Question

A 6.50-g sample of a diprotic acid requires 137.5 mL of a 0.750 M NaOH solution for complete neutralization. Determine the molar mass of the acid.

Short answer

The molar mass of the diprotic acid can be calculated by first determining the moles of NaOH (0.1031 mol) used in the reaction, then finding the moles of the diprotic acid (0.05155 mol) based on the stoichiometry of the balanced equation. Finally, dividing the mass of the diprotic acid (6.50 g) by the moles of the acid results in a molar mass of 126.0 g/mol for the diprotic acid.

Step-by-step solution

Write the balanced chemical equation for the reaction.

The general formula for the reaction between a diprotic acid (H2A) and sodium hydroxide (NaOH) is: H2A + 2NaOH -> 2H2O + Na2A (This equation represents the complete neutralization of the diprotic acid and the formation of water and the sodium salt of the acid.)

Find the moles of NaOH.

We are given the volume and the concentration of the NaOH solution. To find the moles of NaOH, we will use the formula: moles of NaOH = volume (in liters) × concentration moles of NaOH = (137.5 mL × (1 L / 1000 mL)) × 0.750 M moles of NaOH = 0.1031 mol

Determine the moles of the diprotic acid.

Using the stoichiometry from the balanced chemical equation, we can determine the moles of the diprotic acid (H2A): 1 moles of H2A react with 2 moles of NaOH So, for the moles of NaOH calculated in Step 2, we can find the moles of H2A by dividing the moles of NaOH by 2: moles of H2A = moles of NaOH / 2 moles of H2A = 0.1031 mol / 2 moles of H2A = 0.05155 mol

Calculate the molar mass of the diprotic acid.

Now that we have the moles of the diprotic acid, we can calculate its molar mass using the formula: molar mass = mass of the acid / moles of the acid We are given the mass of the diprotic acid as 6.50 g. So: molar mass = 6.50 g / 0.05155 mol molar mass = 126.0 g/mol The molar mass of the diprotic acid is 126.0 g/mol.

Key concepts

Diprotic Acid

A diprotic acid is a type of acid that can donate two protons (H⁺ ions) per molecule in a chemical reaction. It's called "diprotic" because of the prefix 'di-', which means two. These acids participate in chemical reactions where they tend to lose two hydrogen ions sequentially.
Common examples of diprotic acids include sulfuric acid (H₂SO₄) and carbonic acid (H₂CO₃).
To visualize this, think of the diprotic acid initially being nontoxic, then becoming ready to interact twice, indicating the double chance it provides in balance reactions.
In the context of our problem, the diprotic acid, denoted as H₂A, is neutralized by sodium hydroxide (NaOH), showcasing its ability to act over two proton donation processes.

Chemical Stoichiometry

Chemical stoichiometry forms the backbone of understanding quantitative relationships in chemical reactions. It is the fascinating concept that uses the balanced chemical equation to relate the amounts of reactants and products. This ensures we know how much of each substance is needed or produced.
In our exercise, stoichiometry tells us that the reaction between the diprotic acid (H₂A) and sodium hydroxide (NaOH) follows a 1:2 mole ratio.
This means:

• 1 mole of diprotic acid reacts with
• 2 moles of NaOH

For anyone learning about stoichiometry, it's crucial to grasp this mole ratio, as it guides calculations for the amounts required or consumed in reactions. The ratios reveal the efficiency and demands of the chemical process.

Neutralization Reaction

Neutralization reactions are a special type of reaction where an acid and a base interact to form water and a salt. This is one of the most common chemical reactions and is crucial in various applications, from industrial processes to digestion in the human body.
For neutralization to occur, the acid provides H⁺ ions, while the base gives OH⁻ ions, leading to the production of water (H₂O):

• H⁺ from the acid joins with
• OH⁻ from the base

In our case, the diprotic acid H₂A fully neutralizes with NaOH to produce water and a sodium salt (Na₂A).
The neutralization confirms the complete reaction, where no excess reactant remains, allowing us to use the volumes and concentrations for calculation purposes.

Balanced Chemical Equation

A balanced chemical equation is essential to accurately represent a chemical reaction. A balanced equation ensures that the number of atoms for each element is the same on both sides of the reaction. This follows the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction.
For the reaction between diprotic acid and sodium hydroxide, the balanced equation is: H₂A + 2NaOH → 2H₂O + Na₂A
It shows that one molecule of diprotic acid (H₂A) reacts with two molecules of NaOH to yield two molecules of water and one sodium salt molecule.
Having the equation balanced is crucial. It is the foundation upon which all stoichiometric calculations are based. Without a balanced equation, one cannot accurately predict how much reactant is needed or product is formed.