Question

A friend tells you: "The constant \(K_{\text {sp }}\) of a salt is called the solubility product constant and is calculated from the concentrations of ions in the solution. Thus, if salt A dissolves to a greater extent than salt \(\mathrm{B}\), salt \(\mathrm{A}\) must have a higher \(K_{\mathrm{sp}}\) than salt \(\mathrm{B} .\) " Do you agree with your friend? Explain.

Short answer

I partially agree with my friend's statement. A higher \(K_{sp}\) value indicates more of the solid can dissolve in water, but it does not directly compare the solubility of different salts. To accurately compare the solubility of salt A and salt B, we need to consider both their \(K_{sp}\) values and their stoichiometric coefficients in their dissolution reactions.

Step-by-step solution

Understanding Solubility Product Constant

The solubility product constant, denoted as \(K_{sp}\), is a measure of the equilibrium between a solid and its dissolved ions in a saturated solution. It is calculated by multiplying the concentrations of individual ions raised to the power of their respective stoichiometric coefficients.

Comparing Salt Solubility with Solubility Product Constant

A higher \(K_{sp}\) value indicates that more of the solid can dissolve in water, but it does not directly compare the solubility of different salts. Instead, it only provides an indication of relative solubility within a specific set of stoichiometric coefficients. To directly compare the solubilities of two different salts A and B, we need to calculate the molar solubility of each salt. Molar solubility is the maximum number of moles of the solute that can dissolve in one liter of the solvent. It depends on both the solubility product constant and the stoichiometric coefficients of the ions produced in the dissolution reaction.

Conclusion

Agreeing with the friend's statement depends on whether they meant the solubility or the solubility product constant of salt A is greater than that of salt B. If the friend is claiming that salt A has a higher solubility level than salt B solely based on a higher \(K_{sp}\) value, then the statement is not necessarily correct, as different stoichiometric coefficients for the dissolution reactions can affect the solubility of the salts. However, if the friend meant that salt A has a higher solubility product constant and that the stoichiometric coefficients of the dissolution reactions are considered, then the statement can be agreed upon. In summary, it is essential to consider both the \(K_{sp}\) values and the stoichiometric coefficients to accurately compare the solubility of different salts.

Key concepts

Chemical Equilibrium

Understanding chemical equilibrium is key to comprehending how reactions proceed and when they 'pause'. In any reversible chemical process, there comes a point when the rates of the forward and reverse reactions are equal, and the concentrations of reactants and products remain constant over time. This state is called chemical equilibrium. Think of it like a tug-of-war where both teams are equally strong - the rope doesn't move to either side.

Chemical equilibrium is dynamic, meaning that the reactants and products are still converting into each other, but their amounts don't change because the conversions are occurring at the same rate. In the context of solubility, when a solid dissolves in water, it dissociates into its constituent ions. At equilibrium, the rate at which the solid dissolves equals the rate at which the ions combine to form the solid again.

Molar Solubility

Molar solubility is a concept that might sound complex, but it's really just about answering one question: how much of this solid can dissolve in water? Specifically, molar solubility tells us the maximum number of moles of a solute that can dissolve in one liter of solvent to form a saturated solution without any undissolved excess.

This measurement is crucial when comparing different substances, as it gives us a common ground to understand which one dissolves better or worse. To put it simply, it's like comparing how much sugar versus salt you can dissolve in your tea before it can't dissolve any more. Molar solubility depends on a couple of factors, including temperature and the nature of the solute and solvent, but crucially for our purposes, it also depends on the solubility product constant, or Ksp.

Stoichiometric Coefficients

Now let's wrestle with stoichiometric coefficients - they are numbers in front of compounds in a balanced chemical equation. Stoichiometry is the math behind chemistry, which tells us how much of each reactant is needed to produce a certain amount of product. These coefficients help us understand the precise proportions and ratios in which substances react.

For instance, if water (H2O) decomposes into hydrogen (H2) and oxygen (O2), the balanced equation would show a 2:2:1 ratio, represented by the coefficients. In relation to solubility, consider a salt AB2 dissociating into one A²⁺ ion and two B⁻ ions; the stoichiometric coefficients are crucial because they influence the calculation of the solubility product constant, Ksp. A higher Ksp value does not necessarily mean higher molar solubility unless the stoichiometric coefficients are the same for the compared salts.