the solubility product of lead(ii)sulphate in water is 1.6x10^-8 mol2 dm^-6. calculate the solubility of lead(ii)sulphate in (a)pure water (b)0.1M lead(ii)nitrate solution (c)0.01M sodium sulphate solution?
then why is lead(ii)more soluble in them
To calculate the solubility of lead(II) sulfate in different solutions, we need to apply the principles of solubility product and common ion effect.
(a) Solubility in pure water:
In pure water, the solubility product (Ksp) expression for lead(II) sulfate can be written as:
PbSO4(s) ⇌ Pb2+(aq) + SO42-(aq)
Ksp = [Pb2+][SO42-]
Given that Ksp = 1.6x10^-8 mol^2 dm^-6, we assume that the dissociation of lead(II) sulfate is complete, therefore, [Pb2+] = [SO42-] = x (let's assume).
Substituting the values into the Ksp expression, we get:
(1.6x10^-8) = (x)(x)
x^2 = 1.6x10^-8
x = sqrt(1.6x10^-8) = 1.26x10^-4 mol dm^-3
Therefore, the solubility of lead(II) sulfate in pure water is 1.26x10^-4 mol dm^-3.
(b) Solubility in 0.1M lead(II) nitrate solution:
In this case, the common ion effect comes into play. The nitrate ion (NO3-) is common to both the lead(II) nitrate solution and lead(II) sulfate solubility, which explains why lead(II) sulfate is more soluble in this solution compared to pure water. The presence of excess nitrate ions will shift the equilibrium and reduce the precipitation of lead(II) sulfate.
(c) Solubility in 0.01M sodium sulfate solution:
In this case, the common ion effect is again observed, but this time with the sulfate ion (SO42-). The presence of excess sulfate ions from the sodium sulfate solution will also shift the equilibrium, reducing the precipitation of lead(II) sulfate.
The increased solubility in both (b) and (c) can be explained by Le Chatelier's principle, which states that if a system at equilibrium is disturbed by the addition of a reactant or removal of a product, the system will shift in a direction that minimizes the disturbance. In this case, the addition of a common ion (nitrate in (b) and sulfate in (c)) disrupts the equilibrium, prompting the system to shift towards the formation of more soluble lead(II) sulfate.