Problem 44 - Chemistry: Atoms First

Question

Write the balanced equation, then outline the steps necessary to determine the information requested in each of the following: (a) The number of moles and the mass of Mg required to react with \(5.00 \mathrm{g}\) of \(\mathrm{HCl}\) and produce \(\mathrm{MgCl}_{2}\) and \(\mathrm{H}_{2}\). (b) The number of moles and the mass of oxygen formed by the decomposition of \(1.252 \mathrm{g}\) of silver(I) oxide. (c) The number of moles and the mass of magnesium carbonate, \(\mathrm{MgCO}_{3}\), required to produce \(283 \mathrm{g}\) of carbon dioxide. (MgO is the other product.) (d) The number of moles and the mass of water formed by the combustion of \(20.0 \mathrm{kg}\) of acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}\), in an excess of oxygen. (e) The number of moles and the mass of barium peroxide, \(\mathrm{BaO}_{2}\), needed to produce \(2.500 \mathrm{kg}\) of barium oxide, \(\mathrm{BaO}\) \(\left(\mathrm{O}_{2}\right.\) is the other product.)

Step-by-Step Solution

Answer

(a) 0.0685 mol, 1.67 g Mg; (b) 0.00270 mol, 0.0864 g O2; (c) 6.43 mol, 542 g MgCO3; (d) 768.05 mol, 13.838 kg H2O; (e) 16.311 mol, 2.761 kg BaO2.

Step 1: Write Balanced Equations for Each Reaction

Before determining the required information, write balanced chemical equations for each reaction. (a) Mg + 2HCl → MgCl2 + H2. (b) 2Ag2O →4Ag + O2. (c) MgCO3 → MgO + CO2. (d) 2C2H2 + 5O2 → 4CO2 + 2H2O. (e) 2BaO2 → 2BaO + O2.

Step 2: Determine Number of Moles of HCl

Convert mass of HCl to moles by using its molar mass (36.46 g/mol for HCl). (a) 5.00 g HCl * (1 mol HCl / 36.46 g HCl) = 0.137 mol HCl

Step 3: Calculate Moles of Mg Required

Use stoichiometry from balanced equation (a). For every 2 moles of HCl, 1 mole of Mg is required. (0.137 mol HCl) / (2 mol HCl / 1 mol Mg) = 0.0685 mol Mg

Step 4: Calculate Mass of Mg Required

Using the molar mass of Mg (24.31 g/mol), calculate the mass needed. Mass = mole * molar mass. (0.0685 mol Mg) * (24.31 g/mol Mg) = 1.67 g of Mg.

Step 5: Determine Moles of Ag2O Decomposed

Convert mass of Ag2O to moles using its molar mass (231.74 g/mol). (b) 1.252 g Ag2O * (1 mol Ag2O / 231.74 g Ag2O) = 0.00540 mol Ag2O

Step 6: Calculate Moles of O2 Formed

Use stoichiometry from balanced equation (b). For every 2 moles of Ag2O decomposed, 1 mol of O2 is formed. (0.00540 mol Ag2O) / (2 mol Ag2O / 1 mol O2) = 0.00270 mol O2

Step 7: Calculate Mass of O2 Formed

Using the molar mass of O2 (32.00 g/mol), calculate the mass of oxygen. Mass = mole * molar mass. (0.00270 mol O2) * (32.00 g/mol O2) = 0.0864 g of O2.

Step 8: Determine Moles of CO2 Produced

Roll over from (c) MgCO3 → MgO + CO2. Convert mass of CO2 to moles using its molar mass (44.01 g/mol). 283 g CO2 * (1 mol CO2 / 44.01 g CO2) = 6.43 mol CO2

Step 9: Calculate Moles of MgCO3 Required

Use stoichiometry from balanced equation (c). The decomposition is a 1:1 ratio. 6.43 mol CO2 = 6.43 mol MgCO3 needed

Step 10: Calculate Mass of MgCO3 Required

Using the molar mass of MgCO3 (84.31 g/mol), calculate the mass needed. Mass = mole * molar mass. (6.43 mol MgCO3) * (84.31 g/mol MgCO3) = 542 g of MgCO3.

