Which equation represents the combined gas law?

• A. P_1 V_1 = P_2 V_2
• B. P_1 V_1 / T_1 = P_2 V_2 / T_2
• C. V_1 / T_1 = V_2 / T_2
• D. P V = n R T

Answer: (B)

Verified step by step guidance

1. Recall that the combined gas law relates pressure (P), volume (V), and temperature (T) of a fixed amount of gas, combining Boyle's, Charles's, and Gay-Lussac's laws.
2. Write down the individual gas laws: Boyle's law is \(P_1 V_1 = P_2 V_2\) (constant temperature), Charles's law is \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\) (constant pressure), and Gay-Lussac's law is \(\frac{P_1}{T_1} = \frac{P_2}{T_2}\) (constant volume).
3. Understand that the combined gas law incorporates changes in pressure, volume, and temperature simultaneously for a fixed amount of gas, so it combines these relationships into one equation.
4. Express the combined gas law as \(\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}\), which shows that the ratio of the product of pressure and volume to temperature remains constant.
5. Recognize that this equation assumes the amount of gas (number of moles, n) is constant and is useful for solving problems where pressure, volume, and temperature all change.