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Ch.10 - Gases
Brown - Chemistry: The Central Science 14th Edition
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Tutti i libri di testoBrown 14th EditionCh.10 - GasesProblema 107b
Capitolo 10, Problema 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.

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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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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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Ideal Gas Law Formula

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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The Ideal Gas Law: Molar Mass

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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Matter Composition
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