1 \, L$ of a $0.05 \, M$ silver nitrate $(AgNO_3)$ solution to initiate the precipitation of $AgBr$.
- A$1.2 \times 10^{-10} \, g$
- B$1.2 \times 10^{-9} \, g$
- C$6.2 \times 10^{-5} \, g$
- D$5.0 \times 10^{-8} \, g$
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