Question

Suppose that \(27.34 \mathrm{~mL}\) of standard \(0.1021 \mathrm{M} \mathrm{NaOH}\) is required to neutralize \(25.00 \mathrm{~mL}\) of an unknown \(\mathrm{H}_{2} \mathrm{SO}_{4}\) solution. Calculate the molarity and the normality of the unknown solution.

Short answer

The molarity of the unknown H2SO4 solution is 0.0558 M and the normality is 0.1116 N.

Step-by-step solution

Calculate moles of NaOH used in the reaction

We're given that 27.34 mL of 0.1021 M NaOH solution is needed to neutralize the H2SO4 solution. We can calculate the moles of NaOH used as follows: moles of NaOH = volume (in L) × molarity moles of NaOH = \(27.34 * 10^{-3} L * 0.1021 M = 0.00279\) moles

Calculate moles of H2SO4 in the reaction

Since 1 mole of H2SO4 reacts with 2 moles of NaOH, we can set up a proportion to find the moles of H2SO4 in the reaction: 1 mole H2SO4 / 0.00279 moles NaOH = moles H2SO4 / 2 moles NaOH Solving for moles of H2SO4: moles H2SO4 = 0.00279 moles NaOH / 2 = 0.001395 moles

Calculate the molarity of H2SO4

We can now find the molarity of the H2SO4 solution using the formula: molarity = moles of solute / volume of solution (in L) Given the volume of the H2SO4 solution is 25.00 mL, we can convert it to liters: volume = 25.00 * 10^{-3} L = 0.025 L Now we can calculate the molarity of the H2SO4 solution: molarity(H2SO4) = 0.001395 moles / 0.025 L = 0.0558 M

Calculate the normality of H2SO4

To find the normality of H2SO4, we need to consider the number of acidic hydrogen ions (H+) in one molecule of H2SO4, which is 2. Normality is given by the formula: normality = molarity × number of H+ ions (in one molecule) So, the normality of the H2SO4 solution is: normality(H2SO4) = 0.0558 M × 2 = 0.1116 N #Conclusion#: The molarity of the unknown H2SO4 solution is 0.0558 M and the normality is 0.1116 N.

Key concepts

Understanding Molarity

Molarity measures the concentration of a solute in a solution. It is defined as the number of moles of solute divided by the total volume of the solution in liters.
The formula is:

• Molarity (M) = Moles of Solute / Volume of Solution in liters

To find molarity, you first need to determine how many moles of the solute are present, and then divide that by the solution's volume, converted into liters.
This concept is crucial in titration calculations, as it allows us to find the exact concentration of a solution.

Decoding Normality

Normality is another way to express the concentration of a solution, often used in acid-base reactions. It represents the gram equivalent weight of a solute per liter of solution.
A key difference from molarity is that normality also considers the reactive capacity of the solute.
The calculation for normality is:

• Normality (N) = Molarity × Number of Reactive Units (e.g., protons for acid, electrons for redox reactions)

In this exercise, since sulfuric acid ( H_2SO_4 ) is a diprotic acid, it can donate two hydrogen ions per molecule, affecting its normality.
This makes normality especially helpful when dealing with reactions where the change involves more than one reactive species.

Exploring Acid-Base Reactions

Acid-base reactions are chemical processes that involve the transfer of protons (H+ ions) between reactants. An acid donates protons, while a base accepts them.
This type of reaction is key in titrations, where one reactant's concentration is determined by reacting it with a solution of known concentration.
In this specific exercise, sodium hydroxide (NaOH) is a strong base, and sulfuric acid (H_2SO_4) is a strong acid. They react in a 2 to 1 ratio, meaning two moles of NaOH are required to neutralize one mole of H_2SO_4. Understanding this stoichiometry is fundamental to performing titration calculations correctly.

Concept of Neutralization

Neutralization is a specific type of acid-base reaction where an acid and a base react to form water and a salt, effectively canceling each other's reactive properties.
In a titration, reaching the neutralization point means the amounts of acid and base added are stoichiometrically equal, usually signaled by a color change from an indicator.
For example, in the exercise, when NaOH reacts completely with H_2SO_4, the reaction reaches neutralization, allowing the calculation of unknown concentrations precisely. This is particularly useful in analytical chemistry to quantify substance concentration.

Stoichiometry Basics

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the amounts of reactants and products in a chemical reaction.
It is essential for understanding how much of a reactant is needed to completely react with another.
In this exercise, stoichiometry helps us determine how many moles of NaOH are needed to neutralize a specified amount of H_2SO_4.
The relationship, as given by the balanced chemical equation, guides us to use the correct proportions to solve for unknown concentrations, such as molarity and normality. Mastering stoichiometry ensures precise and accurate calculations in chemical reactions.