Final answer:
The pH of a 0.063 M solution of nitrous acid (HNO2) is found by setting up an equilibrium equation using the given Ka, solving for the H+ concentration using the quadratic formula, and then calculating the pH from the H+ concentration.
Step-by-step explanation:
To calculate the pH of a 0.063 M nitrous acid (HNO₂) solution, we use the acid dissociation constant (Ka) given for HNO₂, which is 4.5 x 10⁻⁴. Setting up an equilibrium expression for the dissociation of nitrous acid in water, we have:
HNO₂ (aq) ⇌ H⁺ (aq) + NO₂⁻ (aq)
Let x be the concentration of H⁺ and NO₂⁻ ions at equilibrium. Assuming initial concentrations are 0.063 M for HNO₂ and 0 Moles for H⁺ and NO₂⁻, at equilibrium the concentrations would be (0.063 - x) for HNO₂ and x for H⁺ and NO₂⁻ respectively.
The Ka expression is given by:
Ka = [H⁺][NO₂⁻] / [HNO₂]
This simplifies to:
4.5 x 10⁻⁴ = x² / (0.063 - x)
Applying the quadratic formula, we solve for x, which gives us the [H⁺]. Taking the negative logarithm (base 10) of [H⁺], we find the pH of the solution.
It's important to note that if x is very small compared to the initial concentration, it can sometimes be ignored, resulting in a simpler calculation. However, since we are asked to use the quadratic formula, this assumption does not apply here.