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Ch.10 - Gases: Their Properties & Behavior
McMurry - Chemistry 8th Edition
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Tutti i libri di testoMcMurry 8th EditionCh.10 - Gases: Their Properties & BehaviorProblema 145a
Capitolo 10, Problema 145a

An empty 4.00-L steel vessel is filled with 1.00 atm of CH4(g) and 4.00 atm of O2(g) at 300 °C. A spark causes the CH4 to burn completely, according to the equation
CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(g) ΔH° = -802 kJ
(a) What mass of CO2(g) is produced in the reaction?

Guida verificata passo dopo passo
1
Identify the balanced chemical equation for the reaction: \( \text{CH}_4(g) + 2 \text{O}_2(g) \rightarrow \text{CO}_2(g) + 2 \text{H}_2\text{O}(g) \).
Calculate the initial moles of \( \text{CH}_4 \) and \( \text{O}_2 \) using the ideal gas law: \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is moles, \( R \) is the ideal gas constant, and \( T \) is temperature in Kelvin.
Determine the limiting reactant by comparing the mole ratio of \( \text{CH}_4 \) to \( \text{O}_2 \) with the stoichiometric ratio from the balanced equation.
Use the stoichiometry of the balanced equation to calculate the moles of \( \text{CO}_2 \) produced, based on the limiting reactant.
Convert the moles of \( \text{CO}_2 \) to mass using the molar mass of \( \text{CO}_2 \).

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Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows us to calculate the amounts of substances consumed and produced in a reaction based on balanced chemical equations. In this case, understanding the stoichiometric coefficients from the combustion reaction of methane (CH4) is essential to determine how much carbon dioxide (CO2) is produced.
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Stoichiometry Concept

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 crucial for calculating the number of moles of gases involved in the reaction, especially since the problem provides initial pressures and a specific volume. By applying the Ideal Gas Law, we can convert the given pressures of CH4 and O2 into moles, which are necessary for stoichiometric calculations.
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Ideal Gas Law Formula

Enthalpy Change (ΔH)

Enthalpy change (ΔH) represents the heat absorbed or released during a chemical reaction at constant pressure. In this combustion reaction, the negative ΔH value indicates that the reaction is exothermic, meaning it releases heat. Understanding the enthalpy change helps in assessing the energy dynamics of the reaction, although it is not directly needed to calculate the mass of CO2 produced, it provides context for the reaction's energy profile.
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Enthalpy of Formation
Pratica correlata
Domanda del libro di testo

An empty 4.00-L steel vessel is filled with 1.00 atm of CH4(g) and 4.00 atm of O2(g) at 300 °C. A spark causes the CH4 to burn completely, according to the equation

CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(g) ΔH° = -802 kJ

(b) What is the final temperature inside the vessel after combustion, assuming that the steel vessel has a mass of 14.500 kg, the mixture of gases has an average molar heat capacity of 21 J/(mol·°C), and the heat capacity of steel is 0.449 J/(g·°C)?

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Domanda del libro di testo

A steel container with a volume of 500.0 mL is evacuated, and 25.0 g of CaCO3 is added. The container and contents are then heated to 1500 K, causing the CaCO3 to decompose completely, according to the equation CaCO3(s) → CaO(s) + CO2(g). (b) Now make a more accurate calculation of the pressure inside the container. Take into account the volume of solid CaO (density = 3.34 g/mL) in the container, and use the van der Waals equation to calculate the pressure. The van der Waals constants for CO2(g) are a = 3.59 (L2-atm)/mol2 and b = 0.0427 L/mol.

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Domanda del libro di testo

An empty 4.00-L steel vessel is filled with 1.00 atm of CH4(g) and 4.00 atm of O2(g) at 300 °C. A spark causes the CH4 to burn completely, according to the equation

CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(g) ΔH° = -802 kJ

(c) What is the partial pressure of CO2(g) in the vessel after combustion?

Domanda del libro di testo

A steel container with a volume of 500.0 mL is evacuated, and 25.0 g of CaCO3 is added. The container and contents are then heated to 1500 K, causing the CaCO3 to decompose completely, according to the equation CaCO3(s) → CaO(s) + CO2(g). (a) Using the ideal gas law and ignoring the volume of any solids remaining in the container, calculate the pressure inside the container at 1500 K.

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