Stoichiometry - Acid/Base Titration

In this problem, we're going to determine the solution concentration in an acid-base titration. The problem says that one commercial method is to peel potatoes by soaking them in sodium hydroxide solution for a short time, then removing the potatoes and peeling off the peel. The sodium hydroxide concentration is normally 3 to 6 molarity, and the solution must be analyzed periodically. In one such analysis, 45.7 milliliters of 0.5 molar sulfuric acid is required to neutralize 20.0 milliliters of sodium hydroxide. What is the concentration of sodium hydroxide solution? So, we are given the volume and the molarity of the sulfuric acid is needed to react completely with twenty milliliters of the sodium hydroxide solution. We are asked to calculate the molarity of the sodium hydroxide. Remember that molarity is equal to moles over volume, and we know the volume of the sodium hydroxide is 20 milliliters. This is important to note because we have two volumes here: one for the gas and one for the sodium hydroxide. The concentration of the sodium hydroxide can be found by dividing the moles of sodium hydroxide by the liters obtained from the 20 milliliters, which is 0.02 liters. Next, we need to use the volume and molarity of the sulfuric acid to calculate the number of moles of sulfuric acid. Once we have the moles of sulfuric acid, we can proceed to the next step. That, those moles to moles of sodium hydroxide. We calculate that by using the stoichiometry of the balanced equation of the neutralization reaction. So, we need to look for those coefficients from the balanced equation. So, we have the ratio between the moles of sodium hydroxide and the moles of sulfuric acid. Once we have the moles of sodium hydroxide, that's what we're looking for, we can divide by the volume of sodium hydroxide, which was twenty moles. In that way, we will finally have the concentration of hydroxide moles divided by volume. So, we need to first obtain the moles from sulfuric acid, and this will be the product of the volume change, which is in liters. That's really important. It should be divided or multiplied by the. Concentration of the sulfuric acid: Multiply 45.7 milliliters, which is the volume of the acid, by 1 divided by 1000. This will convert it to liters. You can cancel out the milliliters and then multiply it by the molarity of the sulfuric acid, which is 0.5 moles of sulfuric acid per liter. Cancel out the liter here and the total of this product will be the moles of sulfuric acid. Now, we need to calculate the moles of sodium hydroxide using this moles of sulfuric acid. To do this, we need to look for the balanced equation and the reaction is sodium hydroxide and sulfuric acid. This will produce water and sodium sulfate. Okay, remember that in this case we have two hydrogens that will react with each of the OH groups in sodium hydroxide. So, we need two moles of sodium hydroxide to react with one mole of sulfuric acid. So, the ratio is 2:2:1, with two moles of sodium hydroxide per one mole of sulfuric acid. Now, we can use this ratio to calculate the moles of sodium hydroxide. It will be equal to the moles obtained before, multiplied by 2, divided by 1 mole of sulfuric acid. If we cancel out the sulfuric acid, we will have the moles of sodium hydroxide as the final product. Of certain drugs, and we're looking for the concentration. Remember that we are now trying to calculate the concentration of the sodium hydroxide, and that would be moles over volume. We have here the moles, and the volume was 20 millimeters. We change that to liters by dividing by one thousand, and that will be basically equal to 0.02. So now we have the moles divided by the volume, and that will be equal to 2.28 molarity. Okay, in this case, they are multiplying here, but this is the denominator, so basically it's like division. So we have here 2.28 moles divided by the liters, and that will be the molarity for sodium hydroxide. For the next step here, this volume is the volume for sodium hydroxide, not the 47.5. And then, we move on to the sulfuric acid. We have two volumes, and we need to identify each of them. So, at the end, we can use the correct one to calculate the molarity of the sodium hydroxide.