Question

A solution of phosphoric acid, \(\mathrm{H}_{3} \mathrm{PO}_{4}\), is found to contain \(35.2 \mathrm{g}\) of \(\mathrm{H}_{3} \mathrm{PO}_{4}\) per liter of solution. Calculate the molarity and normality of the solution.

Short answer

The molarity of the H3PO4 solution is \(0.359 \, M\), and the normality is \(1.077 \, N\).

Step-by-step solution

Calculate the molecular weight of H3PO4

To find the molecular weight of H3PO4, add the atomic weights of all the constituent atoms. Atomic weights: H = 1, P = 31, and O = 16. Molecular weight of H3PO4 = (3 × 1) + (1 × 31) + (4 × 16) = 3 + 31 + 64 = 98 g/mol Step 2: Find the moles of H3PO4

Calculate the moles of H3PO4

To find the moles of H3PO4, divide its mass by its molecular weight. Moles of H3PO4 = mass / molecular weight = 35.2 g / 98 g/mol = 0.359 moles Step 3: Calculate the molarity

Calculate the molarity

Molarity is the number of moles of solute present per liter of solution. Molarity = moles of H3PO4 / volume of solution (L) = 0.359 moles / 1 L = 0.359 M Step 4: Determine the number of H+ ions in H3PO4

Calculate the number of H+ ions in H3PO4

Since H3PO4 produces 3 H+ ions when it dissociates (H3PO4 → H+ + H2PO4- → 2H+ + HPO4^2- → 3H+ + PO4^3-), the normality of the solution will be three times the molarity. Step 5: Calculate the normality

Calculate the normality

Normality is the number of gram equivalents of solute per liter of solution. Normality = 3 × molarity = 3 × 0.359 M = 1.077 N The molarity of the H3PO4 solution is 0.359 M, and the normality is 1.077 N.

Key concepts

Phosphoric Acid Solution

Understanding the characteristics of a phosphoric acid solution is fundamental in chemistry, especially when working with acid-base reactions. Phosphoric acid, chemically represented as \( \text{H}_3\text{PO}_4 \), is a triprotic acid, which means it can donate three protons (\( \text{H}^+ \) ions). This is an important detail when calculating the normality of a solution, as normality relates to the reactive capacity of an acid or base in terms of equivalent factor, which in the case of \( \text{H}_3\text{PO}_4 \) is three, one for each dissociable hydrogen ion.

When dissolved in water, \( \text{H}_3\text{PO}_4 \) dissociates sequentially, and the solution's concentration is often expressed in molarity (M), which is the number of moles of the solute per liter of solution. Concentrations of acid solutions influence their chemical behavior and reactivity, making accurate calculations essential for creating desired concentrations for various applications in industry and scientific research.

Moles Calculation

The concept of moles is at the heart of chemical quantification. One mole represents \( 6.022 \times 10^{23} \) entities, such as atoms, molecules, or ions—the Avogadro's number. The mole calculation is crucial for converting between the mass of a substance and the number of particles it contains.

In the context of the exercise, to calculate moles, you divide the mass of the substance by its molecular weight. This conversion from grams to moles enables chemists to work on a molecular level and to understand, predict, and measure the outcome of reactions based on fixed proportions defined by balanced chemical equations. For phosphoric acid, knowing the number of moles in a given mass is the first step in determining how concentrated the solution is and in predicting how it will react in a mix with other substances.

Molecular Weight

The molecular weight (or molecular mass) of a compound is the sum of the atomic weights of all atoms in its chemical formula. It is often expressed in units of grams per mole (g/mol) and is essential for converting between grams of a substance and moles. The molecular weight serves as a conversion factor enabling scientists to scale reactions from the molecular scale to measurable quantities in the lab.

In the phosphoric acid solution exercise, the atomic weights of hydrogen (1), phosphorus (31), and oxygen (16) are used to calculate the molecular weight of \( \text{H}_3\text{PO}_4 \). With its molecular weight determined, calculations concerning the substance's molarity or normality hinge on knowing this fundamental property. In practice, accurate determination of molecular weight is a crucial step for any laboratory preparation or experiment involving chemical substances.