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: \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \).
2. To solve for \( P_2 \), first multiply both sides by \( T_2 \) to eliminate the denominator on the right side: \( T_2 \times \frac{P_1 V_1}{T_1} = P_2 V_2 \).
3. Next, divide both sides by \( V_2 \) to isolate \( P_2 \) on one side of the equation: \( \frac{T_2 \times P_1 V_1}{T_1 V_2} = P_2 \).
4. Rearrange the equation to clearly show \( P_2 \) on the left side: \( P_2 = \frac{P_1 V_1 T_2}{T_1 V_2} \).
5. This equation now expresses \( P_2 \) in terms of the other variables: \( P_1 \), \( V_1 \), \( T_1 \), \( V_2 \), and \( T_2 \).

Key Concepts

Combined Gas Law

The combined gas law is an equation that relates the pressure, volume, and temperature of a gas. It is expressed as (P₁V₁)/T₁ = (P₂V₂)/T₂, where P is pressure, V is volume, and T is temperature. This law combines Boyle's Law, Charles's Law, and Gay-Lussac's Law, allowing for the analysis of gas behavior under varying conditions.

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, isolating P₂ means expressing it in terms of the other variables, which is essential for solving problems related to gas behavior.

Gas Variables

Gas variables include pressure (P), volume (V), and temperature (T), which are interrelated in the behavior of gases. Pressure is the force exerted by gas particles, volume is the space occupied by the gas, and temperature is a measure of the average kinetic energy of the particles. Understanding how these variables interact is crucial for applying the combined gas law effectively.