Question

What volume of \(0.250 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) is needed to react with \(50.0 \mathrm{~mL}\) of \(0.100 \mathrm{M}\) \(\mathrm{NaOH}\) ? The equation is $$ \mathrm{H}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{NaOH}(a q) \longrightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) $$

Short answer

10.0 mL of 0.250 M H2SO4 is needed.

Step-by-step solution

Identify the Balanced Chemical Equation

The balanced chemical equation provided is \(\mathrm{H}_{2} \mathrm{SO}_{4}(a q) + 2 \mathrm{NaOH}(a q) \rightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}(a q) + 2 \mathrm{H}_{2} \mathrm{O}(l)\). This indicates that one mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) reacts with two moles of \(\mathrm{NaOH}\).

Calculate Moles of NaOH

Calculate the number of moles of \(\mathrm{NaOH}\) using its molarity and volume. The formula is: \[\text{moles of NaOH} = \text{Molarity} \times \text{Volume (in Liters)}\]Substituting the given values: \(0.100 \, \text{M} \times 0.0500 \, \text{L} = 0.0050 \, \text{moles of NaOH}\).

Relate Moles of H2SO4 to Moles of NaOH

Using the stoichiometry from the balanced equation, determine the moles of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) needed. From the equation, 2 moles of \(\mathrm{NaOH}\) react with 1 mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\). Therefore, moles of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) = \( 0.0050 \, \text{moles of NaOH} \div 2 = 0.0025 \, \text{moles of H}_{2} \mathrm{SO}_{4}\).

Calculate Volume of H2SO4 Required

Use the moles of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and its molarity to find the required volume: \[\text{Volume (L)} = \frac{\text{Moles of H}_{2} \mathrm{SO}_{4}}{\text{Molarity of H}_{2} \mathrm{SO}_{4}}\]Hence, \(\text{Volume} = \frac{0.0025}{0.250} = 0.0100 \, \text{L}\). Therefore, the volume in mL is \(0.0100 \, \text{L} \times 1000 \, \text{mL/L} = 10.0 \, \text{mL}\).

Key concepts

Understanding Molarity

Molarity is a fundamental concept in chemistry that refers to the concentration of a solution. It is defined as the number of moles of solute per liter of solution. The formula for molarity (\( M \)) is: \[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]This allows chemists to express how concentrated a solution is. For example, if you have 1 mole of a solute in 1 liter of solution, the molarity is 1 M.
Knowing the molarity is crucial for stoichiometry calculations, especially in reactions where precise amounts of chemicals are needed.

• Molarity helps us predict how substances will react.
• It allows for the calculation of the volume of solutions needed to achieve desired reactions.

In our exercise, the molarity of \( \mathrm{NaOH} \) and \( \mathrm{H}_{2} \mathrm{SO}_{4} \) are given as 0.100 M and 0.250 M respectively. These values help determine how much of each reactant is necessary for the reaction to occur completely.

Balanced Chemical Equation

A balanced chemical equation is a representation of a chemical reaction where the number of atoms for each element is the same on both sides – the reactants and the products. This balance adheres to the law of conservation of mass, which states that mass is neither created nor destroyed in a chemical reaction.
For our exercise, the balanced equation is:\[ \mathrm{H}_{2} \mathrm{SO}_{4}(aq) + 2 \mathrm{NaOH}(aq) \rightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}(aq) + 2 \mathrm{H}_{2} \mathrm{O}(l) \]This equation tells us that one mole of sulfuric acid \( \mathrm{H}_{2} \mathrm{SO}_{4} \) reacts with two moles of sodium hydroxide \( \mathrm{NaOH} \) to form sodium sulfate \( \mathrm{Na}_{2} \mathrm{SO}_{4} \) and water.

• The coefficients in front of substances show the ratio of molecules or moles needed.
• This equation ensures that all atoms are accounted for, maintaining mass balance.

Understanding the balance is crucial for performing stoichiometric calculations, such as determining the amount of reactant needed or predicting the amount of product formed.

Acid-Base Titration

Acid-base titration is an analytical technique used to determine the concentration of a solution by reacting it with a solution of known concentration. This process involves slowly adding one solution (the titrant) to another (the analyte) until the reaction reaches completion, which is usually indicated by a change in color (indicator) or a pH change.
In our problem, \( \mathrm{H}_{2} \mathrm{SO}_{4} \) is the solution of known concentration and \( \mathrm{NaOH} \) is the solution we want to react it with.
The balanced equation shows us the stoichiometry needed for the titration process:\[ \mathrm{H}_{2} \mathrm{SO}_{4} + 2 \mathrm{NaOH} \rightarrow \mathrm{Na}_{2} \mathrm{SO}_{4} + 2 \mathrm{H}_{2} \mathrm{O} \]This equation helps determine how much of \( \mathrm{H}_{2} \mathrm{SO}_{4} \) is required to completely react with a given amount of \( \mathrm{NaOH} \).

• The molarity and volume of \( \mathrm{NaOH} \) are used to find its moles.
• The moles are then related to \( \mathrm{H}_{2} \mathrm{SO}_{4} \) using the balanced equation.

Understanding titrations is vital for analytical chemistry, allowing chemists to precisely control the concentrations and amounts of reactants in a chemical reaction.