How do you find the [OH-] of a 1x10^-3 M solution of NH4Cl?
.........NH4^+ + H2O ==> NH3 + H3O^+
I........1E-3.............0.....0
C.........-x..............x......x
E.......1E-3-x............x......x
Ka for NH4^+ = (Kw/Kb for NH3) = (x)(x)/(0/001-x)
Solve for x = (H3O^+).
Then (H3O^+)(OH^-) = Kw = 1E-14 and solve for OH^-
To find the concentration of hydroxide ions ([OH-]) in a solution of NH4Cl, we need to consider the chemical equilibrium that occurs when NH4Cl is dissolved in water.
NH4Cl dissociates in water into NH4+ and Cl- ions. Since NH4+ is a weak acid and Cl- is a spectator ion (it does not affect the pH of the solution), we primarily need to focus on the NH4+ ion.
NH4+ ions can undergo a reaction with water molecules to produce H3O+ (hydronium ions) and NH3 (ammonia) through the process of hydrolysis:
NH4+ (aq) + H2O (l) ⇌ NH3 (aq) + H3O+ (aq)
This equation indicates that NH4+ acts as an acid in water, donating a proton (H+) to water to form hydronium ions and ammonia. While the concentration of NH4+ is given as 1x10^-3 M, we need to find the concentration of [OH-].
To determine the [OH-] concentration, let's first calculate the concentration of H3O+ (or pH) using the given concentration of NH4+. We can then use the pH value to find [OH-].
Here's how to get the solution step-by-step:
1. Write the balanced equation for the hydrolysis of NH4+:
NH4+ (aq) + H2O (l) ⇌ NH3 (aq) + H3O+ (aq)
2. Set up an ICE table (Initial, Change, Equilibrium) to keep track of the concentrations:
NH4+ (aq) + H2O (l) ⇌ NH3 (aq) + H3O+ (aq)
Initial: 1x10^-3 0 0
Change: -x +x +x
Equilibrium: 1x10^-3 - x x x
3. Based on the equilibrium expression, write an expression for the equilibrium constant (Kb) of NH4+:
Kb = [NH3][H3O+] / [NH4+]
4. The Kb value for NH4+ is given as 1.8x10^-5. Substitute the equilibrium concentrations into the equilibrium expression:
1.8x10^-5 = x * x / (1x10^-3 - x)
5. Simplify the equation by assuming that x is much smaller than 1x10^-3:
1.8x10^-5 ≈ x * x / 1x10^-3
x^2 ≈ 1.8x10^-5 * 1x10^-3
x^2 ≈ 1.8x10^-8
6. Take the square root of both sides to solve for x:
x ≈ √(1.8x10^-8)
x ≈ 1.34x10^-4
7. The concentration of H3O+ is approximately 1.34x10^-4 M. This is equal to the concentration of OH- in a neutral solution (water), so we can use the concentration of [H3O+] to calculate the concentration of [OH-]:
[OH-] = 1.0x10^-14 / [H3O+]
[OH-] = 1.0x10^-14 / 1.34x10^-4
[OH-] ≈ 7.46x10^-11 M
Therefore, the concentration of [OH-] in a 1x10^-3 M solution of NH4Cl is approximately 7.46x10^-11 M.