Ch.10 - Gases

Problem 106a

Chapter 10, Problem 106a

Assume that a single cylinder of an automobile engine has a volume of 524 cm3. (a) If the cylinder is full of air at 74 C and 99.3 kPa, how many moles of O2 are present? (The mole fraction of O2 in dry air is 0.2095.) (b) How many grams of C8H18 could be combusted by this quantity of O2, assuming complete combustion with formation of CO2 and H2O?

Verified step by step guidance

Step 1: Convert the temperature from Celsius to Kelvin by using the formula T(K) = T(°C) + 273.15. This will be used in the ideal gas law equation.

Step 2: Use the ideal gas law, PV = nRT, to calculate the total number of moles of air in the cylinder. Here, P is the pressure, V is the volume, n is the number of moles, R is the gas constant (0.0821 L·atm/K·mol for consistency in units), and T is the temperature in Kelvin.

Step 3: Calculate the number of moles of O2 by multiplying the total moles of air by the mole fraction of O2 in air (0.2095).

Step 4: Use the stoichiometry of the combustion reaction of octane (C8H18) with oxygen to determine how many moles of C8H18 can be combusted by the available moles of O2. The balanced equation is 2 C8H18 + 25 O2 → 16 CO2 + 18 H2O.

Step 5: Convert the moles of C8H18 to grams by multiplying by the molar mass of C8H18 (114.23 g/mol).

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Key Concepts

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

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 number of moles of a gas in a given volume and conditions. In this question, it will be used to determine the moles of O2 present in the cylinder of the engine.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture, defined as the ratio of the number of moles of that component to the total number of moles in the mixture. In this case, the mole fraction of O2 in dry air (0.2095) allows us to calculate the specific amount of O2 present in the cylinder based on the total moles of air.

Combustion Reaction

A combustion reaction is a chemical process in which a substance (typically a hydrocarbon) reacts with oxygen to produce carbon dioxide and water, releasing energy. Understanding the stoichiometry of the combustion of C8H18 (octane) is crucial for determining how much of this fuel can be combusted with the available O2, based on the balanced chemical equation.

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