The ideal gas equation can be written as

Explanation

The ideal gas equation is an equation of state for an ideal gas, meaning it describes the relationship between pressure, volume, and temperature for a gas that follows the ideal gas law. The ideal gas law can be written as:

\(PV = nRT\) Where: - P is the pressure - V is the volume - n is the number of moles of gas - R is the ideal gas constant - T is the temperature in Kelvin When comparing two sets of conditions for an ideal gas, we can rearrange the ideal gas equation to show the relationship between the initial conditions (P?, V?, T?) and the final conditions (P?, V?, T?). This is called the combined gas law, and it can be written as: \(P_1V_1T_2 = P_2V_2T_1\) This equation shows that the product of the initial pressure, volume, and final temperature is equal to the product of the final pressure, volume, and initial temperature. This equation is the correct answer, which isOption D. The other options are incorrect because they represent specific cases of the ideal gas equation, where one or more of the variables are held constant: -Option A: \(\cfrac{V_1}{T_1} = \cfrac{V_2}{T_2}\) represents the relationship between volume and temperature when pressure is constant (Charles's law). -Option B: \(P_1V_1 = P_2V_2\) represents the relationship between pressure and volume when temperature is constant (Boyle's law). -Option C: \(V_2 = \cfrac{P_1V_1T_1}{P_2T_2}\) is a rearranged form of the combined gas law, but it does not represent the ideal gas equation in its most general form.