The chief compound in marble is CaCO3. However, marble is readily attacked by acids.
a) Determine the molar solubility of marble (that is, [Ca2+] in a saturated solution).
b) Determine the equilibrium constant for the overall reaction that occurs when marble reacts with acid.
CaCO3 (s) + H3O+ ↔ Ca2+ (aq) + HCO3- (aq) + H2O (l)
What's Ksp for CaCO3?
What's (H3O^+)?
To determine the molar solubility of marble, we need to find the concentration of Ca2+ in a saturated solution.
The first step is to write the dissolution equation for the reaction:
CaCO3 (s) ↔ Ca2+ (aq) + CO3^2- (aq)
The solubility product constant (Ksp) expression for this equilibrium is:
Ksp = [Ca2+] [CO3^2-]
Since marble is a sparingly soluble compound, we assume that the concentration of CaCO3(s) is constant (solids are excluded from the equilibrium expression).
Given that the chief compound in marble is CaCO3 and we are looking for the molar solubility of marble, the concentration of Ca2+ in a saturated solution will be equal to the concentration of CO3^2- because one mole of CaCO3 produces one mole of Ca2+ and one mole of CO3^2- ions.
So, the molar solubility of marble is the concentration of Ca2+ in the saturated solution, which is equal to the concentration of CO3^2-.
Now, to determine the equilibrium constant for the overall reaction when marble reacts with acid, we need to write the balanced chemical equation and the equilibrium expression.
The balanced chemical equation is:
CaCO3 (s) + H3O+ ↔ Ca2+ (aq) + HCO3- (aq) + H2O (l)
The equilibrium expression for this reaction is:
K = [Ca2+] [HCO3-] / [CaCO3] [H3O+]
K represents the equilibrium constant, [Ca2+] and [HCO3-] are the concentrations of the respective ions in the equilibrium state, and [CaCO3] and [H3O+] are the concentrations of the respective compounds.
To determine the equilibrium constant, we need to know the concentrations of the products and reactants at equilibrium.
This information can be obtained through experiments or calculations based on the initial concentrations of the reactants and the stoichiometry of the reaction.
In summary:
a) The molar solubility of marble, which is the concentration of Ca2+ in a saturated solution, is equal to the concentration of CO3^2- ions.
b) The equilibrium constant for the overall reaction when marble reacts with acid, represented by K, can be determined by finding the concentrations of the products and reactants at equilibrium and applying the equilibrium expression.