For this problem, you may ignore the baricity of phosphate ion, PO/, Strontium phosphate (molar mass 452.81 g/mol) is a salt that is sparingly soluble in water. Strontium acetate is considered a soluble salt in water. a. Write the balanced dissolution reaction equation of strontium phosphate. Hint: you will first need to determine the formula of the compound (this is identical to 2f) b. Write the balanced dissolution reaction equation strontium acetate. Hint: you will first need to determine the formula of the compound e. The solubility of strontium phosphate in water is 0.140 mg per liter. What is the Kip for strontium phosphate? Give your answer with 3 sig figs. None
The Correct Answer and Explanation is :
Let’s break the problem into parts:
a. Balanced Dissolution Reaction of Strontium Phosphate
Step 1: Determine the formula of strontium phosphate.
Strontium ion: ( \text{Sr}^{2+} )
Phosphate ion: ( \text{PO}_4^{3-} )
Using the charges to balance, strontium phosphate is ( \text{Sr}_3(\text{PO}_4)_2 ).
Step 2: Write the dissolution equation.
[
\text{Sr}_3(\text{PO}_4)_2 (s) \leftrightharpoons 3\text{Sr}^{2+} (aq) + 2\text{PO}_4^{3-} (aq)
]
b. Balanced Dissolution Reaction of Strontium Acetate
Step 1: Determine the formula of strontium acetate.
Strontium ion: ( \text{Sr}^{2+} )
Acetate ion: ( \text{CH}_3\text{COO}^- )
Since strontium has a ( 2+ ) charge, it will pair with two acetate ions: ( \text{Sr}(\text{CH}_3\text{COO})_2 ).
Step 2: Write the dissolution equation.
[
\text{Sr}(\text{CH}_3\text{COO})_2 (s) \rightarrow \text{Sr}^{2+} (aq) + 2\text{CH}_3\text{COO}^- (aq)
]
c. Calculate the ( K_{sp} ) for Strontium Phosphate
Step 1: Use solubility to find ion concentrations.
Solubility of ( \text{Sr}_3(\text{PO}_4)_2 ) is ( 0.140 \, \text{mg/L} ).
Convert to molarity:
[
\text{Molarity of } \text{Sr}_3(\text{PO}_4)_2 = \frac{0.140 \, \text{mg/L}}{452.81 \, \text{g/mol}} = 3.09 \times 10^{-7} \, \text{mol/L}
]
For every mole of ( \text{Sr}_3(\text{PO}_4)_2 ) dissolved:
- ( 3 \text{Sr}^{2+} ) ions are produced (( 3 \times 3.09 \times 10^{-7} = 9.27 \times 10^{-7} \, \text{mol/L} )).
- ( 2 \text{PO}_4^{3-} ) ions are produced (( 2 \times 3.09 \times 10^{-7} = 6.18 \times 10^{-7} \, \text{mol/L} )).
Step 2: Write the ( K_{sp} ) expression.
[
K_{sp} = [\text{Sr}^{2+}]^3 [\text{PO}_4^{3-}]^2
]
Substitute values:
[
K_{sp} = (9.27 \times 10^{-7})^3 (6.18 \times 10^{-7})^2
]
Calculate:
[
K_{sp} = (7.97 \times 10^{-19})(3.82 \times 10^{-13}) = 3.04 \times 10^{-31}
]
Final Answer:
a. ( \text{Sr}3(\text{PO}_4)_2 (s) \leftrightharpoons 3\text{Sr}^{2+} (aq) + 2\text{PO}_4^{3-} (aq) ) b. ( \text{Sr}(\text{CH}_3\text{COO})_2 (s) \rightarrow \text{Sr}^{2+} (aq) + 2\text{CH}_3\text{COO}^- (aq) ) c. ( K{sp} = 3.04 \times 10^{-31} )
Explanation (300 words)
To solve the problem, we first determined the chemical formulas of strontium phosphate and strontium acetate based on the charges of their constituent ions. The formula of strontium phosphate is ( \text{Sr}_3(\text{PO}_4)_2 ), balancing the ( 3- ) charge of phosphate with ( 2+ ) strontium ions. Its dissolution yields 3 moles of ( \text{Sr}^{2+} ) and 2 moles of ( \text{PO}_4^{3-} ) ions per mole of salt. Strontium acetate, ( \text{Sr}(\text{CH}_3\text{COO})_2 ), dissolves completely in water to produce 1 mole of ( \text{Sr}^{2+} ) and 2 moles of acetate ions.
To calculate the solubility product (( K_{sp} )) of ( \text{Sr}_3(\text{PO}_4)_2 ), we started with its given solubility in water (0.140 mg/L). Converting this to molarity using the molar mass (452.81 g/mol) gave ( 3.09 \times 10^{-7} \, \text{mol/L} ). Since ( \text{Sr}_3(\text{PO}_4)_2 ) dissociates into 3 ( \text{Sr}^{2+} ) ions and 2 ( \text{PO}_4^{3-} ) ions, their concentrations were determined as ( 9.27 \times 10^{-7} \, \text{mol/L} ) and ( 6.18 \times 10^{-7} \, \text{mol/L} ), respectively.
Substituting these into the ( K_{sp} ) expression, ( [\text{Sr}^{2+}]^3 [\text{PO}4^{3-}]^2 ), we calculated ( K{sp} ) as ( 3.04 \times 10^{-31} ). This extremely small value reflects the very low solubility of strontium phosphate, consistent with its classification as a sparingly soluble salt.