Example Calculations

Today, we're going to discuss how to calculate pH for weak acids. Let's start with the general dissociation equation for a weak acid. Who can remind me what that looks like?

I think it’s HA ⇌ H⁺ + A⁻.

That's correct! Now, what about the expression for the acid dissociation constant, Ka?

Ka = [H⁺] × [A⁻] / [HA].

Exactly! Now, here’s a memory aid: think of Ka as the Key Acid that unlocks the 'H' from 'HA'. Now, if we have a weak acid called formic acid with a concentration of 0.020 M and a Ka of 1.8 × 10⁻⁴, how would we find 'x', which represents the concentration of [H⁺]?

We can use the approximation: x ≈ sqrt(Ka × C₀) right, since Ka is small?

Spot on! Let's calculate it. What do we get when we plug in the numbers?

It should be x ≈ sqrt[(1.8 × 10⁻⁴) × (0.020)] which equals about 1.9 × 10⁻³ M.

Yes, which leads us to calculate the pH. Who can tell us how to calculate that?

pH = -log₁₀(x), so pH = -log₁₀(1.9 × 10⁻³).

Great! And what does that give us?

The pH is approximately 2.72.

Perfect! And then what’s the percent ionization?

9.5%!

Wonderful! Always remember, the equation for percent ionization is: percent ionization = (x / C₀) × 100%. Today we covered how to calculate pH and percent ionization!

Now that we've discussed weak acids, let's transition to weak bases. What’s the dissociation equation for a weak base?

B + H₂O ⇌ BH⁺ + OH⁻.

Exactly! And how do we find the Kb for this equation?

Kb = [BH⁺] × [OH⁻] / [B].

Right again! Now, let’s take pyridine with a concentration of 0.10 M and Kb of 1.7 × 10⁻⁹. What will 'x' be using the same approximation we did for weak acids?

x ≈ sqrt(Kb × C₀) = sqrt[(1.7 × 10⁻⁹) × (0.10)].

Correct! Let’s calculate that.

That equals about 1.30 × 10⁻⁵ M.

Excellent! Now how would we find the pH from this?

First we need pOH, which is -log₁₀(1.30 × 10⁻⁵), and that gives us about 4.89. So pH is 14.00 - 4.89.

Exactly! And what’s the final pH?

The pH is approximately 9.11.

Perfect, team! Don’t forget, the process for weak bases mirrors that of weak acids, solidifying your foundational knowledge. Today, we covered weak base calculations!