The Ksp of tin(II) hydroxide, Sn(OH)2, is 5.45 × 10-27. Calculate the solubility of this compound in g/L.
To calculate the solubility of Sn(OH)2 in g/L, we need to determine the number of moles of the compound that can dissolve in one liter of solution. The equilibrium expression for the solubility product constant, Ksp, of Sn(OH)2 is:
Ksp = [Sn^2+][OH^-]^2
Since the stoichiometry of Sn(OH)2 is 1:2 (one mole of Sn^2+ reacts with two moles of OH^-), we can write the equation:
Ksp = (x)(2x)^2 = 4x^3
where x is the molar solubility of Sn(OH)2.
Now, we can substitute the value of the Ksp constant into the equation:
5.45 × 10^−27 = 4x^3
Let's solve for x:
x^3 = 5.45 × 10^−27 / 4
x^3 ≈ 1.36 × 10^−27
x ≈ (1.36 × 10^−27)^(1/3)
x ≈ 3.52 × 10^−9
The molar solubility of Sn(OH)2 is approximately 3.52 × 10^−9 mol/L.
To convert this to g/L, we need to know the molar mass of Sn(OH)2. The molar mass of tin (II) hydroxide (Sn(OH)2) is approximately 150.71 g/mol.
Now, let's calculate the solubility in g/L:
Solubility (g/L) = molar solubility (mol/L) * molar mass (g/mol)
Solubility (g/L) = (3.52 × 10^−9) mol/L * 150.71 g/mol
Solubility (g/L) ≈ 5.3 × 10^−7 g/L
Therefore, the solubility of Sn(OH)2 in g/L is approximately 5.3 × 10^−7 g/L.
To calculate the solubility of tin(II) hydroxide (Sn(OH)2) in grams per liter (g/L), we need to use the solubility product constant (Ksp) information and the molar mass of Sn(OH)2. Here's how:
1. Write the balanced chemical equation for the dissociation of Sn(OH)2:
Sn(OH)2 ⇌ Sn2+ + 2OH-
2. Determine the molar mass of Sn(OH)2:
Tin (Sn) has an atomic mass of 118.71 g/mol, and hydroxide (OH) has an atomic mass of 17.01 g/mol. Since Sn(OH)2 has two OH groups, we multiply the OH atomic mass by 2. Therefore, the molar mass of Sn(OH)2 is:
Molar mass of Sn(OH)2 = (1 × Sn) + (2 × OH) = (1 × 118.71 g/mol) + (2 × 17.01 g/mol) = 153.73 g/mol
3. Use the Ksp equation to calculate the solubility of Sn(OH)2:
Ksp = [Sn2+][OH-]^2
Since Sn(OH)2 is a 1:2 electrolyte, the concentration of Sn2+ ions is equal to the concentration of Sn(OH)2 that dissolves, and the concentration of OH- ions is twice the concentration of Sn(OH)2 that dissolves. Hence,
Ksp = x * (2x^2),
where "x" represents the molar solubility of Sn(OH)2.
4. Solve the Ksp equation for "x":
Ksp = 5.45 × 10^(-27) = x * (2x^2)
Rearrange the equation and solve for "x":
2x^3 = 5.45 × 10^(-27)
x^3 = (5.45 × 10^(-27))/(2)
x^3 = 2.725 × 10^(-27)
x = cube root of (2.725 × 10^(-27))
x ≈ 1.06 × 10^(-9) M
5. Convert the molar solubility to grams per liter (g/L):
To convert the molar solubility from moles per liter (M) to grams per liter (g/L), multiply by the molar mass of Sn(OH)2:
Solubility = (1.06 × 10^(-9) M) × (153.73 g/mol)
Solubility ≈ 1.63 × 10^(-7) g/L
Therefore, the solubility of tin(II) hydroxide in grams per liter (g/L) is approximately 1.63 × 10^(-7) g/L.