/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 31 You have a mixture of gases in d... [FREE SOLUTION] | 91Ó°ÊÓ

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You have a mixture of gases in dry air, with an atmospheric pressure of \(760 \mathrm{~mm}\) Hg. Calculate the partial pressure of each gas if the composition of the air includes: a. \(21 \%\) oxygen, \(78 \%\) nitrogen, \(0.3 \%\) carbon dioxide b. \(40 \%\) oxygen, \(13 \%\) nitrogen, \(45 \%\) carbon dioxide, \(2 \%\) hydrogen c. \(10 \%\) oxygen, \(15 \%\) nitrogen, \(1 \%\) argon, \(25 \%\) carbon dioxide

Short Answer

Expert verified
Partial pressures are: (a) Oxygen: 159.6 mm Hg, Nitrogen: 592.8 mm Hg, CO2: 2.28 mm Hg (b) Oxygen: 304 mm Hg, Nitrogen: 98.8 mm Hg, CO2: 342 mm Hg, H2: 15.2 mm Hg (c) Oxygen: 76 mm Hg, Nitrogen: 114 mm Hg, Argon: 7.6 mm Hg, CO2: 190 mm Hg.

Step by step solution

01

Understand Partial Pressure

Partial pressure refers to the pressure exerted by a single type of gas in a mixture of gases. It can be calculated using Dalton's Law of Partial Pressures, which states that the total pressure exerted by a gaseous mixture is equal to the sum of the partial pressures of each individual gas component.
02

Convert Percentages to Fractions

To find the partial pressure of each gas, we need to convert the percentage of each gas into a fraction. For percentage composition \(x\%\), the fraction becomes \(x / 100\).
03

Calculate Partial Pressure for Each Gas Composition

Use the formula \(P_{gas} = \frac{x}{100} \times P_{total}\), where \(P_{total} = 760\) mm Hg, to calculate the partial pressure for each gas in the mixture.**For case (a):** - Oxygen: \(P_{O_2} = \frac{21}{100} \times 760 = 159.6\) mm Hg - Nitrogen: \(P_{N_2} = \frac{78}{100} \times 760 = 592.8\) mm Hg - Carbon dioxide: \(P_{CO_2} = \frac{0.3}{100} \times 760 = 2.28\) mm Hg**For case (b):** - Oxygen: \(P_{O_2} = \frac{40}{100} \times 760 = 304\) mm Hg - Nitrogen: \(P_{N_2} = \frac{13}{100} \times 760 = 98.8\) mm Hg - Carbon dioxide: \(P_{CO_2} = \frac{45}{100} \times 760 = 342\) mm Hg - Hydrogen: \(P_{H_2} = \frac{2}{100} \times 760 = 15.2\) mm Hg**For case (c):** - Oxygen: \(P_{O_2} = \frac{10}{100} \times 760 = 76\) mm Hg - Nitrogen: \(P_{N_2} = \frac{15}{100} \times 760 = 114\) mm Hg - Argon: \(P_{Ar} = \frac{1}{100} \times 760 = 7.6\) mm Hg - Carbon dioxide: \(P_{CO_2} = \frac{25}{100} \times 760 = 190\) mm Hg

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Partial Pressure Calculation
Partial pressure is a key concept in studying gas behaviour in mixtures. It represents the pressure exerted by an individual gas within a mixture, such as those found in the atmosphere.
The calculation of partial pressure is often guided by Dalton's Law of Partial Pressures. Dalton's Law tells us that the total pressure of a gas mixture is the sum of the partial pressures of all the individual gases. This means each gas contributes its own share to the total pressure, as if it were the only gas present.
To calculate it, you take the fraction of the gas' composition in the mixture and multiply it by the total pressure. For example, if a particular gas makes up 21% of a mixture with a total pressure of 760 mm Hg, you would convert 21% to a fraction (21/100) and multiply it by 760 to find its partial pressure.
This approach helps in understanding how different gases contribute to the total pressure of a system.
Gas Mixtures
A gas mixture is simply a combination of two or more different gases. Think of the air we breathe, which is not purely oxygen but a blend of various gases.
Key characteristics of gas mixtures include:
  • The gases are mixed at the molecular level, so each gas spreads out evenly.
  • Each component gas in a mixture retains its individual properties and exerts its own partial pressure independently.
In environments like the atmosphere, gas mixtures are very common. Understanding how gases work together in mixtures is crucial for fields such as meteorology, chemistry, and environmental science.
By recognizing each gas's contribution through its partial pressure, we can predict how the mixture behaves under different conditions, such as changes in pressure and temperature.
Atmospheric Pressure
Atmospheric pressure is the force exerted by the weight of the air from the atmosphere on a surface. It is often measured in units like millimeters of mercury (mm Hg) or Pascals (Pa). At sea level, standard atmospheric pressure is approximately 760 mm Hg.
Atmospheric pressure can vary based on a location's altitude and the local weather conditions. For example, pressure decreases with altitude because there is less air above a given point pressing down.
Atmospheric pressure is vital in calculating partial pressures in gas mixtures. Given the total pressure, like 760 mm Hg at sea level, one can determine how much pressure each gas in the atmosphere contributes based on its percentage composition.
Understanding atmospheric pressure helps us explain phenomena such as weather patterns, human respiration at different altitudes, and the measurement of gas concentrations in environmental studies.
Percentage Composition Conversion
Percentage composition conversion is a mathematical approach used to express parts of a whole as percentages and then convert these back into usable fractions for calculations.
For gas mixtures, percentages show how much of each gas is present in the mixture. To utilize these percentages in calculations, like in partial pressure calculation, you convert the percentage to a fraction by dividing the percentage by 100.
For example, if a gas makes up 78% of a mixture, its fraction is 0.78. This fraction is then used in formulas to find values like partial pressures.
Conversion is critical in various scientific contexts, helping to simplify complex data and make calculations straightforward and understandable. It enables anyone dealing with chemical compositions, including gases, to perform accurate quantitative analyses easily.
  • Converting data helps in predicting the behavior of gases in mixtures.
  • It is essential in different scientific and engineering disciplines like chemistry and environmental science.

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