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Ch.8 Gases
Timberlake - Chemistry: An Introduction to General, Organic, and Biological Chemistry 14th Edition
Timberlake14th EditionChemistry: An Introduction to General, Organic, and Biological ChemistryISBN: 9781292472249Not the one you use?Change textbook
All textbooksTimberlake 14th EditionCh.8 GasesProblem 42
Chapter 8, Problem 42

Rearrange the variables in the combined gas law to solve for P2.

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Start with the combined gas law formula: PV/T = constant. For two states, the formula becomes: P₁V₁/T₁ = P₂V₂/T₂.
Identify the variable you need to solve for, which is P₂. Rearrange the equation to isolate P₂.
Multiply both sides of the equation by T₂ to eliminate the denominator on the right-hand side: P₁V₁T₂/T₁ = P₂V₂.
Divide both sides of the equation by V₂ to isolate P₂: P₂ = (P₁V₁T₂)/(T₁V₂).
Verify that the rearranged formula makes sense by checking the units of each variable (pressure, volume, and temperature) to ensure dimensional consistency.

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Key Concepts

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

Combined Gas Law

The Combined Gas Law is an equation that relates the pressure, volume, and temperature of a gas. It combines Boyle's Law, Charles's Law, and Gay-Lussac's Law into a single formula: (P₁V₁)/T₁ = (P₂V₂)/T₂. This law is essential for understanding how changes in one variable affect the others in a closed system.
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Rearranging Equations

Rearranging equations involves manipulating an equation to isolate a specific variable. This process often requires using algebraic techniques such as addition, subtraction, multiplication, and division. In the context of the Combined Gas Law, rearranging allows us to solve for P₂ by expressing it in terms of the other variables.
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Variables in Gas Laws

In the context of gas laws, the key variables are pressure (P), volume (V), and temperature (T). Each variable plays a crucial role in determining the state of a gas. Understanding how these variables interact and affect each other is vital for solving problems related to gas behavior, such as finding P₂ in the Combined Gas Law.
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Related Practice
Textbook Question

Suppose a mixture contains helium and oxygen gases. If the partial pressure of helium is the same as the partial pressure of oxygen, what do you know about the number of helium atoms compared to the number of oxygen molecules? Explain.

Textbook Question

A sample of argon gas has a volume of 735 mL at a pressure of 1.20 atm and a temperature of 112 °C. What is the final volume of the gas, in milliliters, when the pressure and temperature of the gas sample are changed to the following, if the amount of gas does not change?

a. 658 mmHg and 281 K

Textbook Question

A solution containing 80. g of NaNO3 in 75 g of H2O at 50 °C is cooled to 20 °C. b. How many grams of solid NaNO3 crystallized after cooling?

Textbook Question

Use the molar volume to calculate each of the following at STP:

a. the number of moles of CO2 in 4.00 L of CO2 gas

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Textbook Question

Use the words inspiration and expiration to describe the part of the breathing cycle that occurs as a result of each of the following:

c. The pressure within the lungs is higher than that of the atmosphere.

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Textbook Question

A gas sample has a volume of 0.256 L with an unknown temperature. The same gas has a volume of 0.198 L when the temperature is 32 °C, with no change in the pressure or amount of gas. What was the initial temperature, in degrees Celsius, of the gas?