7.8 g of calcium fluoride is dissolved in 100 L of water at 25°C. Will a precipitate be formed?
To determine if a precipitate will be formed, we need to calculate the solubility product constant (Ksp) of calcium fluoride (CaF2) and compare it to the ionic product.
The solubility product constant (Ksp) is an equilibrium constant that measures the extent to which a compound can dissolve in water at a given temperature. It is the product of the concentrations of the ions raised to the power of their stoichiometric coefficients in the balanced chemical equation.
The balanced chemical equation for the dissolution of calcium fluoride in water is:
CaF2(s) → Ca2+(aq) + 2F^-(aq)
The solubility product constant (Ksp) expression for calcium fluoride is then:
Ksp = [Ca2+][F^-]^2
To calculate the concentration of Ca2+ and F^- ions, we'll use the given mass of calcium fluoride and the molar mass of CaF2.
Step 1: Calculate the moles of calcium fluoride (CaF2)
Molar mass of CaF2: 40.08 g/mol (calcium) + 2(19.00 g/mol) (fluorine)
= 40.08 g/mol + 38.00 g/mol
= 78.08 g/mol
Moles of CaF2 = mass / molar mass
= 7.8 g / 78.08 g/mol
= 0.0999 mol
Step 2: Calculate the concentration of Ca2+ and F^- ions
Since CaF2 dissociates into one Ca2+ ion and two F^- ions, the concentration of Ca2+ and F^- ions will be equal to twice the concentration of CaF2.
Concentration of Ca2+ and F^- = (2 * moles of CaF2) / volume of solution
= (2 * 0.0999 mol) / 100 L
= 0.001998 M
Step 3: Calculate the ionic product (IP)
The ionic product (IP) is calculated by multiplying the concentrations of the ions in the dissociation reaction.
IP = [Ca2+][F^-]^2
= (0.001998 M)(0.001998 M)^2
= 7.986 × 10^(-9) M^3
Step 4: Compare Ksp with IP
The solubility product constant (Ksp) for calcium fluoride is 3.9 × 10^(-11) at 25°C.
Since the ionic product (IP) is greater than the solubility product constant (Ksp), a precipitate of calcium fluoride will form.
Therefore, based on the calculations, a precipitate of calcium fluoride will be formed when 7.8 g of calcium fluoride is dissolved in 100 L of water at 25°C.