Problem 48 - General Chemistry: Principles and Modern Applications

Question

How many liters of \(\mathrm{H}_{2}(\mathrm{g})\) at STP are produced per gram of \(\mathrm{Al}(\mathrm{s})\) consumed in the following reaction? \(2 \mathrm{Al}(\mathrm{s})+6 \mathrm{HCl}(\mathrm{aq}) \longrightarrow 2 \mathrm{AlCl}_{3}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{g})\)

Step-by-Step Solution

Answer

The number of liters of \(\mathrm{H}_{2}\) gas produced per gram of \(\mathrm{Al}\) can be computed using the stoichiometry from the balance equation and molar volume at standard temperature and pressure (STP).

Step 1: Calculating moles of Aluminium

First, convert the mass of aluminium (Al) to moles using its molar mass (approximately 27.0 g/mol).

Step 2: Using Stoichiometry

Next, use the balanced equation to find out how many moles of hydrogen are produced per mole of Al consumed: \[2 \mathrm{Al}(\mathrm{s})+6 \mathrm{HCl}(\mathrm{aq}) \longrightarrow 2 \mathrm{AlCl}_{3}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{g})\]. From this equation, you can see that 2 moles of Al produce 3 moles of H2. So, the stoichiometry yield is 3/2 moles of hydrogen for every mole of aluminium.

Step 3: Convert moles of Hydrogen to volume

Convert the moles of hydrogen gas to liters using Avogadro set at standard temperature and pressure (STP), which is approximately 22.4 L/mol.

Key Concepts

Molar Mass

Molar mass is an essential concept in chemistry, often serving as the bridge between the mass of a substance and the amount of substance, measured in moles. The molar mass of an element (or compound) is the mass of one mole of that element, expressed in grams per mole (g/mol). For example, the molar mass of aluminum (Al) is approximately 27.0 g/mol.

To find the number of moles, you divide the given mass by the molar mass using the formula:

• \[ \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} \]

Understanding molar mass helps in calculating how many moles are present, which is crucial for solving stoichiometry problems involving chemical reactions.

Moles of Gas

The concept of moles of gas is vital in understanding how gases behave under different conditions. A mole is a measure of quantity that connects mass to the number of particles present. In stoichiometry, moles allow us to relate reactants to products using balanced chemical equations.

For gases, the number of moles helps determine the volume using the ideal gas law. In the given reaction, we calculate the moles of hydrogen gas (\(\text{H}_2\)) produced from aluminum, which are then used to find the corresponding gas volume. Calculating moles helps determine the amount of product formed and plays a crucial role in predicting reaction yields.

Avogadro's Law

Avogadro's Law is fundamental in gas calculations. It states that equal volumes of gases, at the same temperature and pressure, contain an equal number of particles. This means that for gases under standard conditions, one mole occupies a specific volume.

At STP (standard temperature and pressure), one mole of any ideal gas occupies 22.4 liters. This principle allows us to easily convert from moles to volume. In the reaction, knowing the moles of hydrogen gas produced enables us to use Avogadro's Law to find its volume. Understanding Avogadro's Law simplifies converting between moles and volume in gas calculations, making it a cornerstone of stoichiometric conversions.

Standard Temperature and Pressure (STP)

STP refers to a standard set of conditions for measuring gases, defined as a temperature of 0°C (273.15 K) and a pressure of 1 atmosphere (atm). At these conditions, gases have predictable behavior, making calculations uniform and simplifying stoichiometric problems.

The use of STP is crucial in determining the volumes of gases produced or consumed in reactions. For the reaction in question, STP allows us to straightforwardly use the volume of 22.4 liters per mole to find out how much hydrogen gas is generated from the amount of aluminum used. This standardization provides consistency, enabling accurate comparisons and calculations.