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Ch.10 - Gases
All textbooksBrown 14th EditionCh.10 - GasesProblem 107b
Chapter 10, Problem 107b

Assume that an exhaled breath of air consists of 74.8% N2, 15.3% O2, 3.7% CO2, and 6.2% water vapor. (b) If the volume of the exhaled gas is 455 mL and its temperature is 37 °C, calculate the number of moles of CO2 exhaled.

Verified step by step guidance
1
Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature in Celsius: T(K) = 37 + 273.15.
Use the ideal gas law equation, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin.
Assume the pressure is 1 atm if not specified. Convert the volume from mL to L by dividing by 1000: V(L) = 455 / 1000.
Calculate the partial pressure of CO2 using its percentage in the exhaled air: P(CO2) = 0.037 * total pressure.
Rearrange the ideal gas law to solve for n (number of moles): n = (P(CO2) * V) / (R * T). Use R = 0.0821 L·atm/mol·K for the ideal gas constant.

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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 when given its volume and temperature, as it allows us to manipulate these variables to find the unknown quantity.
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Molar Volume of a Gas

At standard temperature and pressure (STP), one mole of an ideal gas occupies 22.4 liters. However, in this problem, we need to consider the conditions of the exhaled breath, specifically the volume and temperature, to determine the actual number of moles of CO2 present in the given volume of gas.
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Composition of Air

Understanding the composition of exhaled air is crucial for this problem. The percentages of different gases (N2, O2, CO2, and water vapor) indicate their relative amounts in the mixture. By applying these percentages to the total volume of exhaled gas, we can calculate the specific volume of CO2, which is necessary for determining the number of moles.
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Related Practice
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Consider the arrangement of bulbs shown in the drawing. Each of the bulbs contains a gas at the pressure shown. What is the pressure of the system when all the stopcocks are opened, assuming that the temperature remains constant? (We can neglect the volume of the capillary tubing connecting the bulbs.)

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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?

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Textbook Question

Assume that an exhaled breath of air consists of 74.8% N2, 15.3% O2, 3.7% CO2, and 6.2% water vapor. (a) If the total pressure of the gases is 99.8 kPa, calculate the partial pressure of each componentof the mixture.

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Textbook Question

Assume that an exhaled breath of air consists of 74.8% N2, 15.3% O2, 3.7% CO2, and 6.2% water vapor. (c) How many grams of glucose (C6H12O6) would need to be metabolized to produce this quantity of CO2? (The chemical reaction is the same as that for combustion of C6H12O6. See Section 3.2 and Problem 10.57.)

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Textbook Question
An 8.40-g sample of argon and an unknown mass of H2are mixed in a flask at room temperature. The partial pressureof the argon is 44.0 kPa, and that of the hydrogen is57.33 kPa. What is the mass of the hydrogen?
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An ideal gas at a pressure of 152 kPa is contained in a bulbof unknown volume. A stopcock is used to connect thisbulb with a previously evacuated bulb that has a volumeof 0.800 L as shown here. When the stopcock is opened,the gas expands into the empty bulb. If the temperatureis held constant during this process and the final pressureis 92.66 kPa, what is the volume of the bulb that wasoriginally filled with gas?

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