What mass of nickel is dissolved in 100. mL of saturated nickel (II) hydroxide? (Ksp = 1.6 X 10^-16)
How do I do this?
Please don't use different names. It helps us to know what we have already told you in other problems if we have some consistency with names.
Use the same concepts as the AgCl problem to solve this problem. You will need to convert molar solubility to grams, then convert from 1 L to 100 mL. Post your work if you get stuck.
To solve this problem, let's break it into steps:
1. Calculate the molar solubility of nickel (II) hydroxide (Ni(OH)2) using the given Ksp value.
The Ksp expression for Ni(OH)2 is:
Ksp = [Ni2+][OH-]^2
Since the formula for nickel (II) hydroxide is Ni(OH)2, it dissociates into one Ni2+ ion and two OH- ions.
Let's assume the molar solubility of nickel (II) hydroxide is "x" mol/L.
So, the expression for Ksp becomes:
Ksp = (x)(2x)^2 = 4x^3
Given: Ksp = 1.6 x 10^-16
Substituting the given value into the Ksp expression, we have:
1.6 x 10^-16 = 4x^3
Now, solve for "x" by taking the cube root of both sides, using a calculator:
x = (1.6 x 10^-16)^(1/3) ≈ 1.26 x 10^-6 mol/L
2. Convert the molar solubility to grams per liter (g/L).
The molar mass of Ni(OH)2 can be calculated as:
Ni = 58.7 g/mol
H = 1.0 g/mol
O = 16.0 g/mol
Molar mass of Ni(OH)2 = (58.7) + (2 × 1.0) + (2 × 16.0) = 98.7 g/mol
To convert mol/L to g/L, multiply the molar solubility by the molar mass:
(1.26 x 10^-6 mol/L) × (98.7 g/mol) = 1.24 x 10^-4 g/L
3. Convert grams per liter to grams per 100 mL.
To convert from grams per liter to grams per 100 mL, we need to consider the volume conversion.
1 L = 1000 mL, so
1 g/L = 0.001 g/mL
Therefore, to convert g/L to g/100 mL, multiply by 0.001:
(1.24 x 10^-4 g/L) × (0.001 g/mL) = 1.24 x 10^-7 g/mL
Finally, we can find the mass of nickel (II) hydroxide dissolved in 100 mL by multiplying the g/mL by 100 mL:
(1.24 x 10^-7 g/mL) × (100 mL) = 1.24 x 10^-5 g
So, the mass of nickel dissolved in 100 mL of saturated nickel (II) hydroxide is approximately 1.24 x 10^-5 grams.