Ch.6 - Gases

Problem 106

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Chapter 6, Problem 106

Ammonium nitrate decomposes explosively upon heating according to the balanced equation: 2 NH4NO3(s)¡2 N2( g) + O2( g) + 4 H2O( g) Calculate the total volume of gas (at 125 °C and 748 mmHg) produced by the complete decomposition of 1.55 kg of ammonium nitrate.

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Convert the mass of ammonium nitrate (1.55 kg) to moles using its molar mass (NH_4NO_3).

Use the stoichiometry of the balanced equation to determine the total moles of gas produced. According to the equation, 2 moles of NH_4NO_3 produce 7 moles of gas (2 N_2 + O_2 + 4 H_2O).

Calculate the total moles of gas produced from the moles of ammonium nitrate decomposed.

Use the ideal gas law, PV = nRT, to calculate the volume of gas. Convert the temperature from Celsius to Kelvin and the pressure from mmHg to atm.

Solve for the volume (V) using the ideal gas law, where P is the pressure in atm, V is the volume in liters, n is the number of moles of gas, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin.

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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 balanced equations. It allows us to determine the relationships between the quantities of substances involved in a reaction. In this case, stoichiometry helps us find out how much gas is produced from a given mass of ammonium nitrate by using the coefficients from the balanced equation.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the volume of gases produced in a reaction under specific conditions. In this problem, we will use the Ideal Gas Law to convert the number of moles of gas produced into a volume at the given temperature and pressure.

Gas Volume Calculations

Gas volume calculations involve determining the volume occupied by a gas under certain conditions of temperature and pressure. The volume can be calculated using the Ideal Gas Law or by applying the concept of molar volume at standard conditions. In this scenario, we will calculate the total volume of gas produced from the decomposition of ammonium nitrate, taking into account the specific temperature and pressure provided.

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Textbook Question

Consider the reaction: 2 Ag₂O(s) → 4 Ag(s) + O₂(g) If this reaction produces 15.8 g of Ag(s), what total volume of gas can be collected over water at a temperature of 25 °C and a total pressure of 752 mmHg?

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Textbook Question

Consider the reaction:

2 SO₂(g) + O₂(g) → 2 SO₃(g)

a. If 285.5 mL of SO₂ reacts with 158.9 mL of O₂ (both measured at 315 K and 50.0 mmHg), what is the limiting reactant and the theoretical yield of SO₃?

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Textbook Question

Ammonium carbonate decomposes upon heating according to the balanced equation: (NH₄)₂CO₃(s) → 2 NH₃(g) + CO₂(g) + H₂O(g) Calculate the total volume of gas produced at 22 °C and 1.02 atm by the complete decomposition of 11.83 g of ammonium carbonate.

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Textbook Question

Olympic cyclists fill their tires with helium to make them lighter. Calculate the mass of air in an air-filled tire and the mass of helium in a helium-filled tire. Assume that the volume of the tire is 855 mL, that it is filled to a total pressure of 125 psi, and that the temperature is 25 °C. Also, assume an average molar mass for air of 28.8 g/mol. Calculate the mass of air in an air-filled tire.