Question

When 15.0 mL of a 9.86×10-4 M magnesium sulfate solution is combined with 22.0 mL of a 6.62×10-4 M potassium carbonate solution does a precipitate form? yes (yes or no) For these conditions the Reaction Quotient, Q, is equal to

Answer 1

Ans :- YES, Precipitates are formed.

Because,

Reaction Quotient (Q_sp) is the product of the molar concentration of products raise to power stoichiometric coefficient at any stage of the reaction.

Solubility product (K_sp) is the product of the molar concentration of products raise to power stoichiometric coefficient at equilibrium stage of the reaction.

# If Q_sp < K_sp , precipitates will not form.

# If Q_sp = K_sp , precipitates will not form.

# If Q_sp > K_sp , precipitates will form.

Given molarity of MgSO₄ = 9.86 × 10^-4 M

Volume = 15.0 mL = 0.015 L

Therefore,

No. of moles of MgSO₄ = Molarity x Volume in L

= 9.86 × 10^-4 M x 0.015 L

= 1.479 x 10^-5 mol

Also,

No. of moles of K₂CO₃ = Molarity x Volume in L

= 6.62 × 10^-4 M x 0.022 L

= 1.4564 x 10^-5 mol

Now, Total volume after mixing = 15.0 mL + 22.0 mL = 37.0 mL = 0.037 L

Molarity of MgSO₄ or Mg²⁺ after mixing = No. of moles / Volume in L

= 1.479 x 10^-5 mol / 0.037 L

= 3.997 x 10^-4 M

Similarly,

Molarity of K₂CO₃ or CO₃^2- after mixing = No. of moles / Volume in L

= 1.4564 x 10^-5 mol / 0.037 L

= 3.936 x 10^-4 M

After mixing of MgSO₄ and K₂CO₃, insoluble compound MgCO₃ is formed whose solubility product (K_sp) is 3.5 × 10^-8 value is and soluble compound K₂SO₄.

Partial dissociation of MgCO₃ is :

MgCO₃ (s) <-------------------> Mg²⁺ (aq) + CO₃^2- (aq)

Expression of Q_sp is :

Q_sp = [Mg²⁺ ].[CO₃^2-]

= (3.997 x 10^-4 ).(3.936 x 10^-4)

= 1.57 x 10^-7

Therefore, Q_sp = 1.57 x 10^-7

Because, Q_sp (1.57 x 10^-7 ) > K_sp (3.5 × 10^-8 ) , therefore precipitates will form.