Question

Write the equilibrium equation and the \(K_{\mathrm{sp}}\) expression for each of the following: (a) \(\mathrm{AgBr}\) (b) \(\mathrm{Ca}(\mathrm{OH})_{2}\) (c) \(\mathrm{Co}_{2} \mathrm{~S}_{3}\) (d) \(\mathrm{Fe}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)

Short answer

In summary, the \(K_{\mathrm{sp}}\) expressions for each compound are as follows: (a) AgBr: ${K}_{\mathrm{sp}}=[\mathrm{Ag^{+}}][\mathrm{Br^{-}}]$ (b) Ca(OH)₂: ${K}_{\mathrm{sp}}=[\mathrm{Ca^{2+}}][\mathrm{OH^{-}}]^2$ (c) Co₂S₃: ${K}_{\mathrm{sp}}=[\mathrm{Co^{2+}}]^2[\mathrm{S^{2-}}]^3$ (d) Fe₃(PO₄)₂: ${K}_{\mathrm{sp}}=[\mathrm{Fe^{3+}}]^3[\mathrm{PO_4^{3-}}]^2$ These expressions describe the equilibrium concentration relationships and solubility products for each compound.

Step-by-step solution

Write the dissolution of the compound

For \(\mathrm{AgBr}\), the dissolution is: $$\mathrm{AgBr}\leftrightarrows \mathrm{Ag^{+}}+\mathrm{Br^{-}}$$

Write the equilibrium equation

The equilibrium equation for the dissolution of \(\mathrm{AgBr}\) is: $$\mathrm{AgBr}\leftrightarrows \mathrm{Ag^{+}}+\mathrm{Br^{-}}$$

Write the \(K_{\mathrm{sp}}\) expression

The \(K_{\mathrm{sp}}\) expression for \(\mathrm{AgBr}\) is given as: $${K}_{\mathrm{sp}}=[\mathrm{Ag^{+}}][\mathrm{Br^{-}}]$$ (b) \(\mathrm{Ca}(\mathrm{OH})_{2}\)

Write the dissolution of the compound

For \(\mathrm{Ca}(\mathrm{OH})_{2}\), the dissolution is: $$\mathrm{Ca}(\mathrm{OH})_{2}\leftrightarrows \mathrm{Ca^{2+}}+2\mathrm{OH^{-}}$$

Write the equilibrium equation

The equilibrium equation for the dissolution of \(\mathrm{Ca}(\mathrm{OH})_{2}\) is: $$\mathrm{Ca}(\mathrm{OH})_{2}\leftrightarrows \mathrm{Ca^{2+}}+2\mathrm{OH^{-}}$$

Write the \(K_{\mathrm{sp}}\) expression

The \(K_{\mathrm{sp}}\) expression for \(\mathrm{Ca}(\mathrm{OH})_{2}\) is given as: $${K}_{\mathrm{sp}}=[\mathrm{Ca^{2+}}][\mathrm{OH^{-}}]^2$$ (c) \(\mathrm{Co}_{2} \mathrm{~S}_{3}\)

Write the dissolution of the compound

For \(\mathrm{Co}_{2} \mathrm{~S}_{3}\), the dissolution is: $$\mathrm{Co}_{2} \mathrm{~S}_{3}\leftrightarrows 2\mathrm{Co^{2+}}+3\mathrm{S^{2-}}$$

Write the equilibrium equation

The equilibrium equation for the dissolution of \(\mathrm{Co}_{2} \mathrm{~S}_{3}\) is: $$\mathrm{Co}_{2} \mathrm{~S}_{3}\leftrightarrows 2\mathrm{Co^{2+}}+3\mathrm{S^{2-}}$$

Write the \(K_{\mathrm{sp}}\) expression

The \(K_{\mathrm{sp}}\) expression for \(\mathrm{Co}_{2} \mathrm{~S}_{3}\) is given as: $${K}_{\mathrm{sp}}=[\mathrm{Co^{2+}}]^2[\mathrm{S^{2-}}]^3$$ (d) \(\mathrm{Fe}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)

Write the dissolution of the compound

For \(\mathrm{Fe}_{3}\left(\mathrm{PO}_{4}\right)_{2}\), the dissolution is: $$\mathrm{Fe}_{3}\left(\mathrm{PO}_{4}\right)_{2}\leftrightarrows 3\mathrm{Fe^{3+}}+2\mathrm{PO_4^{3-}}$$

Write the equilibrium equation

The equilibrium equation for the dissolution of \(\mathrm{Fe}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) is: $$\mathrm{Fe}_{3}\left(\mathrm{PO}_{4}\right)_{2}\leftrightarrows 3\mathrm{Fe^{3+}}+2\mathrm{PO_4^{3-}}$$

Write the \(K_{\mathrm{sp}}\) expression

The \(K_{\mathrm{sp}}\) expression for \(\mathrm{Fe}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) is given as: $${K}_{\mathrm{sp}}=[\mathrm{Fe^{3+}}]^3[\mathrm{PO_4^{3-}}]^2$$