Question

Calculate the normality of each of the following solutions. a. $0.50\mathrm{M}$ acetic acid, ${\mathrm{HC}}_2{\mathrm{H}}_3{\mathrm{O}}_2$ b. $0.00250\mathrm{M}$ sulfuric acid, ${\mathrm{H}}_2{\mathrm{SO}}_4$ c. $0.10\mathrm{M}$ potassium hydroxide, $\mathrm{KOH}$

Short answer

The normality of each solution is: a. Acetic Acid (${\mathrm{HC}}_2{\mathrm{H}}_3{\mathrm{O}}_2$): $0.50\mathrm{N}$ b. Sulfuric Acid (${\mathrm{H}}_2{\mathrm{SO}}_4$): $0.00500\mathrm{N}$ c. Potassium Hydroxide ($\mathrm{KOH}$): $0.10\mathrm{N}$

Step-by-step solution

Review the relationship between molarity and normality

The relationship between molarity (M) and normality (N) is given by the following formula: $$N=M\times n$$ where $n$ is the number of equivalents per mole of solute. More generally, the number of equivalents of a solute is related to its molecular formula. For an acid, the number of equivalents is equal to the number of hydrogen ions (${\mathrm{H}}^{+}$) that can be produced by the acid, and for a base, it is the number of hydroxide ions (${\mathrm{OH}}^{-}$) that can be produced by the base. In this exercise, we need to find the normality of three different solutions, including two acids and one base.

Determine the number of equivalents for each solute

First, we need to determine the number of equivalents per mole of solute for each of the given solutions: a. Acetic Acid (${\mathrm{HC}}_2{\mathrm{H}}_3{\mathrm{O}}_2$): Acetic acid has one hydrogen ion (${\mathrm{H}}^{+}$) that can be released, so it has one equivalent per mole. b. Sulfuric Acid (${\mathrm{H}}_2{\mathrm{SO}}_4$): Sulfuric acid has two hydrogen ions (${\mathrm{H}}^{+}$) that can be released, so it has two equivalents per mole. c. Potassium Hydroxide ($\mathrm{KOH}$): Potassium hydroxide has one hydroxide ion (${\mathrm{OH}}^{-}$) that can be released, so it has one equivalent per mole.

Calculate the normality of each solution

Now, we can calculate the normality of each solution using the formula $N=M\times n$ from Step 1. a. Acetic Acid ($0.50\mathrm{M}$ ${\mathrm{HC}}_2{\mathrm{H}}_3{\mathrm{O}}_2$): $$N=(0.50\mathrm{M})\times (1)=0.50\mathrm{N}$$ b. Sulfuric Acid ($0.00250\mathrm{M}$ ${\mathrm{H}}_2{\mathrm{SO}}_4$): $$N=(0.00250\mathrm{M})\times (2)=0.00500\mathrm{N}$$ c. Potassium Hydroxide ($0.10\mathrm{M}$ $\mathrm{KOH}$): $$N=(0.10\mathrm{M})\times (1)=0.10\mathrm{N}$$ So, the normality of each solution is: a. Acetic Acid (${\mathrm{HC}}_2{\mathrm{H}}_3{\mathrm{O}}_2$): $0.50\mathrm{N}$ b. Sulfuric Acid (${\mathrm{H}}_2{\mathrm{SO}}_4$): $0.00500\mathrm{N}$ c. Potassium Hydroxide ($\mathrm{KOH}$): $0.10\mathrm{N}$

Key concepts

Molarity to Normality Conversion

Understanding how to convert molarity to normality is a critical skill in chemistry that aids in quantifying solution concentrations. Molarity (M) refers to the number of moles of a solute per liter of solution, while normality (N) describes the number of equivalents of the solute per liter of solution.

To perform the conversion, one must first identify the number of equivalents per mole of the solute in question. This is represented by the equation:
$$N=M\times n$$
where $n$ is the number of equivalents per mole. For acids, this is equal to the number of dissociable hydrogen ions, and for bases, it's the number of hydroxide ions the base can donate.

Let's apply this to a practical example:

• A solution with a molarity of $0.50M$ acetic acid has one dissociable hydrogen ion, so its normality is also $0.50N$ because $N=0.50\times 1$.
• In contrast, sulfuric acid, with a molarity of $0.00250M$, can dissociate two hydrogen ions. This doubles the number of equivalents per mole, resulting in a normality of $0.00500N$ because $N=0.00250\times 2$.

By understanding this conversion, students can accurately measure and predict the outcomes of reactions where the concentration of reactive species is crucial, such as in titrations.

Equivalents per Mole

The concept of equivalents per mole is integral to the field of chemistry, especially when dealing with reactions involving ions. An equivalent is the amount of a substance that can react with a specified number of moles of another substance. In the case of acids and bases, the equivalent is linked to the substance's ability to donate or accept protons.

For instance:

• Acetic acid, ${\mathrm{HC}}_2{\mathrm{H}}_3{\mathrm{O}}_2$, has one reactive hydrogen ion per molecule, corresponding to one equivalent per mole.
• Sulfuric acid, ${\mathrm{H}}_2{\mathrm{SO}}_4$, has two reactive hydrogen ions per molecule, meaning it has two equivalents per mole.
• Similarly, potassium hydroxide, $\mathrm{KOH}$, can produce one hydroxide ion per molecule, leading to one equivalent per mole.

Students must grasp the concept of equivalents to understand how substances will behave and interact in various chemical processes, particularly when balancing equations or converting between different concentration units.

Acid-Base Titration Chemistry

Acid-base titration is a laboratory technique used to determine the concentration of a known reactant in a solution. During the titration process, a solution of known concentration (the titrant) is gradually added to a solution of the substance being measured (the analyte) until the reaction between the two is complete. Indicators or pH meters are typically used to detect the completion point or endpoint of the titration.

In acid-base titrations, the normality of the acid or base plays a crucial role as it directly correlates to the solution's ability to neutralize the other reactant. For example, when titrating acetic acid with a base, knowing the normality of the acetic acid solution allows for precise calculations on how much base is needed to reach the equivalence point – where the number of acid equivalents equals the number of base equivalents.

Successful titrations lead to accurate determinations of solution concentrations, involving the following key steps:

• Accurately measuring the volume of titrant used.
• Understanding the stoichiometry of the reaction involved.
• Appropriately selecting an indicator or using a pH meter for detecting the endpoint.

Titration curves are often plotted to visualize changes in pH and to pinpoint the exact moment of neutralization, which is central to the evaluation of an acid-base titration's outcome.