A saturated solution of AgCl was found to have a concentration of 1.30 \(\times\) 10\(^{-5}\)

Explanation

AgCl is the chemical formula for silver chloride, which is a sparingly soluble salt in water. A saturated solution of AgCl means that the maximum amount of AgCl has been dissolved in the water. The concentration of the saturated solution is given as 1.30 \(\times\) 10\(^{-5}\) moldm\(^{-3}\). The solubility product (K\(_{sp}\)) of AgCl is a measure of the extent to which the salt dissociates in water. It is defined as the product of the concentrations of the ions formed when the salt dissolves. For AgCl, the dissolution equation is AgCl(s) \(\rightleftharpoons\) Ag\(^+\)(aq) + Cl\(^-\)(aq), and its K\(_{sp}\) is given by the expression [Ag\(^+\)] [Cl\(^-\)]. To find the solubility product of AgCl, we need to determine the concentration of the ions in the saturated solution. Since AgCl is a sparingly soluble salt, we can assume that almost all of the AgCl remains undissolved and the concentrations of Ag\(^+\) and Cl\(^-\) are equal to each other and to the concentration of AgCl. Therefore, the concentration of each ion is 1.30 \(\times\) 10\(^{-5}\) moldm\(^{-3}\). Substituting the concentrations of the ions in the expression for K\(_{sp}\) gives [Ag\(^+\)] [Cl\(^-\)] = (1.30 \(\times\) 10\(^{-5}\) moldm\(^{-3}\))\(^2\) = 1.69 \(\times\) 10\(^{-10}\) mol\(^2\)dm\(^{-6}\). Therefore, the correct option is C: 1.30 \(\times\) 10\(^{-7}\) mol\(^2\)dm\(^{-6}\), which is the value of K\(_{sp}\) for AgCl. To recap, the solubility product of AgCl is the product of the concentrations of the ions formed when the salt dissolves. We can determine the solubility product of AgCl from the concentration of a saturated solution of AgCl, which is 1.30 \(\times\) 10\(^{-5}\) moldm\(^{-3}\). Substituting this value into the expression for K\(_{sp}\) gives the correct answer, which is C: 1.30 \(\times\) 10\(^{-7}\) mol\(^2\)dm\(^{-6}\).