Problem 61 - General Chemistry: Principles and Modern Applications

Question

A 0.3126 g sample of oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4},\) requires 26.21 mL of a particular concentration of \(\mathrm{NaOH}(\mathrm{aq})\) to complete the following reaction. What is the molarity of the \(\mathrm{NaOH}(\mathrm{aq}) ?\) \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(\mathrm{s})+2 \mathrm{NaOH}(\mathrm{aq}) \longrightarrow\) $$ \mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) $$

Step-by-Step Solution

Answer

The molarity of the \(\mathrm{NaOH(aq)}\) is 0.265 M.

Step 1: Convert the mass of oxalic acid to moles.

Using the molar mass of oxalic acid, which is 90.03g/mol, the number of moles of oxalic acid can be calculated as follows: Moles of oxalic acid = mass / molar mass = 0.3126g / 90.03g/mol = 0.00347 mol.

Step 2: Apply stoichiometry.

According to the balanced chemical equation, 1 mol of oxalic acid reacts completely with 2 moles of \(NaOH\). Therefore, the moles of \(NaOH\) required for the complete reaction is double the moles of oxalic acid, i.e., = 2 * 0.00347 mol = 0.00694 mol.

Step 3: Calculate molarity

The volume of \(NaOH\) solution used is given as 26.21 mL, which should be converted to liters as molarity is expressed in mol/L: Volume = 26.21 mL = 0.02621 L. From the definition of molarity (moles/volume), we can now calculate the molarity of the \(NaOH\) solution: Molarity of \(NaOH\) = moles/volume = 0.00694 mol / 0.02621 L = 0.265 M.

Key Concepts

Stoichiometry

Stoichiometry is a core concept in chemistry, often involved in the calculation of reactants and products in chemical reactions. It provides a quantitative relationship between the substances involved. In the provided example, stoichiometry is used to determine the amount of sodium hydroxide (\(\text{NaOH}\)) needed to react with a known amount of oxalic acid.When looking at chemical equations, stoichiometry helps you understand:

• The proportion of reactants consumed and products formed.
• The mole-to-mole ratio, which is essential for converting between different substances.

In this exercise, the balanced equation shows that \(1\) mole of oxalic acid needs \(2\) moles of \(\text{NaOH}\). This relationship helps calculate how much \(\text{NaOH}\) is required when the amount of oxalic acid is known.

Oxalic Acid

Oxalic acid (\(\text{H}_{2} \text{C}_{2} \text{O}_{4}\)) is an organic compound with a relatively simple structure. It is a dicarboxylic acid, meaning it has two carboxyl groups, which can release protons. This makes it a diprotic acid used in various chemical reactions, including titrations.Key characteristics of oxalic acid include:

• It is a crystalline solid often found in its dihydrate form.
• It acts as a reducing agent in some chemical processes.
• Due to its acidic nature, it can react with bases such as sodium hydroxide to produce salts.

In the given problem, oxalic acid reacts with sodium hydroxide in a neutralization reaction. This type of reaction is common in stoichiometric calculations, helping us find the exact amount of base required to react with the acid.

Sodium Hydroxide

Sodium hydroxide (\(\text{NaOH}\)) is a highly caustic base, widely used in various chemical reactions and industrial processes. Often referred to as lye or caustic soda, it easily dissolves in water to form a strongly alkaline solution.Properties of sodium hydroxide include:

• It is a strong base, meaning it fully ionizes in water.
• It is used in processes like soap making, paper production, and water treatment.
• Handling requires care due to its corrosive nature.

In our exercise, sodium hydroxide reacts with oxalic acid to form sodium oxalate and water. Understanding the properties of sodium hydroxide aids in safely conducting experiments and achieving accurate stoichiometric calculations, such as determining its molarity from used volume and moles reacted.