Step 11: Determine Moles of C2H2 Combusted

Convert mass of C2H2 to moles using its molar mass (26.04 g/mol). (d) 20.0 kg C2H2 * (1 mol C2H2 / 26.04 g C2H2) = 768.05 mol C2H2

Step 12: Calculate Moles of H2O Formed

Use stoichiometry from balanced equation (d). For every 2 moles of C2H2 combusted, 2 moles of H2O are formed. (768.05 mol C2H2) * (2 mol H2O / 2 mol C2H2) = 768.05 mol H2O

Step 13: Calculate Mass of H2O Formed

Using the molar mass of H2O (18.02 g/mol), calculate the mass of water. Mass = mole * molar mass. (768.05 mol H2O) * (18.02 g/mol H2O) = 13,838 g or 13.838 kg of H2O.

Step 14: Calculate Moles of BaO2 Needed

From equation (e) 2BaO2 → 2BaO + O2, use the molar mass of BaO (153.33 g/mol) and BaO2 (169.34 g/mol) to determine moles of BaO2 needed to form 2.500 kg of BaO. (2.500 kg BaO) * (1 mol BaO / 153.33 g BaO) = 16.311 mol BaO

Step 15: Determine Ratio for BaO2 to BaO

From the balanced equation (e), the ratio of BaO2 to BaO is 1:1. 16.311 mol BaO = 16.311 mol BaO2 needed

Step 16: Calculate Mass of BaO2 Needed

Convert moles of BaO2 to mass. Mass = mole * molar mass. (16.311 mol BaO2) * (169.34 g/mol BaO2) = 2,761 g or 2.761 kg of BaO2.

Key Concepts

Balanced Chemical Equations

Understanding balanced chemical equations is essential for the study of chemical reactions, as they show the conservation of mass. In a balanced chemical equation, the number of atoms on the reactant side must equal the number on the product side.

For example, the equation for the reaction between magnesium and hydrochloric acid is written as Mg + 2HCl → MgCl₂ + H₂. Here, we have one magnesium atom, two chlorine atoms, and two hydrogen atoms on both sides of the equation.

Importance in Stoichiometry

Balanced equations are instrumental in stoichiometry, as they provide the mole ratios needed to solve for quantities in a chemical reaction. By using the mole ratio from the balanced equation, students can calculate the moles of another substance reacting or produced. Therefore, ensuring the chemical equation is balanced before proceeding with calculations is a crucial step.

Mole Concept

The mole concept is a bridge between the micro-world of atoms and molecules and the macro-world that we can measure. One mole is defined as exactly 6.022 x 10²³ (Avogadro's number) of particles (atoms, molecules, ions, or electrons).

In chemical stoichiometry, moles provide a consistent method to convert between atoms/molecules and grams. For example, if we have 0.137 moles of HCl, we're referring to 0.137 x 6.022 x 10²³ molecules of hydrochloric acid.

Role in Calculations

By knowing the number of moles, we can use the molar mass of a substance to calculate the mass needed in a reaction. Molar mass is the weight of one mole of a substance and can be found on the periodic table. The concept simplifies complex chemical calculations and allows chemists to predict the outcomes of reactions quantitatively.

Molar Mass Calculations

Molar mass calculations are vital for converting between moles and grams, enabling chemists to accurately measure substances for reactions. The molar mass is the mass of one mole of a substance and is usually expressed in grams per mole (g/mol).

Each element's molar mass is found on the periodic table and is equivalent to its atomic weight. For compounds, the molar mass is the sum of the molar masses of all atoms in the molecule. For instance, the molar mass of H₂O is 18.02 g/mol since it has two hydrogen atoms (1.01 g/mol each) and one oxygen atom (16.00 g/mol).

Applying Molar Mass in Calculations

Calculating the mass of a substance requires multiplying its number of moles by its molar mass. In one of our exercise examples, the mass of magnesium carbonate (MgCO₃) required to produce carbon dioxide is found by multiplying the moles of MgCO₃ by its molar mass (84.31 g/mol). Such calculations are the cornerstone of predicting the amounts of reactants needed and products formed in a chemical reaction.