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Ch.10 - Gases
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
All textbooksBrown 14th EditionCh.10 - GasesProblem 116
Chapter 10, Problem 116

It turns out that the van der Waals constant b equals four times the total volume actually occupied by the molecules of a mole of gas. Using this figure, calculate the fraction of the volume in a container actually occupied by Ar atoms (b) at 20.27 MPa pressure and 0 °C. (Assume for simplicity that the ideal-gas equation still holds.)

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1
Identify the van der Waals constant b for argon (Ar) from a reference source.
Use the relationship that b equals four times the total volume occupied by the molecules of a mole of gas to find the volume occupied by the Ar atoms: \( V_{molecules} = \frac{b}{4} \).
Calculate the volume of the container using the ideal gas law: \( PV = nRT \), where \( P = 20.27 \text{ MPa} \), \( n = 1 \text{ mole} \), \( R = 8.314 \text{ J/(mol K)} \), and \( T = 273.15 \text{ K} \).
Convert the pressure from MPa to Pa for consistency in units: \( 1 \text{ MPa} = 10^6 \text{ Pa} \).
Calculate the fraction of the volume in the container actually occupied by Ar atoms using the formula: \( \text{Fraction} = \frac{V_{molecules}}{V_{container}} \).

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Key Concepts

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

Van der Waals Equation

The Van der Waals equation is an adjustment of the ideal gas law that accounts for the volume occupied by gas molecules and the attractive forces between them. It introduces two constants, 'a' and 'b', where 'b' represents the volume occupied by one mole of gas molecules. This equation is crucial for understanding real gas behavior under various conditions, especially at high pressures and low temperatures.
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Molar Volume

Molar volume is the volume occupied by one mole of a substance, typically measured in liters per mole. In the context of gases, it helps to determine how much space the gas molecules occupy compared to the total volume of the container. Understanding molar volume is essential for calculating the fraction of volume occupied by gas atoms in a given scenario.

Fraction of Volume Occupied

The fraction of volume occupied by gas atoms is a ratio that compares the volume occupied by the gas molecules to the total volume of the container. This concept is important for understanding the efficiency of gas packing and the behavior of gases under different conditions. It can be calculated using the molar volume and the total volume of the container, providing insight into the physical properties of the gas.
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Related Practice
Textbook Question

Cyclopropane, a gas used with oxygen as a general anesthetic, is composed of 85.7% C and 14.3% H by mass. (a) If 1.56 g of cyclopropane has a volume of 1.00 L at 99.7 kPa and 50.0 °C, what is the molecular formula of cyclopropane?

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Textbook Question

Consider the following gases, all at STP: Ne, SF6, N2, CH4. (g) Which one would have the largest van der Waals b parameter?

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Textbook Question

Consider the following gases, all at STP: Ne, SF6, N2, CH4. (f) Which one would effuse more rapidly than N2?

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Textbook Question

An herbicide is found to contain only C, H, N, and Cl. The complete combustion of a 100.0-mg sample of the herbicide in excess oxygen produces 83.16 mL of CO2 and 73.30 mL of H2O vapor expressed at STP. A separate analysis shows that the sample also contains 16.44 mg of Cl. (b) Calculate its empirical formula.

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