Problem 80 - Chemistry An Atoms First Approach

Question

The concentration of a certain sodium hydroxide solution was determined by using the solution to titrate a sample of potassium hydrogen phthalate (abbreviated as KHP). KHP is an acid with one acidic hydrogen and a molar mass of \(204.22 \mathrm{g} / \mathrm{mol}\). In the titration, \(34.67 \mathrm{mL}\) of the sodium hydroxide solution was required to react with 0.1082 g KHP. Calculate the molarity of the sodium hydroxide.

Step-by-Step Solution

Answer

The molarity of the sodium hydroxide solution is 0.0153 M.

Step 1: 1. Write the balanced equation for the reaction between NaOH and KHP

The reaction between sodium hydroxide (NaOH) and potassium hydrogen phthalate (KHP) can be written as follows: \(NaOH + KHC_8H_4O_4 \rightarrow NaKC_8H_4O_4 + H_2O\) This balanced equation shows that one mole of NaOH reacts with one mole of KHP.

Step 2: 2. Calculate the moles of KHP

We are given the mass of KHP, 0.1082 g, and its molar mass, 204.22 g/mol. We can calculate the moles of KHP in the sample using the following formula: Moles of KHP = (mass of KHP) / (molar mass of KHP) Moles of KHP = \(0.1082\ g / 204.22\ g/mol = 5.30 \times 10^{-4}\ mol\)

Step 3: 3. Determine the moles of NaOH that reacted with KHP

From the balanced equation, we know that one mole of NaOH reacts with one mole of KHP. So, the moles of NaOH that reacted with KHP will be the same as the moles of KHP. Moles of NaOH = moles of KHP = \(5.30 \times 10^{-4} \ mol\)

Step 4: 4. Calculate the molarity of the sodium hydroxide

We are given the volume of the sodium hydroxide solution used in the titration, 34.67 mL. To calculate the molarity (M) of the NaOH solution, we will use the following formula: Molarity of NaOH = (moles of NaOH) / (volume of NaOH in liters) First, we need to convert the volume of NaOH to liters: \(34.67\ mL \times \frac{1\ L}{1000\ mL} = 0.03467\ L\) Now, we can calculate the molarity of the NaOH solution: Molarity of NaOH = \(\frac{5.30 \times 10^{-4} \ mol}{0.03467\ L} = 0.0153\ M\) So, the molarity of the sodium hydroxide solution is 0.0153 M.

Key Concepts

Molarity calculation

When conducting a titration, molarity is a crucial concept that determines the concentration of a solution. Molarity, often denoted as M, refers to the number of moles of a solute present in one liter of solution. In the given exercise, we calculated the molarity of the sodium hydroxide (NaOH) solution by dividing the number of moles of NaOH by the volume of NaOH solution used in liters.
To convert the volume from milliliters to liters, remember that 1 liter equals 1000 milliliters. So, the conversion involves dividing the milliliters by 1000. This step is essential to ensure the consistency of units when calculating molarity.
The formula for molarity is:

• Molarity (M) = \( \frac{\text{moles of solute}}{\text{volume of solution in liters}} \).

In this instance, the result was 0.0153 M, indicating that the sodium hydroxide solution concentration is 0.0153 moles per liter.

Balanced chemical equation

A balanced chemical equation is key in describing the chemical reaction that occurs in a titration. It gives us the ratio of reactants to products, which helps us calculate the required amounts and concentrations.
For the reaction between sodium hydroxide (NaOH) and potassium hydrogen phthalate (KHP), the balanced equation is:

• \( \text{NaOH} + \text{KHC}_8\text{H}_4\text{O}_4 \rightarrow \text{NaKC}_8\text{H}_4\text{O}_4 + \text{H}_2\text{O} \)

This equation shows that one mole of NaOH reacts with one mole of KHP, exemplifying a 1:1 molar ratio. Understanding the stoichiometry, or balance, is critical for determining the moles of one reactant knowing the moles of the other in the chemical equation.

Sodium hydroxide solution

Sodium hydroxide, commonly known as NaOH, is a strong base used frequently in titrations. It dissolves well in water to produce hydroxide ions, making it an excellent choice for titrating acidic substances. During titration, a known volume of the NaOH solution is added to the acid, in this case, KHP, until the acid is completely neutralized.
The concentration of the NaOH solution is specifically crucial since it determines the volume necessary to neutralize a specific amount of KHP. Accurate measurements and calculations ensure the correct determination of the molarity, which is why precise calculations involving molarity are continuously emphasized in titration exercises.

Potassium hydrogen phthalate

Potassium hydrogen phthalate, abbreviated as KHP, is often utilized as a primary standard in titrations. It is favored because of its stable, non-hygroscopic nature and well-defined composition. KHP contains one acidic hydrogen, allowing it to serve as a monoprotic acid in reactions, which means it donates only one hydrogen ion (H+) per molecule during the reaction. This characteristic is critical in establishing a direct 1:1 correlation with bases like NaOH in titrations.
Given its molar mass of 204.22 g/mol, the quantity of KHP is usually calculated in moles using its mass (weight) in grams. Then, by applying the balanced chemical equation, the corresponding moles of NaOH that have reacted can be directly inferred, simplifying the process of determining the concentration of the base being analyzed.