Question

What volume of \(0.850 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) is required to neutralize \(20.00 \mathrm{~mL}\) of \(0.1033 \mathrm{MaOH}\) ? (Begin by writing a balanced chemical equation for the reaction.)

Short answer

Therefore, the volume of \(0.850 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) required to neutralize \(20.00 \mathrm{~mL}\) of \(0.1033 \mathrm{MaOH}\) is approximately 1.214 mL.

Step-by-step solution

Write the Balanced Chemical Equation

The balanced equation for the neutralization of sulfuric acid (H2SO4) with the hydroxide ion (OH-) is: \[ H_2SO_4 + 2 OH^- \to SO_4^{2-} + 2 H_2O \] This shows that one mole of H2SO4 reacts with two moles of OH-.

Calculate the Number of Moles of OH-

Molarity (M) is defined as moles of solute per liter of solution. So, the number of moles of OH- in the 20.00 mL of 0.1033 M NaOH, using the relation \(Moles = Molarity \times Volume\) (volume in liters), is given by: \[ Moles(OH^-) = 0.1033 M \times 20.00 ml \times \frac{1L}{1000 ml} = 0.002066 moles (OH^-) \]

Calculate the Required Volume of H2SO4

From the balanced chemical equation, it can be seen that 1 mole of H2SO4 neutralizes 2 moles of OH-. So, the number of moles of H2SO4 required to neutralize 0.002066 moles of OH- will be \(0.002066 moles (OH^-) \times \frac{1 mol(H2SO4)}{2 mol(OH^-)} = 0.001033 moles (H2SO4)\). The volume of H2SO4 required can be calculated by rearranging the molarity formula: \[ Volume (H2SO4) = \frac{Moles(H2SO4)}{Molarity(H2SO4)} = \frac{0.001033 mol}{0.850 M} = 0.001214 liters = 1.214 ml \]

Key concepts

Molarity

Molarity is a key concept in chemistry, especially when dealing with solutions and reactions. It is a measure of the concentration of a solute in a solution. Specifically, molarity (M) is defined as the number of moles of solute per liter of solution. The formula used to calculate molarity is:
\[M = \frac{\text{moles of solute}}{\text{liters of solution}}\]This means that if you know the number of moles of a substance and the volume of the solution, you can determine its molarity by dividing the two. Molarity is crucial for understanding how solutions react with each other, as it allows chemists to calculate exactly how much of one substance is needed to react with another. In the context of the given problem, molarity is used to determine how many moles of hydroxide ions are present in the sodium hydroxide solution.

Balanced Chemical Equation

A balanced chemical equation is foundational to understanding chemical reactions. It shows the reactants and products in a chemical reaction and ensures that the law of conservation of mass is followed; meaning, atoms are neither created nor destroyed in a chemical reaction.
Each side of the equation must have the same number of each type of atom. In the exercise, the balanced equation for the reaction between sulfuric acid (\(\text{H}_2\text{SO}_4\))and hydroxide ions (\(\text{OH}^-\)) is given by:
\[\text{H}_2\text{SO}_4 + 2\text{OH}^- \rightarrow \text{SO}_4^{2-} + 2\text{H}_2\text{O}\]This equation makes it clear that one mole of sulfuric acid reacts with two moles of hydroxide ions to produce sulfate ions and water. Such equations are necessary to identify the mole ratios between reactants and products, which informs how much of a reactant is needed or how much product will be formed in a reaction.

Stoichiometry

Stoichiometry involves calculations that relate the quantities of reactants and products in a chemical reaction. It derives from the balanced chemical equation, providing a quantitative roadmap for predicting how much of a substance will react or be produced.
In the given exercise, stoichiometry was used to determine the amount of sulfuric acid (\(\text{H}_2\text{SO}_4\)) necessary to neutralize a given amount of sodium hydroxide (\(\text{NaOH}\)).

• First, the moles of hydroxide ions were calculated using the formula: \[\text{Moles (OH}^-\text{)} = \text{Molarity} \times \text{Volume}\]
• Then, using the stoichiometric ratio from the balanced equation, the moles of \(\text{H}_2\text{SO}_4\) needed to neutralize the hydroxide ions were determined.
• Finally, the volume of sulfuric acid solution needed was determined by rearranging the molarity equation to solve for volume.

Stoichiometry is essential for predicting the outcomes of reactions and ensuring that chemical processes are both efficient and economical.