Question

An impure sample of zinc \((\mathrm{Zn})\) is treated with an excess of sulfuric acid \(\left(\mathrm{H}_{2} \mathrm{SO}_{4}\right)\) to form zinc sulfate \(\left(\mathrm{ZnSO}_{4}\right)\) and molecular hydrogen \(\left(\mathrm{H}_{2}\right) .\) (a) Write a balanced equation for the reaction. (b) If \(0.0764 \mathrm{~g}\) of \(\mathrm{H}_{2}\) is obtained from \(3.86 \mathrm{~g}\) of the sample, calculate the percent purity of the sample. (c) What assumptions must you make in part ( \(b\) )?

Short answer

The percent purity of the zinc sample is 64.0%. We assume all hydrogen comes from the zinc reaction with no side reactions.

Step-by-step solution

Write the balanced chemical equation

The reaction between zinc \((\mathrm{Zn})\) and sulfuric acid \((\mathrm{H}_{2} \mathrm{SO}_{4})\) yields zinc sulfate \((\mathrm{ZnSO}_{4})\) and hydrogen gas \((\mathrm{H}_{2})\). The balanced equation for this reaction is:\[ \mathrm{Zn} + \mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{ZnSO}_{4} + \mathrm{H}_{2}\]

Calculate moles of hydrogen gas produced

Given the mass of hydrogen gas produced is 0.0764 g, we can calculate the moles of hydrogen gas using the molar mass of \(\mathrm{H}_{2}\), which is approximately 2.02 g/mol. The moles of \(\mathrm{H}_{2}\) are calculated as:\[\text{Moles of } \mathrm{H}_{2} = \frac{0.0764 \text{ g}}{2.02 \text{ g/mol}} = 0.0378 \text{ mol}\]

Calculate moles of zinc reacted

From the balanced equation, we see that 1 mole of \(\mathrm{Zn}\) produces 1 mole of \(\mathrm{H}_{2}\). Therefore, 0.0378 moles of \(\mathrm{H}_{2}\) correspond to 0.0378 moles of \(\mathrm{Zn}\).

Calculate the mass of zinc reacted

Now, we calculate the mass of zinc that reacted using the molar mass of zinc, which is approximately 65.38 g/mol.\[\text{Mass of } \mathrm{Zn} = 0.0378 \text{ mol} \times 65.38 \text{ g/mol} = 2.47 \text{ g}\]

Calculate percent purity of the sample

The percent purity of zinc in the sample is calculated by dividing the mass of zinc that reacted (2.47 g) by the total mass of the impure sample (3.86 g) and then multiplying by 100 to get a percentage.\[\text{Percent Purity} = \left(\frac{2.47 \text{ g}}{3.86 \text{ g}}\right) \times 100 = 64.0\%\]

Assumptions in the calculation

In part (b), we assume that all of the produced hydrogen gas came from zinc reacting with sulfuric acid. We also assume there are no side reactions or other sources of hydrogen.

Key concepts

Stoichiometry

Stoichiometry is at the heart of understanding chemical reactions, allowing us to quantify how reactants transform into products. It hinges on the principle of the conservation of mass, meaning what you put into a reaction must come out, just rearranged. By using stoichiometry, you can predict the outcomes of chemical reactions and determine the required amounts of reactants.

In a chemical reaction, the coefficients in the balanced equation tell us the ratio of moles of each substance involved. For example, in the reaction between zinc and sulfuric acid:

• 1 mole of Zn reacts with 1 mole of H₂SO₄
• This produces 1 mole of ZnSO₄ and 1 mole of H₂

This provides a straightforward way to relate amounts of substances. By knowing the mole of one component, we can calculate the amount of each other substance involved in the reaction.

Percent Purity Calculation

Percent purity is a measure of the amount of a specific substance contained in a given sample. It's often used when dealing with impure substances that undergo a chemical transformation. In this context, understanding how to calculate percent purity is useful for determining the quality of a sample.

To calculate percent purity:

• Determine the mass of the pure substance that reacted, in our case, the zinc.
• Divide the mass of the reacted pure substance by the total mass of the sample.
• Multiply the result by 100 to express it as a percentage.

This allows chemists to assess how much of a sample is the actual useful material versus impurities.

Balanced Chemical Equations

Balanced chemical equations are essential in reactions to illustrate how reactants transform into products according to stoichiometry. Balancing equations means ensuring that atoms of each element are conserved in the reaction.

In the equation for zinc and sulfuric acid,

• Zn + H₂SO₄ → ZnSO₄ + H₂

This balanced equation indicates that each atom involved is accounted for. We have one zinc atom and one mole of sulfuric acid transforming into one mole of zinc sulfate and one mole of molecular hydrogen.
Balancing equations is often about ensuring the same number of atoms per element on both sides of the equation, and it reflects the stoichiometry of the reaction.

Mole Concept

The mole concept is a cornerstone of chemistry, serving as a bridge between the atomic and macroscopic worlds. It allows scientists to count atoms, molecules, or particles using a dedicated unit called the mole. One mole contains exactly Avogadro's number of molecules or atoms, which is approximately \( 6.022 \times 10^{23} \), allowing us to translate mass into moles and vice versa.

To apply the mole concept:

• Identify the substance's molar mass.
• Use the mass of the given sample to calculate moles using the formula: \[ \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} \]

In our exercise, the calculation of moles of hydrogen gas helps to understand the relationship between the amounts of reactants and products involved in the reaction.