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: 9781292472249당신이 사용하는 게 아니라요?교과서 변경

Timberlake 14th Edition

Ch.8 Gases

문제 42

8장, 문제 42

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

검증된 단계별 안내

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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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.

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