Ch. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law

Problem 41

Chapter 17, Problem 41

What is the pressure inside a 41.0-L container holding 105.0 kg of argon gas at 21.6°C?

Verified step by step guidance

Step 1: Start by identifying 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 the temperature in Kelvin.

Step 2: Convert the given temperature from Celsius to Kelvin using the formula

T(K) = T(°C) + 273.15

. Substitute the given temperature of 21.6°C into the formula.

Step 3: Calculate the number of moles of argon gas (n) using the formula

n = \(\frac{m}{M}\)

, where m is the mass of the gas (105.0 kg) and M is the molar mass of argon (approximately 39.95 g/mol). Be sure to convert the mass from kilograms to grams before substituting.

Step 4: Rearrange the ideal gas law equation to solve for pressure:

P = \(\frac{nRT}{V}\)

. Use the calculated value of n, the given volume (41.0 L), the ideal gas constant R (8.314 J/(mol·K)), and the temperature in Kelvin from Step 2.

Step 5: Ensure the volume is in cubic meters (m³) if using SI units for R. Convert 41.0 L to m³ using the conversion factor

1 \(\text{ L}\) = 0.001 \(\text{ m³}\)

. Substitute all values into the equation to find the pressure.

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Key Concepts

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

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in thermodynamics that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as 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. This law allows us to calculate the pressure of a gas when its volume, temperature, and amount are known.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For argon, the molar mass is approximately 40.0 g/mol. Understanding molar mass is essential for converting the mass of a gas into moles, which is necessary for applying the Ideal Gas Law to find pressure.

Temperature Conversion

Temperature conversion is the process of changing temperature from one scale to another, commonly from Celsius to Kelvin in scientific calculations. The conversion is done by adding 273.15 to the Celsius temperature. Accurate temperature measurement is crucial in gas law calculations, as the Ideal Gas Law requires temperature to be in Kelvin to ensure proper proportionality in the equation.

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