Question

What volume of \(0.905 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) will react with \(26.7 \mathrm{~mL}\) of \(0.554 \mathrm{M} \mathrm{NaOH} ?\) \(\mathrm{H}_{2} \mathrm{SO}_{4}+2 \mathrm{NaOH} \rightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}+2 \mathrm{H}_{2} \mathrm{O}\)

Short answer

8.18 mL of \(0.905\, M \mathrm{H}_{2} \mathrm{SO}_{4}\) is needed.

Step-by-step solution

Identify the Reaction

The balanced chemical equation is \( \mathrm{H}_{2} \mathrm{SO}_{4} + 2 \mathrm{NaOH} \rightarrow \mathrm{Na}_{2} \mathrm{SO}_{4} + 2 \mathrm{H}_{2} \mathrm{O} \). For every 1 mole of \( \mathrm{H}_{2} \mathrm{SO}_{4} \), 2 moles of \( \mathrm{NaOH} \) react.

Calculate Moles of NaOH

Use the concentration and volume of \( \mathrm{NaOH} \) to find moles. The formula to find moles is \( Molarity \times Volume = Moles \). Thus, \( 0.554 \, \mathrm{mol/L} \times 26.7 \, \mathrm{mL}/1000 = 0.0148 \, \mathrm{mol} \) of \( \mathrm{NaOH} \).

Determine Moles of H2SO4 Required

From the balanced equation, \( 1 \, \mathrm{mol} \) of \( \mathrm{H}_{2} \mathrm{SO}_{4} \) reacts with \( 2 \, \mathrm{mol} \) of \( \mathrm{NaOH} \). Thus, \( 0.0148 \, \mathrm{mol} \) of \( \mathrm{NaOH} \) would require \( \frac{0.0148}{2} = 0.0074 \, \mathrm{mol} \) of \( \mathrm{H}_{2} \mathrm{SO}_{4} \).

Calculate Volume of H2SO4 Needed

Use the moles of \( \mathrm{H}_{2} \mathrm{SO}_{4} \) and its concentration to find the volume needed. With \( 0.0074 \, \mathrm{mol} \) and a \( 0.905 \, \mathrm{M} \) solution, \( Volume = \frac{Moles}{Molarity} = \frac{0.0074}{0.905} = 0.00818 \, \mathrm{L} \) which is \( 8.18 \, \mathrm{mL} \).

Key concepts

Stoichiometry

In chemistry, stoichiometry is the science of calculating the quantities of reactants and products in chemical reactions. It relies on the balanced chemical equation to help determine the relationship between the different substances involved. When tackling a problem like the one in our exercise, the first step is identifying the balanced chemical equation. Here, the equation is \( \mathrm{H}_{2} \mathrm{SO}_{4} + 2 \mathrm{NaOH} \rightarrow \mathrm{Na}_{2} \mathrm{SO}_{4} + 2 \mathrm{H}_{2} \mathrm{O} \), indicating that 1 mole of sulfuric acid (\( \mathrm{H}_{2} \mathrm{SO}_{4} \)) reacts with 2 moles of sodium hydroxide (\( \mathrm{NaOH} \)).
Understanding these ratios is essential because they tell us exactly how much of one substance will react with another. This ratio is used to calculate the required moles of reactants. In any stoichiometry problem:

• Identify the mole ratio from the balanced chemical equation.
• Use the mole ratio to find out how much of each substance is needed or produced.

In our exercise, knowing that \( 1 \) mole of \( \mathrm{H}_{2} \mathrm{SO}_{4} \) reacts with \( 2 \) moles of \( \mathrm{NaOH} \) allows us to calculate precisely how many moles of \( \mathrm{H}_{2} \mathrm{SO}_{4} \) are needed for a given amount of \( \mathrm{NaOH} \).

Molarity

Molarity is a measurement of concentration, specifically the number of moles of a solute per liter of solution. It's symbolized by \( M \). The formula to calculate molarity is:\[ Molarity = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \]In our exercise, we use molarity to find the number of moles of \( \mathrm{NaOH} \) in a given volume of solution. With a molarity of \( 0.554 \) M and a volume of \( 26.7 \) mL, which is \( 0.0267 \) L (since you must convert mL to L by dividing by 1000), you can calculate the moles of \( \mathrm{NaOH} \):\[ 0.554 \, \mathrm{mol/L} \times 0.0267 \, \mathrm{L} = 0.0148 \, \mathrm{mol} \]This establishes the base for our stoichiometric calculations. Always remember to:

• Convert the volume of your solution into liters before using it with molarity.
• Use molarity to bridge the gap between volume and moles of a solute in reactions.

Chemical Reactions

Chemical reactions are processes in which substances interact to form new substances with different properties. These reactions are often represented using chemical equations, which show the reactants transforming into products.
The balanced chemical equation for our exercise is \( \mathrm{H}_{2} \mathrm{SO}_{4} + 2 \mathrm{NaOH} \rightarrow \mathrm{Na}_{2} \mathrm{SO}_{4} + 2 \mathrm{H}_{2} \mathrm{O} \). This equation provides critical insights into the nature of the reaction:

• It indicates the number of molecules or moles involved (1 mole of \( \mathrm{H}_{2} \mathrm{SO}_{4} \) reacts with 2 moles of \( \mathrm{NaOH} \)).
• It shows the reactants (what you start with) and the products (what you end with).

Understanding chemical reactions and their stoichiometry helps in predicting the outcomes of reactions, determining the necessary reactant quantities, and optimizing conditions for desired product yields.