Question

Thalium (I) Iodate (TlIO₃) is only slightly soluble in water. Its K_SP at 25⁰c is 3.07X10^-6. Estimate the solubility of Thalium (I) iodate in water in units of grams per 100.00 ml of water.

Short answer

Thallium(I) Iodate and solubility

• Thallium(I) iodate is added to mercury are lamps to improve their performance. This mainly used for underwater lighting.
• The solubility of most solid and liquid increases with increasing temperature.

Step-by-step solution

Step(1)- [Answer of the question]

Given:-K_SP at 25^oc is 3.07X10^-6 .

The solubility of thalium (I) iodate in water in units of grams per 100.00ml of water is 0.0664gm.

Step(2):- Calculation of the solubility of Thalium Iodate

The solubility reaction of Thalium(I) iodate-

$TlI{O}_3\left(s\right)\rightleftarrows T{l}^{+}\left(aq\right)+I{O}_3^{-}\left(aq\right)$

So, the solubility product is-

role="math" localid="1663579923815" $$\begin{gathered} 3.07\times {10}^{-6}=S^2 \\ {S}^2=3.07\times {10}^{-6} \\ S=\sqrt{3.07\times {10}^{-6}} \\ S=1.75\times {10}^{-3}mol/liter \\ 379.29gm/mol \\ \left(TlI{O}_3\right) \end{gathered}$$$K_{SP}={\left[T{l}^{+}\right]}^{\text{'}}X{\left[I{O}_3^{-}\right]}^{\text{'}}$

Let, S if (TlIO₃) dissolves. Then the equilibrium concentration of Tl⁺ and IO₃^- will be:-

[Tl⁺]' = S and [IO₃^-]' =S

Then, K_SP = S X S

$$\begin{gathered} 3.07\times {10}^{-6}=S^2 \\ {S}^2=3.07\times {10}^{-6} \\ S=\sqrt{3.07\times {10}^{-6}} \\ S=1.75\times {10}^{-3} \end{gathered}$$

The molar solubility is 1.75X10^-3mol/litre .

Step-3: Calculation of the solubility of thalium(I) iodate

The molar mass of (TlIO₃) is 379.29gm/mol

Gram solubility= molar solubility X molar mass

Gram solubility = ( 379.29gm/mol ) X ( 1.75X10^-3mol/litre)

= 663.72X10^-3gm/lit

Thus, the solubility in gram per 100ml in water is:-

Gram/100ml solubility= $\frac{663.75\times {10}^{-3}}{1000ml}X1LX\frac{g}{L}$

= $\frac{663.75\times {10}^{-3}}{100ml}$

= 0.0664gm/100ml

Step-4:- Conclusion

Hence, gram solubility represents the solubility of thalium iodate in units of gm/100ml.

Hence the solubility is 0.0664gm/100ml.