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According to the Ideal Gas Law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
If the number of moles and the temperature are doubled while the pressure remains constant, we can write:
(P)(2V) = (2n)(2R)(T)
Simplifying this equation, we get:
2PV = 4nRT
Dividing both sides by 2, we get:
PV = 2nRT
This equation shows that the new volume is directly proportional to the number of moles and temperature.
If we assume that the initial number of moles and temperature are 1 and T, respectively, and the initial volume is 3.0 L, then the new volume can be calculated as:
V' = (2n)(2R)(2T)/(P)
V' = 8(1)(0.0821)(2T)/P
V' = 1.65T/P
Therefore, the new volume is directly proportional to the temperature and inversely proportional to the pressure. Since the pressure remains constant, the new volume will be directly proportional to the temperature, which is doubled in this case.
Thus, the new volume will be double the original volume, and the correct answer is D: "The new volume is double the original volume."
Step-by-step explanation:
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