Ch.4 - Chemical Reactions and Chemical Quantities

Problem 38

Chapter 4, Problem 38

Sulfuric acid dissolves aluminum metal according to the reaction:
2 Al(s) + 3 H₂SO₄(aq) → Al₂(SO₄)₃(aq) + 3 H₂(g)
Suppose you want to dissolve an aluminum block with a mass of 11.3 g. What minimum mass of H₂SO₄ (in g) do you need? What mass of H₂ gas (in g) does the complete reaction of the aluminum block produce?

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Calculate the moles of aluminum (Al) using its molar mass: \( \text{Molar mass of Al} = 26.98 \, \text{g/mol} \). Use the formula: \( \text{moles of Al} = \frac{\text{mass of Al}}{\text{molar mass of Al}} \).

Use the stoichiometry of the balanced chemical equation to find the moles of \( \text{H}_2\text{SO}_4 \) needed. According to the equation, 2 moles of Al react with 3 moles of \( \text{H}_2\text{SO}_4 \).

Calculate the mass of \( \text{H}_2\text{SO}_4 \) required using its molar mass: \( \text{Molar mass of H}_2\text{SO}_4 = 98.08 \, \text{g/mol} \). Use the formula: \( \text{mass of H}_2\text{SO}_4 = \text{moles of H}_2\text{SO}_4 \times \text{molar mass of H}_2\text{SO}_4} \).

Determine the moles of \( \text{H}_2 \) gas produced using the stoichiometry of the reaction. From the balanced equation, 2 moles of Al produce 3 moles of \( \text{H}_2 \).

Calculate the mass of \( \text{H}_2 \) gas using its molar mass: \( \text{Molar mass of H}_2 = 2.02 \, \text{g/mol} \). Use the formula: \( \text{mass of H}_2 = \text{moles of H}_2 \times \text{molar mass of H}_2} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It allows us to determine the proportions of substances involved in a reaction. In this case, the stoichiometric coefficients from the balanced equation indicate the molar ratios of aluminum to sulfuric acid and hydrogen gas, which are essential for calculating the required mass of sulfuric acid and the mass of hydrogen produced.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is crucial for converting between the mass of a substance and the number of moles, which is necessary for stoichiometric calculations. For aluminum (Al) and sulfuric acid (H2SO4), knowing their molar masses allows us to calculate how much sulfuric acid is needed to react with a given mass of aluminum.

Gas Laws

Gas laws describe the behavior of gases under various conditions of temperature and pressure. In this context, the production of hydrogen gas (H2) from the reaction can be analyzed using the ideal gas law if needed. Understanding gas laws helps in predicting the volume of gas produced and its behavior, although in this case, we focus on the mass of hydrogen generated from the stoichiometric calculations.

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Textbook Question

Consider the balanced equation:

SiO₂(s) + 3 C(s) → SiC(s) + 2 CO(g)

Complete the table showing the appropriate number of moles of reactants and products. If the number of moles of a reactant is provided, fill in the required amount of the other reactant, as well as the moles of each product that forms. If the number of moles of a product is provided, fill in the required amount of each reactant to make that amount of product, as well as the amount of the other product that forms.

Textbook Question

Consider the balanced equation:

SiO₂(s) + 3 C(s) → SiC(s) + 2 CO(g)

Textbook Question

Hydrobromic acid dissolves solid iron according to the reaction:

Fe(s) + 2 HBr(aq) → FeBr₂(aq) + H₂(g)

What mass of HBr (in g) do you need to dissolve a 2.80-g pure iron bar on a padlock? What mass of H₂ would the complete reaction of the iron bar produce?

Textbook Question

For each of the reactions, calculate the mass (in grams) of the product that forms when 15.39 g of the underlined reactant completely reacts. Assume that there is more than enough of the other reactant.

a. 2 K(s) + Cl₂(g) → 2 KCl(s)

b. 2 K(s) + Br₂(l) → 2 KBr(s)

c. 4 Cr(s) + 3 O₂(g) → 2 Cr₂O₃(s)

d. 2 Sr(s) + O₂(g) → 2 SrO(s)

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Textbook Question

Find the limiting reactant for each initial amount of reactants. 2 Na(s) + Br₂( g) → 2 NaBr(s) c. 1.5 mol Na, 2.1 mol Br₂