Ch.10 - Gases

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.10 - Gases

Problem 59

Chapter 10, Problem 59

During a person's typical breathing cycle, the CO2 concentration in the expired air rises to a peak of 4.6% by volume.(a) Calculate the partial pressure of the CO2 in the expiredair at its peak, assuming 1 atm pressure and a body temperature of 37 °C.

Verified step by step guidance

Identify the given values: CO2 concentration is 4.6% by volume, total pressure is 1 atm, and temperature is 37 °C.

Recall that partial pressure can be calculated using the formula: \( P_{\text{CO}_2} = \text{mole fraction of CO}_2 \times \text{total pressure} \).

Convert the percentage concentration to a mole fraction: \( \text{mole fraction of CO}_2 = \frac{4.6}{100} \).

Substitute the mole fraction and total pressure into the partial pressure formula: \( P_{\text{CO}_2} = \frac{4.6}{100} \times 1 \text{ atm} \).

Calculate the partial pressure of CO2 using the values from the previous step.

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Key Concepts

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

Partial Pressure

Partial pressure refers to the pressure exerted by a single component of a gas mixture. It can be calculated using Dalton's Law, which states that the total pressure of a gas mixture is equal to the sum of the partial pressures of its individual gases. In this case, the partial pressure of CO2 can be determined by multiplying its volume fraction by the total pressure.

Gas Laws

Gas laws describe the behavior of gases under various conditions of temperature and pressure. The Ideal Gas Law (PV=nRT) is particularly relevant here, as it relates pressure (P), volume (V), number of moles (n), the ideal gas constant (R), and temperature (T). Understanding these relationships is crucial for calculating the partial pressure of gases in different scenarios.

Body Temperature and Gas Behavior

Body temperature, typically around 37 °C (310 K), affects the behavior of gases, including their pressure and volume. At higher temperatures, gas molecules have more kinetic energy, which can influence their pressure when confined in a space. In this question, recognizing the importance of temperature is essential for accurate calculations involving gas behavior in the human body.

Related Practice

Textbook Question

Acetylene gas, C2H21g2, can be prepared by the reaction ofcalcium carbide with water:CaC21s2 + 2 H2O1l2¡Ca1OH221aq2 + C2H21g2Calculate the volume of C2H2 that is collected over water at23 °C by reaction of 1.524 g of CaC2 if the total pressure ofthe gas is 100.4 kPa. (The vapor pressure of water is tabulatedin Appendix B.)

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Textbook Question

Consider the apparatus shown in the following drawing. (a) When the valve between the two containers is opened and the gases are allowed to mix, what is the partial pressure of N2 after mixing?

1135

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Textbook Question

Consider the apparatus shown in the following drawing. (a) When the valve between the two containers is opened and the gases are allowed to mix, how does the volume occupied by the N2 gas change?

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Textbook Question

Magnesium can be used as a 'getter' in evacuated enclosuresto react with the last traces of oxygen. (The magnesium isusually heated by passing an electric current through a wireor ribbon of the metal.) If an enclosure of 5.67 L has a partialpressure of O2 of 7.066 mPa at 30 °C, what mass of magnesiumwill react according to the following equation?2 Mg1s2 + O21g2¡2 MgO1s2

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Textbook Question

The molar mass of a volatile substance was determined bythe Dumas-bulb method described in Exercise 10.53. Theunknown vapor had a mass of 2.55 g; the volume of thebulb was 500 mL, pressure 101.33 kPa, and temperature37 °C.Calculate the molar mass of the unknown vapor.

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