Final answer:
The concentration of Ca₂⁺(aq) in a saturated solution of CaCO₃ with a Ksp of 4.9 × 10⁻⁹ is 7.0 × 10⁻⁵ M, which is option C.
Step-by-step explanation:
To find the concentration of Ca₂⁺(aq) in a saturated solution of CaCO₃, we set up an ICE table and use the solubility product constant Ksp. The dissolution of CaCO₃ can be represented as follows:
CaCO₃(s) → Ca₂⁺(aq) + CO₃²⁺(aq)
The Ksp for CaCO₃ is given as 4.9 × 10⁻⁹, which can be represented by the equation:
Ksp = [Ca₂⁺][CO₃²⁺]
Since the dissolution of CaCO₃ produces equal molar amounts of Ca₂⁺ and CO₃²⁺ ions, we can say that the concentration of Ca₂⁺ ions is equal to s and the concentration of CO₃²⁺ ions is also s. Therefore, we can write the Ksp expression as:
Ksp = s²
To solve for s, we take the square root of Ksp:
s = √(4.9 × 10⁻⁹) = 7.0 × 10⁻⁵ M
The concentration of Ca₂⁺(aq) is 7.0 × 10⁻⁵ M, which corresponds to option C.