Question

Calculate the volume in milliliters of a \(1.420 \mathrm{M} \mathrm{NaOH}\) solution required to titrate the following solutions: a) \(25.00 \mathrm{~mL}\) of a \(2.430 \mathrm{M} \mathrm{HCl}\) solution b) \(25.00 \mathrm{~mL}\) of a \(4.500 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) solution c) \(25.00 \mathrm{~mL}\) of a \(1.500 \mathrm{M} \mathrm{H}_{3} \mathrm{PO}_{4}\) solution

Short answer

42.8 mL, 158.5 mL, and 79.2 mL of 1.420 M NaOH are required, respectively.

Step-by-step solution

Understanding the Reaction

For titration, it's important to understand the reaction between the acid and the NaOH. Specifically, each HCl molecule will react with 1 molecule of NaOH, each H2SO4 molecule with 2 molecules of NaOH, and each H3PO4 with 3 molecules of NaOH. The general reaction for neutralization is: acid + base -> salt + water.

Calculating Moles of Acid (HCl)

First, we calculate the moles of HCl using the formula: \( \text{moles} = \text{molarity} \times \text{volume in liters} \). For HCl: \( 2.430 \, \mathrm{M} \times 0.025 \, \mathrm{L} = 0.06075 \, \mathrm{mol} \) of HCl.

Calculating Moles of NaOH for HCl

Since HCl reacts with NaOH in a 1:1 ratio, the moles of NaOH needed are equal to the moles of HCl. Thus, 0.06075 mol NaOH is required.

Calculating Volume of NaOH for HCl

Using the moles and molarity of NaOH, we find the volume required. Using the formula: \( \text{volume} = \frac{\text{moles}}{\text{molarity}} \), we get: \( \frac{0.06075}{1.420} = 0.0428 \, \mathrm{L} \) or 42.8 mL.

Calculating Moles of Acid (H2SO4)

Next, for H2SO4, we calculate the moles: \( 4.500 \, \mathrm{M} \times 0.025 \, \mathrm{L} = 0.1125 \, \mathrm{mol} \) of H2SO4.

Calculating Moles of NaOH for H2SO4

Because H2SO4 reacts with NaOH in a 1:2 ratio, we need 2 moles of NaOH for each mole of H2SO4. Thus, \( 2 \times 0.1125 = 0.225 \, \mathrm{mol} \) of NaOH is required.

Calculating Volume of NaOH for H2SO4

Again, using the moles and molarity formula: \( \frac{0.225}{1.420} = 0.1585 \, \mathrm{L} \) or 158.5 mL.

Calculating Moles of Acid (H3PO4)

For H3PO4, find the moles: \( 1.500 \, \mathrm{M} \times 0.025 \, \mathrm{L} = 0.0375 \, \mathrm{mol} \) of H3PO4.

Calculating Moles of NaOH for H3PO4

H3PO4 reacts with NaOH in a 1:3 ratio, meaning 3 moles of NaOH per mole of H3PO4. We calculate: \( 3 \times 0.0375 = 0.1125 \, \mathrm{mol} \) of NaOH is needed.

Calculating Volume of NaOH for H3PO4

Finally, using the formula again: \( \frac{0.1125}{1.420} = 0.0792 \, \mathrm{L} \) or 79.2 mL.

Key concepts

Neutralization Reaction

In chemistry, a neutralization reaction occurs when an acid reacts with a base, producing a salt and water: acid + base -> salt + water.
In an acid-base titration, this concept is crucial. It involves adding a base (in this case, a sodium hydroxide NaOH solution) to an acid solution until the acid is completely neutralized.
A unique factor here is the number of protons (H+) each acid can donate. This affects how much base is required for neutralization:

• For hydrochloric acid (HCl), it is a monoprotic acid, meaning it releases one proton per molecule, thus reacting 1:1 with NaOH.
• Sulfuric acid (H₂SO₄) is diprotic—each molecule releases two protons. Hence, it requires twice the amount of NaOH for neutralization.
• Phosphoric acid (H₃PO₄) is triprotic, releasing three protons each, necessitating three times the NaOH amount for complete reaction.

Understanding these ratios allows us to calculate the appropriate amount of base needed to achieve neutralization.

Molarity

Molarity is a measure of concentration, defining how many moles of a dissolved substance, termed solute, exist in one liter of solution. It is expressed in the units of moles per liter (M). Given the formula for molarity, we can write:\( ext{Molarity} (M) = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\)In the context of titration, we often know the molarity of both acid and base. This allows us to determine the exact stoichiometric amounts needed for complete neutralization.
For example, when a solution of HCl is described as 2.430 M, it means there are 2.430 moles of HCl per liter of solution. Similarly, the 1.420 M NaOH solution contains 1.420 moles of sodium hydroxide per liter.

Stoichiometry

Stoichiometry entails the quantitative relationship between reactants and products in a chemical reaction. This concept is essential during titrations because it enables us to balance the reaction according to available amounts. The stoichiometric coefficients in a balanced equation tell you the ratio in which reactants combine and products form. In neutralization reactions:

• For HCl + NaOH, the reaction is in a 1:1 stoichiometry, meaning one mole of HCl reacts with one mole of NaOH.
• For H₂SO₄ + NaOH, the stoichiometry is 1:2, where one mole of sulfuric acid needs two moles of NaOH for full neutralization.
• For H₃PO₄ + NaOH, it is a 1:3 stoichiometry, requiring three moles of NaOH per mole of phosphoric acid.

These relationships are crucial for calculating how much NaOH is required based on the initial mole quantity of the acids.

Volume Calculation

Volume calculations in acid-base titrations rely on knowing the stoichiometry and molarity. It involves determining the amount of titrant needed to completely neutralize a given concentration and volume of analyte. The formula used is:\( ext{Volume} = \frac{\text{moles of titrant}}{\text{molarity of titrant}}\)This gives us the necessary volume to achieve neutralization, expressed typically in liters or milliliters.
Let's break down the steps using HCl as an example:

• First, determine the moles of HCl present using its molarity and volume in liters.
• Knowing it's a 1:1 reaction, establish that the moles of NaOH needed equal the moles of HCl.
• Determine the volume of NaOH by dividing the moles required by its molarity (1.420 M), thus finding the titrant volume required.

This approach can be applied to other acids (like H₂SO₄ and H₃PO₄) by considering their respective stoichiometries.