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Artyom0805 [142]
3 years ago
13

The correct mathematical expression for finding the molar solubility (s) of calcium phosphate is

Chemistry
1 answer:
GalinKa [24]3 years ago
6 0

Answer is: The molar solubility of calcium phosphate is 108s⁵ = Ksp.

<span> Balanced chemical reaction: Ca</span>₃(PO₄)₂(s) → 3Ca²⁺(aq) + 2PO₄³⁻(aq).<span>
[Ca²</span>⁺] = 3s(Ca₃(PO₄)₂) = 3s.<span>
[PO</span>₄³⁻] = 2s.<span>
Ksp = [Ca²</span>⁺]³ · [PO₄³⁻]².<span>
Ksp = (3s)³ · (2s)².
Ksp = 108s</span>⁵.

s = ⁵√(Ksp ÷ 108).

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Equilibrium constant expression for \rm 2\; H^{+}\, (aq) + {CO_3}^{2-}\, (aq) \rightleftharpoons H_2CO_3\, (aq):

\displaystyle K = \frac{\left(a_{\mathrm{H_2CO_3\, (aq)}}\right)}{\left(a_{\mathrm{H^{+}}}\right)^2\, \left(a_{\mathrm{{CO_3}^{2-}\, (aq)}}\right)} \approx \frac{[\mathrm{H_2CO_3}]}{\left[\mathrm{H^{+}\, (aq)}\right]^{2} \, \left[\mathrm{CO_3}^{2-}\right]}.

Where

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Explanation:

<h3>Equilibrium Constant Expression</h3>

The equilibrium constant expression of a (reversible) reaction takes the form a fraction.

Multiply the activity of each product of this reaction to get the numerator.\rm H_2CO_3\; (aq) is the only product of this reaction. Besides, its coefficient in the balanced reaction is one. Therefore, the numerator would simply be \left(a_{\mathrm{H_2CO_3\, (aq)}}\right).

Similarly, multiply the activity of each reactant of this reaction to obtain the denominator. Note the coefficient "2" on the product side of this reaction. \rm 2\; H^{+}\, (aq) + {CO_3}^{2-}\, (aq) is equivalent to \rm H^{+}\, (aq) + H^{+}\, (aq) + {CO_3}^{2-}\, (aq). The species \rm H^{+}\, (aq) appeared twice among the reactants. Therefore, its activity should also appear twice in the denominator:

\left(a_{\mathrm{H^{+}}}\right)\cdot \left(a_{\mathrm{H^{+}}}\right)\cdot \, \left(a_{\mathrm{{CO_3}^{2-}\, (aq)}})\right = \left(a_{\mathrm{H^{+}}}\right)^2\, \left(a_{\mathrm{{CO_3}^{2-}\, (aq)}})\right.

That's where the exponent "2" in this equilibrium constant expression came from.

Combine these two parts to obtain the equilibrium constant expression:

\displaystyle K = \frac{\left(a_{\mathrm{H_2CO_3\, (aq)}}\right)}{\left(a_{\mathrm{H^{+}}}\right)^2\, \left(a_{\mathrm{{CO_3}^{2-}\, (aq)}}\right)} \quad\begin{matrix}\leftarrow \text{from products} \\[0.5em] \leftarrow \text{from reactants}\end{matrix}.

<h3 /><h3>Equilibrium Constant of Concentration</h3>

In dilute solutions, the equilibrium constant expression can be approximated with the concentrations of the aqueous "(\rm aq)" species. Note that all the three species here are indeed aqueous. Hence, this equilibrium constant expression can be approximated as:

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