Titration of a 50.0-milliliter sample of hydrochloric acid required 35.23 milliliters of 0.250 molar aqueous sodium hydroxide. Calculate the concentration of the hydrochloric acid.
So, this question is asking us about an acid–base titration. A good place to start in answering this question is to write out the equation of this reaction. We know that we’re reacting together HCl and NaOH. What it forms doesn’t actually matter for the purpose of this question. But for completeness, I’ll fill in the products. Remember that acid plus base gives you salt plus water.
In this question, we’re given volumes and a concentration. So, the next thing we can do is write down the relationship between volume, concentration, and number of moles. Here, I’ve written a relationship between moles, concentration, and volume in a Sparky’s triangle. Whichever value we want to calculate, we cover up and perform the calculation of whatever is left.
I like to lay these calculations out in a table. So, let’s start by adding in the volumes of each of the reactants. I’ve taken these values straight from the question. We’re given the concentration of the sodium hydroxide. But the answer to the question is going to fill in the gap with the question mark, the concentration of the hydrochloric acid. We know from our reaction equation that the stoichiometry is one equivalent of NaOH to one equivalent of HCl. That means that the number of moles in our 35.23-milliliter solution of sodium hydroxide has to be exactly the same number of moles of HCl.
So, if we work out the number of moles of NaOH, we can then get the number of moles of HCl. So, let’s do that now. If we cover up moles in our Sparky’s triangle, we’re left with concentration multiplied by volume. But don’t forget, always be careful with your units. Molar means moles per liter. And we’re given the volumes in milliliters. To convert from milliliters to liters, we divide by 1000. Alternatively, you can write it as multiplying by 10 to the minus three.
So, now that we have our volumes in liters, we can work out the number of moles. If we multiply the volume of NaOH by its concentration, we get the number of moles. In this case, this works out at 0.0088075 moles. Again, because there’s a one-to-one molar ratio between the hydrochloric acid and the sodium hydroxide. This means we have the exact same number of moles of HCl. So, now we can work out the concentration of our hydrochloric acid. This time, using our Sparky’s triangle, we want to work out concentration. So, if we cross that out, we’re left with moles divided by volume. So, if we do 0.0088075 moles divided by 50 times 10 to the minus three liters, we get the concentration 0.17615 molar.
But of course the values given to us in the question are all to three significant figures, or greater. So, we should also give our answer to three significant figures. So, the final answer is 0.176 molar. I like to lay my calculations out in a table like this. Because then, if you start to get confused and mixed up about what you’re trying to multiply or divide or indeed what you’re trying to work out, it’s quite nice to have the table so you can just fill in the gaps. So, if you’re ever in doubt, just think, where have I got gaps in my table? Can I fill those in somehow? And I always like to write out my Sparky’s triangle.