Step 1: Understanding the Concept:
Solubility (\(s\)) refers to the maximum amount of a solute that can dissolve in a specific amount of solvent at a given temperature to form a saturated solution.
The Solubility Product Constant (\(K_{sp}\)) is the equilibrium constant for a solid substance dissolving in an aqueous solution. It represents the product of the molar concentrations of its constituent ions, each raised to the power of its stoichiometric coefficient.
Step 2: Key Formula or Approach:
For a salt \(AgBr\) (Silver Bromide), the dissociation equilibrium in a saturated solution is:
\[ \text{AgBr}(s) \rightleftharpoons \text{Ag}^+(aq) + \text{Br}^-(aq) \]
If the molar solubility is \(s\), then:
\([\text{Ag}^+] = s\) mol/dm\(^3\)
\([\text{Br}^-] = s\) mol/dm\(^3\)
The expression for the solubility product is:
\[ K_{sp} = [\text{Ag}^+][\text{Br}^-] \]
Substituting the values:
\[ K_{sp} = s \cdot s = s^2 \]
Therefore, the solubility is the square root of the solubility product:
\[ s = \sqrt{K_{sp}} \]
Step 3: Detailed Explanation:
Given: \(K_{sp} = 4.9 \times 10^{-13}\).
We need to calculate: \(s = \sqrt{4.9 \times 10^{-13}}\).
To make the square root calculation easier, we can rewrite the number in scientific notation such that the power of 10 is an even number:
\[ s = \sqrt{49 \times 10^{-14}} \]
Now, calculate the square root of the number and the power of 10 separately:
\[ s = \sqrt{49} \times \sqrt{10^{-14}} \]
\[ s = 7 \times 10^{-7} \text{ mol/dm}^3 \]
The unit "mol dm\(^{-3}\)" is equivalent to moles per liter (M).
Step 4: Final Answer:
The solubility of AgBr is 7 \(\times\) 10\(^{-7}\) mol dm\(^{-3}\).
Hence, the correct option is (C).