Problem 113 - Chemistry

Question

An impure sample of zinc (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 (b)?

Step-by-Step Solution

Answer

a) The balanced chemical equation is: \( Zn_{(s)} + H_{2}SO_{4_{(aq)}} \rightarrow ZnSO_{4_{(aq)}} + H_{2_{(g)}}\). b) The percent purity of the zinc sample is approximately 61.4%. c) Assumptions include: The hydrogen gas produced came solely from the reaction of zinc with sulfuric acid. 2) The volume of hydrogen gas was measured at STP. 3) There weren't any other reactions involved besides the one specified.

Step 1: Write a balanced equation for the reaction

First, a balanced chemical equation needs to be formed for the given reaction. This is: \( Zn_{(s)} + H_{2}SO_{4_{(aq)}} \rightarrow ZnSO_{4{(aq)}} + H_{2_{(g)}}\). It's balanced because there are equal amounts of each atom on both the reactant and product sides.

Step 2: Calculate the percent purity of the sample

The reaction tells us that for every one mole of zinc reacted, one mole of hydrogen gas is produced. Thanks to Avogadro's law, it's known that one mole of any gas at STP is about 22.4L. Also, 1 mole of hydrogen gas has a mass of about 2g. Given that 0.0764g of \(H_{2}\) was obtained, its volume can be calculated using \(V = \frac{{0.0764g}}{{2g/mol}} * 22.4 L/mol\) which equals about 0.86L. This volume corresponds to the amount of zinc that reacted. Consequently, the mass of pure zinc in the sample can be derived thus: \(\frac{{0.86L}}{{22.4L/mol}} * 65.38g/mol\), which equals approximately 2.37g. The percent purity of the sample is then \(\frac{{2.37g}}{{3.86g}} * 100% = 61.4% \)

Step 3: Assumptions made in the calculations

The assumptions include: 1) All the hydrogen gas produced came solely from the reaction of zinc with sulfuric acid. 2) The volume of hydrogen gas was measured at STP. 3) There were no other reactions involved besides the one provided.

Key Concepts

Chemical Reaction Balancing

At the heart of understanding any chemical process is the concept of chemical reaction balancing. This involves making sure that the number of atoms for each element involved is equal on both sides of the chemical equation. Why is this important? Well, it takes us back to a fundamental principle known as the Law of Conservation of Mass, which indicates that mass is neither created nor destroyed in a chemical reaction. Thus, the mass of the reactants must equal the mass of the products.

To balance a chemical equation, we write coefficients in front of the chemical formulas to ensure that the number of atoms of each element is the same on both sides of the equation. For instance, in our example with zinc reacting with sulfuric acid, we ensure that there is one zinc atom, one sulfur atom, four oxygen atoms, and two hydrogen atoms reacting to yield one zinc atom, one sulfur atom, four oxygen atoms, and two hydrogen atoms in the products. Balancing chemical reactions is pivotal not only for theoretical exercises but also for practical lab work where measurements need to be precise.

Avogadro's Law

When dealing with gases, Avogadro's law becomes a crucial player in chemical calculations. It tells us that equal volumes of gases, at the same temperature and pressure, contain equal numbers of molecules. In simpler terms, one mole of any gas occupies the same volume as one mole of any other gas, when measured at the same temperature and pressure. The standard volume is often taken as 22.4 liters (L) at standard temperature and pressure (STP).

For our zinc purity example, we used Avogadro's law to derive the volume of hydrogen gas from the mass of the gas produced. Knowing that one mole of hydrogen gas has a molar mass of approximately 2 grams allows us to convert the given mass of hydrogen gas into moles and then into volume using the standard molar volume. This standardization makes calculations universal and comparisons between experiments feasible.

Stoichiometry

Stoichiometry is the mathematical relationship between the quantities of reactants and products in a chemical reaction. It's the calculation that chemists use to determine how much of each substance is consumed and produced in a reaction - based on the balanced chemical equation. Stoichiometric calculations inform us how much reactant is needed to produce a certain amount of product, or, conversely, how much product can be made from a certain amount of reactant.

In the example where we calculate the percent purity of zinc, stoichiometry is key. After balancing the equation, we know the molar ratio between zinc and hydrogen gas is 1:1. If we know the amount of hydrogen produced, we can work out how much zinc reacted and eventually deduce its purity. Stoichiometry guides us through this quantitative analysis to reliably interpret experimental data.

Chemical Equation

A chemical equation is essentially a recipe for a chemical reaction. It tells you what substances react, known as reactants, and what substances are produced, known as products. While writing a chemical equation, we ensure that it is balanced; this reflects the Law of Conservation of Mass. Chemical equations provide a shorthand method of representing a reaction in a clear, concise way, using chemical symbols and formulas, rather than words. Knowing how to interpret and use these equations is fundamental for studying and understanding chemistry.

To illustrate, in the given exercise, the chemical equation we balanced describes the reaction of zinc with sulfuric acid to produce zinc sulfate and hydrogen gas. By understanding this equation, we can discern the mole-to-mole relationships between reactants and products, which then sets the stage for stoichiometric calculations, like finding the percent purity of a sample.