Math Problem Statement

The solubility product of Car 3.4×10-11 What is its solubility in 0.01 M solution of NaF

a. 3.4×10-7 mol L-1

C. 3.4×10-2 mol L-1

b. 3.4×10-5 mol L-1

d. 3.4 mol L-1

Solution

To solve this problem, we'll assume that the compound in question is CaF2CaF_2, which dissociates in water as follows:

CaF2Ca2++2FCaF_2 \leftrightarrow Ca^{2+} + 2F^-

Given:

  • The solubility product, Ksp=3.4×1011K_{sp} = 3.4 \times 10^{-11}
  • The concentration of NaFNaF is 0.01 M, meaning the initial concentration of FF^- ions is 0.01 M.

Let SS be the solubility of CaF2CaF_2 in the 0.01 M NaFNaF solution. The concentration of Ca2+Ca^{2+} ions will be SS and the concentration of FF^- ions will be 0.01+2S0.01 + 2S (since each CaF2CaF_2 produces 2 FF^- ions).

The solubility product expression for CaF2CaF_2 is:

[ K_{sp} = [Ca^{2+}][F^-]^2 ]

Substituting the values:

3.4×1011=S×(0.01+2S)23.4 \times 10^{-11} = S \times (0.01 + 2S)^2

Since KspK_{sp} is very small, the solubility SS will be much smaller than 0.01 M, so 2S2S can be neglected compared to 0.01 M:

3.4×1011S×(0.01)23.4 \times 10^{-11} \approx S \times (0.01)^2

3.4×1011=S×1043.4 \times 10^{-11} = S \times 10^{-4}

S=3.4×1011104=3.4×107 mol/LS = \frac{3.4 \times 10^{-11}}{10^{-4}} = 3.4 \times 10^{-7} \text{ mol/L}

Thus, the correct answer is:

a. 3.4×107 mol/L3.4 \times 10^{-7} \text{ mol/L}

Would you like more details or have any questions? Here are some related questions you might find interesting:

  1. How does the common ion effect influence the solubility of CaF2CaF_2?
  2. What would be the solubility of CaF2CaF_2 in pure water?
  3. How does KspK_{sp} vary with temperature?
  4. What happens to the solubility of CaF2CaF_2 if NaFNaF concentration increases?
  5. Can you explain the significance of the solubility product constant?

Tip: When dealing with solubility in the presence of a common ion, always consider simplifying assumptions to make the calculation more straightforward.

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Math Problem Analysis

Mathematical Concepts

Chemical Equilibrium
Solubility Product

Formulas

Solubility Product Expression

Theorems

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Suitable Grade Level

High School