Problem 151 - General Chemistry

Question

An alloy of aluminum and magnesium was treated with sodium hydroxide solution, in which only aluminum reacts. \(2 \mathrm{Al}(s)+2 \mathrm{NaOH}(a q)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow{2 \mathrm{NaAl}(\mathrm{OH})_{4}(a q)+3 \mathrm{H}_{2}(g)}\) If a sample of alloy weighing \(1.118\) g gave \(0.1068 \mathrm{~g}\) of hydrogen, what is the percentage of aluminum in the alloy?

Step-by-Step Solution

Answer

The percentage of aluminum in the alloy is approximately 85.86%.

Step 1: Calculate moles of Hydrogen

To find the moles of hydrogen gas produced, use its mass and molar mass. The molar mass of hydrogen \((\mathrm{H}_2)\) is 2 g/mol. Therefore, the moles of hydrogen \((n_{\mathrm{H}_2})\) is given by \( n_{\mathrm{H}_2} = \frac{0.1068 \text{ g}}{2 \text{ g/mol}} = 0.0534 \text{ mol} \).

Step 2: Relate moles of Hydrogen to moles of Aluminum

According to the balanced equation, 3 moles of \(\mathrm{H}_2\) are produced from 2 moles of \(\mathrm{Al}\). Use this stoichiometry to calculate the moles of aluminum involved. Therefore, moles of aluminum \(n_{\mathrm{Al}}\) is \( n_{\mathrm{Al}} = \frac{2}{3} \times n_{\mathrm{H}_2} = \frac{2}{3} \times 0.0534 \text{ mol} = 0.0356 \text{ mol} \).

Step 3: Calculate mass of Aluminum

Now find the mass of aluminum using the moles calculated. The molar mass of aluminum is 26.98 g/mol. Therefore, the mass of aluminum \(m_{\mathrm{Al}}\) is \( m_{\mathrm{Al}} = n_{\mathrm{Al}} \times 26.98 \text{ g/mol} = 0.0356 \text{ mol} \times 26.98 \text{ g/mol} = 0.96 \text{ g} \).

Step 4: Calculate percentage of Aluminum in the alloy

Finally, calculate the percentage of aluminum in the alloy using the formula: \( \text{Percentage of Al} = \left( \frac{\text{mass of Al}}{\text{total mass of alloy}} \right) \times 100 \). Substitute the known values: \( \text{Percentage of Al} = \left( \frac{0.96 \text{ g}}{1.118 \text{ g}} \right) \times 100 \approx 85.86\% \).

Key Concepts

Aluminum and Magnesium Alloy

An alloy is a mixture of two or more metals, combining their properties to create a material with enhanced characteristics. When dealing with aluminum and magnesium alloy, it's crucial to understand its composition. In this exercise, not both components react with sodium hydroxide (NaOH). Only the aluminum participates in the reaction, producing hydrogen gas and a sodium aluminate product. Identifying the percentage of a specific metal in an alloy requires careful analysis of the chemical reactions involved, focusing only on the components that undergo change in the reaction process. This composition analysis is vital in materials science, where the metal's properties like strength, weight, conductivity, and reactivity can significantly impact its application.

Stoichiometry

Stoichiometry is the mathematical foundation of chemistry that relates reactants to products in a balanced chemical equation. It is like a recipe that tells you how much of each ingredient you need. In this exercise, stoichiometry is used to relate the amount of aluminum that reacts to the amount of hydrogen gas produced. By examining the coefficients in the balanced reaction equation, one can deduce that 2 moles of aluminum yield 3 moles of hydrogen gas. Thus, stoichiometry allows us to calculate backward: from the known quantity of hydrogen gas, we determine the corresponding amount of aluminum that reacted. This connection is fundamental in chemical calculations, enabling chemists to predict yields and optimize reactions.

Chemical Reaction Balancing

Every chemical equation must be balanced to reflect the conservation of mass and matter. This exercise involves a chemical reaction where aluminum reacts with sodium hydroxide and water to produce sodium aluminate and hydrogen gas. Balancing means making sure that there is the same number of each type of atom on both sides of the equation. By doing so, we ensure that the calculation based on the equation, like how much aluminum reacted to produce a specific amount of hydrogen gas, is accurate. The balanced equation helps guide the stoichiometric calculations to maintain consistency and correctness in determining the reaction's quantitative aspects. Without a balanced equation, predicting the outcome of reactions would be unreliable.

Molar Mass Calculation

The molar mass of a chemical is a key factor in converting between mass and moles. Molar mass is the mass of one mole of a given substance, usually expressed in grams per mole (g/mol). In this problem, we determine the molar mass of hydrogen ( H_2 dotagg = 2 g/mol) to convert the given mass of hydrogen gas into moles. Similarly, knowing the molar mass of aluminum (26.98 g/mol) allows us to convert moles of aluminum into its mass form. These conversions are essential for calculating how much of a substance there is in terms of its macroscopic (mass) or microscopic (moles) quantities. Understanding molar mass enables a seamless transition between these scales, making calculations in chemistry both practical and precise.