Question

Samples of \(1.0 \mathrm{~g}\) of \(\mathrm{Al}\) are treated separately with an excess of sulphuric acid and an excess of sodium hydroxide. The ratio of the number of moles of the hydrogen gas evolved is (a) \(1: 1\) (b) \(3: 2\) (c) \(2: 1\) (d) \(9: 4\)

Short answer

The ratio of the number of moles of hydrogen gas evolved is 1:1.

Step-by-step solution

Write down the chemical reactions

Identify the chemical reactions that take place when aluminum (\text{Al}) reacts with sulfuric acid (\text{H}_2\text{SO}_4) and sodium hydroxide (\text{NaOH}). The reactions are:\[2\text{Al} + 3\text{H}_2\text{SO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + 3\text{H}_2 \]and \[2\text{Al} + 2\text{NaOH} + 6\text{H}_2\text{O} \rightarrow 2\text{NaAl}(\text{OH})_4 + 3\text{H}_2\text{.}\]

Determine the moles of aluminum

Calculate the number of moles of aluminum (\text{Al}) in a 1.0 g sample. Use the atomic mass of aluminum, which is approximately 27 g/mol.\[ \text{number of moles of } \text{Al} = \frac{1.0 \text{ g}}{27 \text{ g/mol}} \text{.} \]

Calculate the moles of hydrogen gas from each reaction

Use the stoichiometric coefficients from the balanced equations to find the mole ratios between aluminum and hydrogen gas.\[ \text{For sulfuric acid: } 2 \text{Al} : 3 \text{H}_2 \text{ (which gives } 1 \text{Al} : 1.5 \text{H}_2 \text{)} \]\[ \text{For sodium hydroxide: } 2 \text{Al} : 3 \text{H}_2 \text{ (which gives } 1 \text{Al} : 1.5 \text{H}_2 \text{)} \]Since both these ratios with respect to 1 mole of Al give the same amount of H_2, the ratio of the number of moles of hydrogen gas evolved is 1:1.

Key concepts

Understanding Chemical Reactions

When delving into stoichiometry problems, the first step always involves understanding the chemical reactions at play. A chemical reaction is a process where reactants are transformed into products. This transformation is based on the breaking and forming of chemical bonds, which correspond to a rearrangement of atoms.

For example, when aluminum (Al) reacts with sulfuric acid (H₂SO₄), we witness the reactants changing into new substances. This reaction produces aluminum sulfate (Al₂(SO₄)₃) and hydrogen gas (H₂). In a separate reaction, aluminum reacts with sodium hydroxide (NaOH) and water (H₂O) to form sodium aluminate (NaAl(OH)₄) and hydrogen gas.

It is crucial to write correct balanced chemical equations. These equations must reflect the law of conservation of mass, meaning the number of atoms for each element should be the same on both the reactants and products side. Balancing equations is fundamental to stoichiometry as it sets the stage for all subsequent calculations.

The Mole Concept

The 'mole' is a central concept in chemistry that serves as a bridge between the microscopic world of atoms and the macroscopic world of grams and liters. One mole corresponds to Avogadro's number, which is approximately 6.022 x 10²³ entities (whether atoms, molecules, ions, etc.).

The mole concept allows chemists to count atoms by weighing. When we say a sample contains 1 mole of atoms, we mean it contains 6.022 x 10²³ atoms of that element. The atomic or molecular mass expressed in grams of a substance is its molar mass, which is the mass of 1 mole of that substance. In our exercise, we use the molar mass of aluminum, 27 g/mol, to convert the mass of an aluminum sample into moles. This step is vital for stoichiometric calculations because stoichiometry deals with the mole ratio between reactants and products in a chemical reaction.

Stoichiometric Calculations

Stoichiometric calculations are at the heart of solving chemistry problems. These calculations use the mole ratios derived from the balanced chemical equations to predict the amounts of reactants needed or products formed in a chemical reaction.

In our textbook problem, stoichiometric coefficients tell us that for every 2 moles of aluminum, 3 moles of hydrogen gas are produced with sulfuric acid, and similarly, 3 moles are produced with sodium hydroxide, leading to a 1:1.5 mole ratio for aluminum to hydrogen gas in both reactions. These mole ratios are used to directly compute the amount of hydrogen gas that evolves from a given amount of aluminum.

By understanding stoichiometric relationships, students can solve complex problems by simple arithmetic. It is important to approach these calculations methodically: start by identifying the chemical reaction, move on to converting mass to moles, and then use the mole ratios to find the answer. Recognizing that stoichiometry is a quantitative comparison helps in visualizing amounts of substances in a reaction, thus making these problems more approachable.

Bringing these concepts together, stoichiometry can be seen as a recipe for chemical reactions, with the mole concept as the 'measuring cups' and the balanced equations as the 'recipe instructions'. Grasping these principles is essential for anyone looking to master chemistry.