Question

Calculate the normality of each of the following solutions. a. \(0.250 \mathrm{M} \mathrm{HCl}\) b. \(0.105 M \mathrm{H}_{2} \mathrm{SO}_{4}\) c. \(5.3 \times 10^{-2} \mathrm{M} \mathrm{H}_{3} \mathrm{PO}_{4}\)

Short answer

The normality of the given solutions are: a. 0.250 N for 0.250 M HCl b. 0.210 N for 0.105 M H₂SO₄ c. \(1.59 \times 10^{-1} N\) for \(5.3 \times 10^{-2} M H_{3} PO_{4}\)

Step-by-step solution

Find the molarity and number of hydrogen ions released for each solution

For solution (a) 0.250 M HCl, The molarity is given as 0.250 M, and since HCl releases 1 hydrogen ion, the number of hydrogen ions released is 1. For solution (b) 0.105 M H₂SO₄, The molarity is given as 0.105 M, and since H₂SO₄ releases 2 hydrogen ions, the number of hydrogen ions released is 2. For solution (c) \(5.3 \times 10^{-2} M H_{3} PO_{4}\), The molarity is given as \(5.3 \times 10^{-2} M\), and since H₃PO₄ releases 3 hydrogen ions, the number of hydrogen ions released is 3.

Calculate the normality of each solution using the formula

For solution (a) 0.250 M HCl, Normality = Molarity × No. of \(H^+\) ions released = 0.250 M × 1 = 0.250 N For solution (b) 0.105 M H₂SO₄, Normality = Molarity × No. of \(H^+\) ions released = 0.105 M × 2 = 0.210 N For solution (c) \(5.3 \times 10^{-2} M H_{3} PO_{4}\), Normality = Molarity × No. of \(H^+\) ions released = \(5.3 \times 10^{-2} M \) × 3 = \(1.59 \times 10^{-1} N\)

Write the final answer

The normality of each solution is: a. 0.250 N for 0.250 M HCl b. 0.210 N for 0.105 M H₂SO₄ c. \(1.59 \times 10^{-1} N\) for \(5.3 \times 10^{-2} M H_{3} PO_{4}\)

Key concepts

Molarity

Molarity, often denoted by the symbol 'M', is a measure of concentration used in chemistry to describe the amount of a solute contained in a solution. Specifically, it represents the number of moles of solute per liter of solution. This concept is vital when you're working with solutions, as it allows chemists to quantify how concentrated or dilute a solution is.

For instance, if we say a solution has a molarity of 1 M, it means that there is 1 mole (which is 6.022 × 10^23 particles) of the solute dissolved in 1 liter of the total solution. To calculate molarity, you can use the formula:
\[ M = \frac{n}{V} \]
where \(M\) stands for molarity, \(n\) is the number of moles of the solute, and \(V\) is the volume of the solution in liters.

Understanding molarity is essential when studying chemical reactions, as the concentration of reactants often determines the rate and extent of a reaction. It's also the first step when calculating normality of a solution, especially when dealing with acids and bases where the number of reactive particles needs to be considered.

Hydrogen Ions

Hydrogen ions, denoted as \(H^+\), are central to understanding acidity and the behavior of acids in aqueous solutions. When an acid dissolves in water, it donates hydrogen ions to the solution, which is the defining trait of acidity. The number of hydrogen ions an acid can release influences its reactivity and is a key factor in its normality, a concept closely related to molarity.

For example, hydrochloric acid (HCl) releases one hydrogen ion per molecule, sulfuric acid (H₂SO₄) releases two, and phosphoric acid (H₃PO₄) releases three. In calculations for normality, each hydrogen ion has the potential to react, so they directly impact the calculation's result. In the processes like neutralization, the ability of an acid to furnish these ions makes them valuable in determining how much acid is needed to react completely with a given base.

Acid Concentration

Acid concentration is a quantitative measure of the amount of acid in a solution and is generally expressed in terms of molarity (M). But, when we're dealing with reactions like titrations, we often use another term called normality (N). Normality is the concentration of reactive units in a solution, and for acids, it is related to the number of hydrogen ions that one molecule of acid can donate.

To calculate the normality of an acid, you multiply the molarity of the acid by the number of hydrogen ions it can release upon dissociation. The formula is:
\[Normality = Molarity \times No. of \(H^+\) ions released\]
This is why the normality of sulfuric acid (H₂SO₄) is twice its molarity while that of phosphoric acid (H₃PO₄) is three times its molarity. Recognizing the normality of an acid solution is especially significant when the solution is used in quantitative analysis or in titration, where the stoichiometry of the reaction must be carefully balanced.