Respuesta :
Answer: The mass of [tex]MX_2[/tex] that will dissolve is 0.0786 grams
Explanation:
Solubility product is defined as the product of concentration of ions present in a solution each raised to the power its stoichiometric ratio.
The chemical equation for the ionization of [tex]MX_2[/tex] follows:
[tex]MX_2(aq.)\rightleftharpoons M^{2+}(aq.)+2X^-(aq.)[/tex]
s 2s
The expression of [tex]K_{sp}[/tex] for above equation follows:
[tex]K_{sp}=s\times (2s)^2[/tex]
We are given:
[tex]K_{sp}=7.2\times 10^{-8}[/tex]
Putting values in above expression, we get:
[tex]7.2\times 10^{-8}=s\times (2s)^2\\\\s=2.62\times 10^{-3}M[/tex]
To calculate the mass of solute, we use the equation used to calculate the molarity of solution:
[tex]\text{Molarity of the solution}=\frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Volume of solution (in mL)}}[/tex]
Molar mass of [tex]MX_2[/tex] = 108.75 g/mol
Molarity of solution = [tex]2.62\times 10^{-3}mol/L[/tex]
Volume of solution = 276 mL
Putting values in above equation, we get:
[tex]2.62\times 10^{-3}mol/L=\frac{\text{Mass of }MX_2\times 1000}{108.75/mol\times 276}\\\\\text{Mass of }MX_2=\frac{2.62\times 10^{-3}\times 108.75\times 276}{1000}=0.0786g[/tex]
Hence, the mass of [tex]MX_2[/tex] that will dissolve is 0.0786 grams
The mass of MX₂ that will dissolve is 0.0786 grams.
What is Solubility Product?
Solubility product is defined as the product of concentration of ions present in a solution each raised to the power its stoichiometric ratio.
The chemical equation for the ionization of follows:
[tex]MX_2--- > M^{2+}+2X^-[/tex]
s 2s
Calculation for "s" :
Given: [tex]K_{sp}= 7.2*10^{-8}[/tex]
[tex]K_{sp}=s*(2s)^2\\\\7.2*10^{-8}=s*(2s)^2\\\\s=2.62*10^{-3}M[/tex]
To calculate the mass of solute, we use the equation used to calculate the molarity of solution:
M = n/ V
Molar mass of = 108.75 g/mol
Molarity of solution = [tex]2.62*10^{-3}mol/L[/tex]
Volume of solution = 276 mL
On substituting the values:
[tex]2.62*10^{-3} mol/L=\frac{\text{ Mass of } MX_2 * 1000}{108.75g/mol*276} \\\\\text{ Mass of } MX_2=\frac{2.62*10^{-3} mol/L*108.75g/mol*276}{1000} \\\\\text{ Mass of } MX_2=0.0786 g[/tex]
Hence, the mass of MX₂ that will dissolve is 0.0786 grams.
Find more information about Solubility product here:
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