Ch.10 - Gases

Problem 59

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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 expired air at its peak, assuming 1 atm pressure and a body temperature of 37 °C.

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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.

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Textbook Question

Calcium hydride, CaH2, reacts with water to form hydrogen gas: CaH21s2 + 2 H2O1l2¡Ca1OH221aq2 + 2 H21g2 This reaction is sometimes used to inflate life rafts, weather balloons, and the like, when a simple, compact means of generating H2 is desired. How many grams of CaH2 are needed to generate 145 L of H2 gas if the pressure of H2 is 110 kPa at 21 °C?

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Open Question

The metabolic oxidation of glucose, C6H12O6, in our bodies produces CO2, which is expelled from our lungs as a gas: C6H12O6(aq) + 6 O2(g) → 6 CO2(g) + 6 H2O(l). (a) Calculate the volume of dry CO2 produced at normal body temperature, 37 °C, and 101.33 kPa when 10.0 g of glucose is consumed in this reaction. (b) Calculate the volume of oxygen you would need, at 100 kPa and 298 K, to completely oxidize 15.0 g of glucose.

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Both Jacques Charles and Joseph Louis Guy-Lussac were avid balloonists. In his original flight in 1783, Jacques Charles used a balloon that contained approximately 31,150 L of H2. He generated the H2 using the reaction between iron and hydrochloric acid: Fe1s2 + 2 HCl1aq2 ¡ FeCl21aq2 + H21g2 How many kilograms of iron were needed to produce this volume of H2 if the temperature was 22 °C?

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Textbook Question

Acetylene gas, C2H21g2, can be prepared by the reaction of calcium carbide with water: CaC21s2 + 2 H2O1l2¡Ca1OH221aq2 + C2H21g2 Calculate the volume of C2H2 that is collected over water at 23 °C by reaction of 1.524 g of CaC2 if the total pressure of the gas is 100.4 kPa. (The vapor pressure of water is tabulated in Appendix B.)

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Textbook Question

Consider a mixture of two gases, A and B, confined in a closed vessel. A quantity of a third gas, C, is added to the same vessel at the same temperature. How does the addition of gas C affect the following: (a) the partial pressure of gas A?

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A mixture containing 0.50 mol H2(g), 1.00 mol O2(g), and 3.50 mol N2(g) is confined in a 25.0-L vessel at 25 °C. Calculate the partial pressure of H2, O2, and N2.