Question

When small quantities of elemental hydrogen gas are needed for laboratory work, the hydrogen is often generated by chemical reaction of a metal with acid. For example, zinc reacts with hydrochloric acid, releasing gaseous elemental hydrogen: $$\mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \rightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g)$$ What mass of hydrogen gas is produced when \(2.50 \mathrm{g}\) of zinc is reacted with excess aqueous hydrochloric acid?

Short answer

When 2.50 g of zinc reacts with excess aqueous hydrochloric acid, 0.077 g of hydrogen gas is produced.

Step-by-step solution

Write down the balanced chemical equation

The balanced chemical equation is: \( \mathrm{Zn}(s) + 2 \mathrm{HCl}(aq) \rightarrow \mathrm{ZnCl}_{2}(aq) + \mathrm{H}_{2}(g) \)

Find the molar mass of the substances involved in the reaction

Using the periodic table, we find the molar masses of the substances involved in the reaction: - Molar mass of Zn: 65.38 g/mol - Molar mass of H₂: 2.02 g/mol

Calculate the moles of zinc reacted

Use the molar mass of Zn to convert the mass of zinc reacted into moles: Moles of Zn = (Mass of Zn) / (Molar mass of Zn) = (2.50 g) / (65.38 g/mol) = 0.0383 mol

Use the stoichiometry of the balanced equation

From the equation, we know that one mole of zinc reacts to produce one mole of hydrogen gas: 1 mole Zn → 1 mole H₂ So, the moles of hydrogen gas produced is the same as the moles of zinc reacted, which is 0.0383 moles.

Calculate the mass of hydrogen gas produced

Use the molar mass of H₂ to convert moles of hydrogen gas produced to mass: Mass of H₂ = (Moles of H₂) * (Molar mass of H₂) = (0.0383 mol) * (2.02 g/mol) = 0.077 g Therefore, when 2.50 g of zinc reacts with excess aqueous hydrochloric acid, 0.077 g of hydrogen gas is produced.

Key concepts

Chemical Reactions

Understanding chemical reactions is fundamental to grasping various concepts in chemistry. A chemical reaction involves the transformation of one or more substances, known as reactants, into one or more different substances, known as products. This transformation occurs through the breaking and forming of chemical bonds.

As seen in the textbook exercise, zinc reacts with hydrochloric acid, a reaction that is critical for laboratory procedures that require elemental hydrogen gas. The hydrogen gas is not just a byproduct; it is essential in various scientific experiments. The chemical equation \( \text{Zn}(s) + 2 \text{HCl}(aq) \rightarrow \text{ZnCl}_2(aq) + \text{H}_2(g) \) illustrates a single replacement reaction where zinc displaces hydrogen in hydrochloric acid, leading to the creation of zinc chloride and hydrogen gas.

What makes this reaction particularly interesting is the 1:1 molar ratio between zinc and hydrogen gas, which becomes the basis for stoichiometric calculations. This ratio means that for every mole of zinc reacting, a mole of hydrogen gas is produced.

Molar Mass Calculation

The concept of molar mass is a cornerstone in stoichiometry, as it relates the mass of a substance to the amount of substance in moles. Calculating the molar mass of a substance requires knowing the atomic masses of the constituent elements and combining them according to the molecular formula.

For example, to find the molar mass of zinc \( \text{Zn} \), one would look up the atomic mass on the periodic table, which is approximately 65.38 g/mol. Similarly, hydrogen gas \( \text{H}_2 \) has a molar mass calculated by doubling the atomic mass of hydrogen since there are two hydrogen atoms in each molecule of hydrogen gas. Thus, the molar mass of \( \text{H}_2 \) is approximately 2.02 g/mol.

These numbers are not arbitrary; they represent the amount of the substance that contains Avogadro's number of molecules or atoms. In other words, one mole of any substance contains the same number of entities as there are atoms in exactly 12 grams of carbon-12.

Reacting Masses

Reacting masses in stoichiometry refer to the quantities of reactants and products involved in a chemical reaction, often measured in grams. Stoichiometric calculations allow us to predict the mass of a substance that will react or be produced in a chemical reaction based on the balanced chemical equation.

The key to these calculations is the mole ratio derived from the balanced equation. This is critical for problems where one needs to calculate the number of moles of each reactant needed to produce a given amount of product, or conversely, the amount of product generated from specific moles or masses of reactants.

In the case of the zinc and hydrochloric acid reaction given in the original exercise, one uses the molar mass of zinc to determine the moles of zinc reacted. Those moles, in turn, provide the ratio needed to calculate the mass of hydrogen gas produced. The solution is straightforward because the mole ratio is 1:1, illustrating the elegance and simplicity of stoichiometric principles in relating the reacting masses of substances through their molar equivalences.