Question

Consider the following reaction: $$ \mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \rightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g) $$ What mass of zinc metal should be taken so as to produce \(125 \mathrm{~mL}\) of \(\mathrm{H}_{2}\) measured at STP when reacted with excess hydrochloric acid?

Short answer

A mass of approximately 0.364 g of zinc metal should be taken to produce 125 mL of hydrogen gas when reacted with excess hydrochloric acid, considering the stoichiometric ratio and conditions at STP.

Step-by-step solution

Understand the given reaction

The given reaction is a single replacement reaction, where zinc reacts with hydrochloric acid to produce zinc chloride and hydrogen gas. Here's the balanced chemical equation: \[ \mathrm{Zn}(s) + 2 \mathrm{HCl}(aq) \rightarrow \mathrm{ZnCl}_{2}(aq) + \mathrm{H}_{2}(g) \] First, we need to relate the amount of hydrogen gas production to the amount of zinc.

Determine the stoichiometric ratio

From the balanced equation, we can see that 1 mole of zinc reacts with 2 moles of hydrochloric acid to produce 1 mole of hydrogen gas. Hence, the stoichiometric ratio between zinc and hydrogen gas is 1:1. That is, for every mole of zinc, 1 mole of hydrogen gas is produced.

Calculate moles of hydrogen gas

We are given that 125 mL of hydrogen gas is produced at STP. At STP, 1 mole of any gas occupies 22.4 L or 22400 mL. Based on this, we can calculate the moles of hydrogen gas produced: Moles of hydrogen gas = \( \frac{Volume \ of \ hydrogen \ gas}{Molar \ volume \ at \ STP} \) Moles of hydrogen gas = \( \frac{125 \, mL}{22400 \, mL/mol} \approx 0.00558 \, mol \)

Calculate moles of zinc required

Since the stoichiometric ratio between zinc and hydrogen gas is 1:1, the number of moles of zinc required is the same as the moles of hydrogen gas produced: Moles of zinc required = 0.00558 mol

Determine the mass of zinc required

Now that we know the moles of zinc required, we can calculate the mass of zinc required using the molar mass of zinc (65.38 g/mol): Mass of zinc required = Moles of zinc required × Molar mass of zinc Mass of zinc required = 0.00558 mol × 65.38 g/mol ≈ 0.364 g Therefore, a mass of approximately 0.364 g of zinc metal should be taken to produce 125 mL of hydrogen gas when reacted with excess hydrochloric acid.

Key concepts

Chemical Reaction Equations

A chemical reaction equation is a symbolic representation showing both the starting compounds (reactants) and the compounds that are produced (products). These equations are balanced to conform with the law of conservation of mass, meaning the number of atoms for each element should be the same on both sides of the equation.

When writing reaction equations, it’s crucial to balance them so that they illustrate equivalent amounts of reactants and products reflecting the actual stoichiometry of the chemical reaction. For instance, in the reaction of zinc with hydrochloric acid, it's shown that one zinc atom reacts with two hydrochloric acid molecules to produce one molecule of zinc chloride and one molecule of hydrogen gas. This balancing act is the backbone of chemical equations and is vital for understanding the quantitative nature of reactions.

Mole Concept

The mole concept is a fundamental aspect of chemistry that allows chemists to count atoms, molecules, and ions in a macroscopic amount of a substance. A mole is defined as the amount of substance containing as many entities (atoms, ions, molecules, etc.) as there are atoms in 12 grams of carbon-12. One mole is approximately equal to \(6.022 \times 10^{23}\) entities, known as Avogadro's number.

This concept ties in closely with the idea of molar mass, which is the mass of one mole of a substance, measured in grams per mole (g/mol). For calculations, it's essential to convert between mass, moles, and number of particles to accurately compute reactant and product quantities in a chemical reaction.

Molar Volume at STP

Molar volume is the volume occupied by one mole of any gas at standard temperature and pressure (STP), which is defined as 0 degrees Celsius (273.15 K) and 1 atmosphere of pressure. At STP, the molar volume of any ideal gas is approximately 22.4 liters or 22,400 milliliters.

Involving this constant is particularly useful because it provides a direct way to convert between the volume of a gas at STP and the amount of substance (in moles). It is vital for solving problems such as determining how much zinc metal is needed to produce a specific volume of hydrogen gas at STP. As seen in the exercise, the volume of gas produced allows us to calculate moles of gas, which in turn dictates the stoichiometry of the rest of the reactants and products.

Single Replacement Reactions

Single replacement reactions, or single displacement reactions, occur when an element displaces another element in a compound, producing a new compound and an isolated element. These reactions are prevalent in various chemical processes including the reaction of a metal with an acid to produce a salt and a gas.

In the textbook exercise, zinc (Zn) replaces the hydrogen in hydrochloric acid (HCl) to form zinc chloride (ZnCl2) and hydrogen gas (H2). Recognizing a single replacement reaction is important for predicting the products of the reaction and for understanding reaction mechanisms. The activity series of metals can be used to predict whether a particular single replacement reaction can occur, based on the reactivity of the metals involved.