Question

A \(3.664-\mathrm{g}\) sample of a monoprotic acid was dissolved in water. It took \(20.27 \mathrm{~mL}\) of a \(0.1578 \mathrm{M} \mathrm{NaOH}\) solution to neutralize the acid. Calculate the molar mass of the acid.

Short answer

The molar mass of the acid is approximately 1145.70 g/mol.

Step-by-step solution

Understand the Neutralization Reaction

In this problem, the neutralization reaction occurs between a monoprotic acid (HA) and a base (NaOH). The balanced chemical equation for a monoprotic acid reaction with NaOH is \( \text{HA} + \text{NaOH} \rightarrow \text{NaA} + \text{H}_2\text{O} \). Each mole of the acid will react with one mole of the base.

Calculate Moles of NaOH Used

Use the volume (in liters) and molarity of the NaOH solution to find the moles of NaOH used. Convert the volume from mL to liters. Volume in liters: \( 20.27 \text{ mL} = \frac{20.27}{1000} \text{ L} = 0.02027 \text{ L} \)Calculate moles of NaOH:\[ \text{moles of NaOH} = 0.1578 \text{ M} \times 0.02027 \text{ L} = 0.003198486 \text{ mol} \]

Determine Moles of Acid Neutralized

Since the reaction is a 1:1 molar ratio, the moles of the acid are equal to the moles of NaOH used.\[ \text{moles of acid} = 0.003198486 \text{ mol} \]

Calculate Molar Mass of the Acid

The molar mass of the acid is determined by dividing the mass of the acid sample by the moles of acid.\[ \text{Molar Mass} = \frac{3.664 \text{ g}}{0.003198486 \text{ mol}} \approx 1145.70 \text{ g/mol} \]

Interpret the Result

The molar mass calculation shows a large value; double-check each calculation step for any potential errors, as this value is inconsistent with typical molecular weights for monoprotic acids. Ensure that correct units and conversions were consistently applied.

Key concepts

Monoprotic Acid

A monoprotic acid is a type of acid that can donate just one proton (hydrogen ion, H⁺) per molecule in a chemical reaction. This is why it's termed "mono-" indicating one. A classic example is hydrochloric acid (HCl), which dissociates in water to release one hydrogen ion and one chloride ion. Understanding this property is crucial because when you conduct experiments involving neutralization, such as reacting with a base like sodium hydroxide (NaOH), each mole of the monoprotic acid will react with one mole of NaOH. This 1:1 stoichiometry simplifies calculations and is essential for balancing the chemical equation involved in such reactions.

Neutralization Reaction

Neutralization reactions are chemical reactions that occur between an acid and a base, resulting in the formation of water and a salt. For a typical neutralization involving a monoprotic acid and a base like NaOH, the general equation is:

• \( ext{HA} + ext{NaOH} ightarrow ext{NaA} + ext{H}_2 ext{O} \)

This shows that one molecule of a monoprotic acid (HA) reacts with one molecule of the base (NaOH) to produce water and a salt (NaA). The salt is composed of the cation from the base and the anion from the acid. This 1:1 reaction ratio allows for straightforward calculations when determining molar relationships in experiments.

Moles of NaOH

In a neutralization reaction, knowing the moles of sodium hydroxide (NaOH) used is pivotal for further calculations. From the exercise, we converted the volume of NaOH from milliliters to liters since molarity, which is moles per liter, needs volume in liters for calculations.

• Volume conversion: \( 20.27 ext{ mL} = 0.02027 ext{ L} \)

The formula to find moles based on molarity is:

• Moles of NaOH = Molarity (M) \( \times \) Volume (L)

By substituting the given values, you calculate the moles of NaOH, which directly help in further calculations to determine the moles of the acid.

Molarity and Volume

Molarity is a measure of the concentration of a solution, described as the number of moles of solute per liter of solution. In the context of neutralization reactions, this concept helps in quantifying the amount of a reagent (like NaOH) used, based on the volume of the solution. The volume, often measured in milliliters, must be converted to liters for calculations using molarity.

• For example, 20.27 mL becomes 0.02027 L.

Understanding both molarity and volume allows one to perform accurate stoichiometric calculations necessary for determining the moles of reactants and products involved in the reaction.

Chemical Equation Balancing

Balancing a chemical equation is crucial as it ensures the conservation of mass in a chemical reaction. For a monoprotic acid reacting with a base like sodium hydroxide, ensuring the equation correctly reflects a 1:1 molar relationship is key for calculating reactant and product quantities.

• The balanced equation for a monoprotic acid (HA) with NaOH is:
• \( ext{HA} + ext{NaOH} ightarrow ext{NaA} + ext{H}_2 ext{O} \)

Here, equal moles of each reactant combine to form water and a salt, preserving the number of atoms of each element on both sides.Balancing helps avoid mistakes in further stoichiometric calculations, leading to accurate results in determining molecular weights and concentrations.