Sodium sulfate is soluble in water,whereas barium sulfate is sparingly soluble. Why?

Determine the solubilities of silver chromate,barium chromate,ferric hydroxide,lead chloride,and mercurous iodide at $298 \, K$ from their solubility product constants. Determine also the molarities of individual ions. (Given $K_{sp}$ values: $Ag_{2}CrO_{4} = 1.1 \times 10^{-12}$,$BaCrO_{4} = 1.2 \times 10^{-10}$,$Fe(OH)_{3} = 1.0 \times 10^{-38}$,$PbCl_{2} = 1.6 \times 10^{-5}$,$Hg_{2}I_{2} = 4.5 \times 10^{-29}$)

The conductivity of a saturated solution of $BaSO_4$ is $3.06 \times 10^{-6} \ \Omega^{-1} \ cm^{-1}$ and its equivalent conductance is $1.53 \ \Omega^{-1} \ cm^{2} \ equivalent^{-1}$. The $K_{sp}$ of the $BaSO_4$ will be

Assertion : $BaCO_3$ is more soluble in $HNO_3$ than in plain water.
Reason : Carbonate is a weak base and reacts with the $H^+$ from the strong acid,causing the barium salt to dissociate.

The solubility of silver chromate in $0.01 \, M$ $K_2CrO_4$ is $2 \times 10^{-8} \, mol \, dm^{-3}$. The solubility product of silver chromate will be

The solubility product of a salt having general formula $MX_2$ in water is $4 \times 10^{-12}$. The concentration of $M^{2+}$ ions in the aqueous solution of the salt is