Problem 90 - Chemistry and Chemical Reactivity

Question

What volume of \(0.054 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) is required to react completely with \(1.56 \mathrm{g}\) of \(\mathrm{KOH} ?\)

Step-by-Step Solution

Answer

257 mL of 0.054 M \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is needed.

Step 1: Write the balanced chemical equation

First, identify the balanced chemical equation for the reaction between sulfuric acid (\(\mathrm{H}_{2} \mathrm{SO}_{4}\)) and potassium hydroxide (\(\mathrm{KOH}\)). The balanced equation is: \[\mathrm{H}_{2} \mathrm{SO}_{4}(aq) + 2\mathrm{KOH}(aq) \rightarrow \mathrm{K}_{2}\mathrm{SO}_{4}(aq) + 2\mathrm{H}_{2}\mathrm{O}(l)\] This equation tells you that one mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) reacts with two moles of \(\mathrm{KOH}\).

Step 2: Calculate moles of KOH

Next, calculate how many moles of \(\mathrm{KOH}\) you have using its molar mass. The molar mass of \(\mathrm{KOH}\) is approximately \(56.11 \, \mathrm{g/mol}\). So the number of moles of \(\mathrm{KOH}\) is given by: \[\text{moles of } \mathrm{KOH} = \frac{1.56 \, \text{g}}{56.11 \, \mathrm{g/mol}} \approx 0.0278 \, \text{mol}\]

Step 3: Use the stoichiometry of the reaction

Using the balanced chemical equation, we know that 2 moles of \(\mathrm{KOH}\) react with 1 mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\). Therefore, 0.0278 moles of \(\mathrm{KOH}\) would react with: \[\text{moles of } \mathrm{H}_{2} \mathrm{SO}_{4} = \frac{0.0278}{2} \approx 0.0139 \, \text{mol}\]

Step 4: Calculate the volume of H2SO4 solution required

Now that we have the moles of \(\mathrm{H}_{2} \mathrm{SO}_{4}\), we can find the volume needed using the molarity of the solution. The formula for molarity is: \[\text{molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\] Rearranging for volume:\[\text{volume} = \frac{\text{moles of } \mathrm{H}_{2} \mathrm{SO}_{4}}{\text{molarity}} = \frac{0.0139}{0.054}\approx 0.257 \text{ L} = 257 \text{ mL} \] Therefore, approximately 257 mL of \(0.054 \, \mathrm{M} \, \mathrm{H}_{2} \mathrm{SO}_{4}\) is required.

Key Concepts

Chemical Reaction

In a chemical reaction, substances known as reactants interact to form new substances dubbed products. An example of a chemical reaction is when sulfuric acid (\(\mathrm{H}_{2}\mathrm{SO}_{4}\)) and potassium hydroxide (\(\mathrm{KOH}\)) react. Here, the reactants \(\mathrm{H}_{2}\mathrm{SO}_{4}\) and \(\mathrm{KOH}\) combine to produce potassium sulfate (\(\mathrm{K}_{2}\mathrm{SO}_{4}\)) and water (\(\mathrm{H}_{2}\mathrm{O}\)).

• A chemical reaction is a process where chemical bonds are formed or broken to create different substances.
• Evidence of a reaction includes color changes, temperature changes, gas production, or the formation of a precipitate.

By understanding this concept, we can predict the products and understand the conversion of reactants into products.

Molarity

Molarity is an essential concept in chemistry. It tells us the concentration of a solution. Technically, molarity is defined as the number of moles of solute per liter of solution. The unit of molarity is \(\text{M}\), which stands for moles per liter.

• Molarity (\(M\)) is calculated using the formula: \(M = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\).
• A high molarity means a more concentrated solution.

In the given problem, the sulfuric acid has a molarity of \(0.054 \text{M}\), indicating how many moles of sulfuric acid are present in one liter of the solution.

Balanced Chemical Equation

A balanced chemical equation is crucial because it tells us the proportions in which reactants combine to form products. It ensures that the law of conservation of mass is satisfied, meaning atoms are neither created nor destroyed.

• The coefficients in a balanced equation indicate the number of moles involved for each substance.

For our example, the balanced equation\[\mathrm{H}_{2}\mathrm{SO}_{4}(aq) + 2\mathrm{KOH}(aq) \rightarrow \mathrm{K}_{2}\mathrm{SO}_{4}(aq) + 2\mathrm{H}_{2}\mathrm{O}(l)\]indicates that one mole of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) reacts with two moles of \(\mathrm{KOH}\) to yield one mole of \(\mathrm{K}_{2}\mathrm{SO}_{4}\) and two moles of water. Correctly balancing equations is fundamental for accurate chemical analysis and calculations.

Mole Calculations

Mole calculations are a fundamental aspect of solving chemistry problems involving quantities. A mole is a standard unit in chemistry that quantifies the amount of substance.

• To find moles from mass, use the formula: \(\text{moles} = \frac{\text{mass in grams}}{\text{molar mass}}\).
• Mole calculations help in determining the proportions of reactants needed or products formed in a reaction.

In the original problem, the analysis starts by calculating the moles of \(\mathrm{KOH}\) from its given mass of \(1.56 \, \text{g}\) using its molar mass of \(56.11 \, \mathrm{g/mol}\), resulting in approximately \(0.0278 \, \text{mol}\). Understanding mole calculations helps bridge the gap between the micro world of atoms and the macro world of grams and liters.