Which of the following correctly represents the combined gas law?

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

Answer: (A)

Verified step by step guidance

1. Recall that the combined gas law relates the pressure (P), volume (V), and temperature (T) of a fixed amount of gas, combining Boyle's, Charles's, and Gay-Lussac's laws into one expression.
2. Start from the ideal gas law: \(P V = n R T\), where \(n\) and \(R\) are constants for a given amount of gas, so changes in P, V, and T can be related.
3. Since the amount of gas \(n\) and the gas constant \(R\) remain constant, the ratio \(\frac{P V}{T}\) must also remain constant for two different states of the gas.
4. Express this relationship mathematically as \(\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}\), where the subscripts 1 and 2 refer to the initial and final states respectively.
5. This equation shows how pressure, volume, and temperature change together, and it is the correct representation of the combined gas law.