91Ó°ÊÓ

When it comes to figuring out how soluble a compound is, we often compare their solubility by looking at something called the solubility product constant, or \(K_{sp}\). The \(K_{sp}\) gives us an idea of how much of a compound can dissolve in water.

Here's a simple way to think about it:

• Higher \(K_{sp}\) values mean that more of the compound can dissolve in water. It's more soluble.
• Lower \(K_{sp}\) values indicate that less of the compound can dissolve. It's less soluble.

It's just like if you were trying to dissolve some sugar versus salt in your tea. If sugar dissolves easier than salt, you could say sugar is more soluble. In this same way, comparing \(K_{sp}\) values lets us know which compound has a higher or lower solubility.

The solubility product constant, \(K_{sp}\), is crucial in describing the solubility of ionic compounds. But what exactly is it? For a compound that dissolves into its ions in water, \(K_{sp}\) is determined by the concentrations of those ions at equilibrium.

A simple example is a compound \(AB\) that breaks down into \(A^+\) and \(B^-\) ions. The \(K_{sp}\) would be:\[K_{sp} = [A^+][B^-]\]Here, \([A^+]\) and \([B^-]\) represent the concentrations of the ions.

In practice, many factors can influence these concentrations, like temperature. But in general, we focus on the \(K_{sp}\) values as they help us directly compare how soluble different substances are in ideal conditions. When given in scientific notation, these values tell a lot: a smaller exponent means a smaller \(K_{sp}\), hinting that the compound is less soluble.

To find the least soluble compound among several options, we focus on comparing their \(K_{sp}\) values. Remember, the smaller the \(K_{sp}\), the less soluble the compound. This is because a lower \(K_{sp}\) means fewer ions are present in solution.

In scenarios like our exercise problem, we received several compounds with different \(K_{sp}\) values:

• \(\operatorname{MnS}: K_{sp} = 7 \times 10^{-16}\)
• \(\mathrm{FeS}: K_{sp} = 4 \times 10^{-19}\)
• \(\operatorname{PtS}: K_{sp} = 8 \times 10^{-73}\)
• \(\mathrm{NiS}: K_{sp} = 3 \times 10^{-12}\)

"\(\operatorname{PtS}\)" has the smallest \(K_{sp}\) value of \(8 \times 10^{-73}\), making it the least soluble among the given compounds. This means, in comparison, this compound dissolves the least amount in water, resulting in very low concentrations of ions in solution.