Here it says consider the titration of 75 MLS of 0.300 molar off pyruvic acid, which has a K_a of 4.1×10−3 with 12 mills of 0.0450 molar of potassium hydroxide. Here we need to calculate the pH. All right, So what we have here is pyruvic acid, which has a K_a of less than 1, so it's a weak acid. And then potassium hydroxide is a strong base. We have a weak species mixing with a strong species. So that's why in step one, we set up an ICF chart.

So remember we set up an ICF chart if it's weak and strong, mixing together here with an ICF chart, the strong species is set up as a reactant. The strong species then reacts with its chemical opposite. So our strong species is the potassium hydroxide KOH. It reacts with its chemical opposite. What's the opposite of a base? An acid. So it would react with that pyruvic acid. Following Bronsted-Lowry definitions of acids and bases, the acid would donate an H⁺ that H⁺ would go to the OH⁻ of potassium hydroxide to create water which will be a liquid. And then here what's left would be the potassium and pyruvate which is C₃H₃O₃ aqueous.

Here we have our equation. Now this is an ICF chart, which remember stands for Initial Change Final, and we know that with an ICF chart our units need to be in moles. Remember moles equal liters times molarity, So you would divide these MLS by 1000 to get liters and then multiply them by their molarities and you'd have the moles of your weak acid and your strong base. So when we do that we get here 0.00225 moles of pyruvic acid and for KOH we get 0.00054 moles. So using the initial row, we place the given amounts in moles and in an ICF chart, we only care about three things. We only care about the weak acid and its conjugate base and then whatever the strong thing is, whether it be a strong acid or a strong base.

So here we don't have any information on the conjugate base. So this is 0. Initially, we only care about three things, and this is our fourth thing, so we don't care about it. Besides, it's water, which is a liquid in an ICF chart, just like an ICE chart. We ignore solids and liquids. Now this is where things get a little bit different. So this is a deviation from what we typically do with an ICE chart with an ICF chart. For Step 3. Using the change row, look at the reactants. Subtract from their initial amounts by the smaller mole amount. So if we take a look here, we have these two moles as the initial amounts for our reactants. The moles of the strong base are smaller in amount, so we subtract both of them by the smaller amount.

Now using the law of conservation of mass, whatever you lose as a reactant, you gain that amount to products. So we're losing 0.00054 moles on the reactant side, so we're gaining that on the product side. Remember, matter is neither created nor destroyed, it just changes forms. So it's not that we're actually losing. You don't say that you're destroying the acid by that amount. You're basically saying that you're transforming it into your conjugate base. All right, so now after we do the subtracting, what do we have left? We have 0.00171 moles of this zero of our strong base and we have 0.00054 of our conjugate base.

This takes us to Step 4. The Henderson-Hasselbalch equation for a buffer is used for a buffer to find the pH of a solution. Using the final row, use the moles of the weak acid and conjugate base to find the pH. Since we're dealing with K_a within the question, we've used this form of the Henderson-Hasselbalch equation, which is pH equals pK_a plus log of conjugate base over weak acid. So we come back over here. So I'm going to say pH equals pK_a. So that's negative log of our K_a, which is 4.1×10−3 plus log of our conjugate base. So 0.00054 of this conjugate base divided by the weak acid, which is our pyruvic acid, 0.00171. When we do that, we get 1.89 as the pH for this particular buffer solution.