Problem 96 - Chemistry The Molecular Science

Question

Potassium hydrogen phthalate, \(\mathrm{KHC}_{8} \mathrm{H}_{4} \mathrm{O}_{4},\) is used to standardize solutions of bases. The acidic anion reacts with bases according to this net ionic equation: $$\mathrm{HC}_{8} \mathrm{H}_{4} \mathrm{O}_{4}^{-}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{C}_{8} \mathrm{H}_{4} \mathrm{O}_{4}^{2-}(\mathrm{aq})$$ A \(0.902-g\) sample of potassium hydrogen phthalate requires \(26.45 \mathrm{~mL} \mathrm{NaOH}\) to react; determine the molarity of the \(\mathrm{NaOH}\).

Step-by-Step Solution

Answer

The molarity of NaOH is 0.1672 M.

Step 1: Write the reaction equation

Identify and write down the balanced net ionic equation for the reaction:\[\mathrm{HC}_{8} \mathrm{H}_{4} \mathrm{O}_{4}^{-} (aq) + \mathrm{OH}^{-} (aq) \rightarrow \mathrm{H}_{2} \mathrm{O} (\ell) + \mathrm{C}_{8} \mathrm{H}_{4} \mathrm{O}_{4}^{2-} (aq)\]

Step 2: Calculate moles of potassium hydrogen phthalate

Determine the molar mass of potassium hydrogen phthalate (\(\mathrm{KHC}_{8} \mathrm{H}_{4} \mathrm{O}_{4}\)) using atomic masses: K (39.1), H (1.0), C (12.0), O (16.0).Calculate: \[ 39.1 + 1 + (8 \times 12.0) + (4 \times 1.0) + (4 \times 16.0) = 204.22 \text{ g/mol} \]Now, calculate moles:\[\frac{0.902 \text{ g}}{204.22 \text{ g/mol}} = 0.00442 \text{ mol} \]

Step 3: Use stoichiometry to find moles of NaOH

In the reaction, the ratio of \(\mathrm{HC}_{8} \mathrm{H}_{4} \mathrm{O}_{4}^{-}\) to \(\mathrm{OH}^{-}\) is 1:1. Thus, the moles of \(\mathrm{NaOH}\) required are equal to the moles of \(\mathrm{KHC}_{8} \mathrm{H}_{4} \mathrm{O}_{4}\):\[0.00442 \text{ mol NaOH}\]

Step 4: Calculate the molarity of NaOH solution

Use the formula for molarity \(M = \frac{\text{moles of solute}}{\text{liters of solution}}\).Convert the volume from mL to L:\[26.45 \text{ mL} = 0.02645 \text{ L}\]Calculate the molarity:\[M = \frac{0.00442 \text{ mol}}{0.02645 \text{ L}} = 0.1672 \text{ M} \]

Key Concepts

Potassium Hydrogen Phthalate

Potassium hydrogen phthalate, known as KHP in the chemistry world, plays a crucial role in acid-base titrations. This compound has the formula \(\mathrm{KHC}_8\mathrm{H}_4\mathrm{O}_4\) and is very useful because it acts as a primary standard. Its significance stems from its stability, high purity, and non-hygroscopic nature, meaning it doesn’t absorb moisture from the air easily.
In the context of titrations, KHP is used to standardize base solutions like sodium hydroxide (NaOH). When it reacts with a base, the acidic hydrogen in KHP is neutralized. This neutralization is represented by the net ionic equation where the acidic phthalate ion \(\mathrm{HC}_8\mathrm{H}_4\mathrm{O}_4^{-}\) reacts with the hydroxide ion \(\mathrm{OH}^-\) from the base to form water and a phthalate ion \(\mathrm{C}_8\mathrm{H}_4\mathrm{O}_4^{2-}\).
Due to its predictable reaction with bases, it serves as a reliable method to determine the concentration of the base accurately.

Molarity Calculation

Calculating molarity is a fundamental skill in chemistry, specifically when dealing with solutions like titrants. Molarity (M) is defined as the number of moles of solute per liter of solution.
Here’s how to calculate it step-by-step:

• First, determine the number of moles of your substance. Use the formula for molar mass, adding the atomic masses of all atoms in the compound, for example, in KHP, you add the masses from potassium, carbon, hydrogen, and oxygen.
• Next, obtain the sample mass—in this case, 0.902 grams of KHP—and divide it by the molar mass (204.22 g/mol) to get the number of moles.
• Finally, find the volume of your solution in liters. Convert the volume from milliliters to liters (26.45 mL to 0.02645 L). Use these values to calculate molarity using the formula \( M = \frac{\text{moles of solute}}{\text{liters of solution}} \).

In practice, this enables you to accurately determine how concentrated your solution is, which is vital in reactions where precise measurements are required.

Net Ionic Equation

A net ionic equation provides a simplified way to understand chemical reactions, focusing only on the species that undergo change. It is especially useful in titrations where you’re interested in the process of neutralization between acids and bases.
For the titration involving KHP and NaOH, the relevant net ionic equation is:\[\mathrm{HC}_{8} \mathrm{H}_{4} \mathrm{O}_{4}^{-} (\mathrm{aq}) + \mathrm{OH}^{-} (\mathrm{aq}) \rightarrow \mathrm{H}_{2} \mathrm{O} (\ell) + \mathrm{C}_{8} \mathrm{H}_{4} \mathrm{O}_{4}^{2-} (\mathrm{aq})\]
This equation highlights that only the ions directly participating in the reaction are shown, omitting the spectator ions like \(\mathrm{Na}^+\) and \(\mathrm{K}^+\).
The net ionic equation essentially says: "An acidic phthalate ion reacts with a basic hydroxide ion to form water and another type of phthalate ion." This equation is balanced in terms of both mass and charge, which is crucial for accurately representing the chemical process taking place.