### Video Transcript

What volume of 0.5-molar sulfuric acid would completely neutralize 125 milliliters of 0.1-molar sodium hydroxide?

To answer this question, we need to use the volume and concentration of sodium hydroxide given along with the concentration of sulfuric acid in order to determine the volume of sulfuric acid needed in order to completely neutralize the sodium hydroxide solution. This problem can be solved in a series of steps. In order to relate two different substances to one another that are involved in a chemical reaction, we’ll need to know the number of moles of one of the substances and their molar ratio. As the question provides us with two pieces of information about sodium hydroxide and only one piece of information about sulfuric acid, we’ll start by determining the number of moles of sodium hydroxide in 125 milliliters of a 0.1-molar solution.

To do this, we’ll use the equation 𝑛 equals 𝑐𝑉, where 𝑛 represents the amount in moles, 𝑐 is the concentration in moles per liter, and 𝑉 is the volume in liters. We are given the concentration of sodium hydroxide in molar, which is the same as the concentration in moles per liter. The volume is given in milliliters. But in order to use the equation, the volume must be in liters. One liter is equivalent to 1000 milliliters. We can convert 125 milliliters into liters by multiplying by one liter per 1000 milliliters. The unit milliliters will cancel, and we’ll get a value of 0.125 liters.

Now, we can solve for the number of moles of sodium hydroxide. The liter units will cancel, and we’ll get a value of 0.0125 moles. Now that we know the number of moles of sodium hydroxide, we need to know the molar ratio of sodium hydroxide to sulfuric acid. So we’ll need to write a balanced chemical equation. The chemical formula of sulfuric acid is H2SO4, and the chemical formula of sodium hydroxide is NaOH.

When sulfuric acid, a strong acid, reacts with sodium hydroxide, a strong base, a salt and water are produced. Water is produced from a hydrogen ion from the acid and a hydroxide ion from the base. This means that the salt must be formed when the sulfate ion from the acid combines with the sodium ion from the base. Sodium ions have a charge of one plus, while sulfate ions have a charge of two minus. In order for the compound to have an overall neutral charge, there must be two sodium ions for each sulfate ion.

We’ve written the products of this chemical equation, but the equation isn’t balanced. We see that there are two atoms of sodium on the product side and only one atom of sodium on the reactant side. So we’ll need to place a coefficient of two in front of sodium hydroxide. With this coefficient in place, we can see that there are four atoms of hydrogen on the reactant side and only two atoms of hydrogen on the product side. So we’ll need to place a coefficient of two in front of water.

Now that we have a balanced chemical equation, we can see that the molar ratio of sulfuric acid to sodium hydroxide is one to two. We can use a smaller ratio to calculate the number of moles of sulfuric acid from the number of moles of sodium hydroxide. The reaction involved 0.0125 moles of sodium hydroxide. We can multiply this value by the molar ratio written as a fraction with moles of sodium hydroxide in the denominator so that the units cancel. Performing the calculation gives us a value of 0.00625 moles of sulfuric acid.

Now, we can finally calculate the volume of sulfuric acid. Once again, we’ll use the equation 𝑛 equals 𝑐𝑉. The concentration was provided in the question, and we just calculated the number of moles of sulfuric acid. So we can substitute these values into the equation. To solve for the volume, we need to divide both sides of the equation by 0.5 moles per liter. The unit moles will cancel, leaving us with a volume in liters. Performing the calculation gives us a volume of 0.0125 liters.

As the question doesn’t specify a unit, we could end the problem here. But as the volume of sodium hydroxide was given in milliliters, it would be nice to report our answer with the same volume unit. As one liter is equal to 1000 milliliters, we can multiply our volume in liters by 1000 milliliters per one liter. The liter units will cancel, and we’ll get a value of 12.5 milliliters.

So the volume of 0.5-molar sulfuric acid that would completely neutralize 125 milliliters of a 0.1-molar sodium hydroxide solution is 12.5 milliliters.