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

Verified step by step guidance

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

Key Concepts

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.