An ideal gas is contained in a vessel with a moveable piston. Initially, the gas has a volume of 0.024 m^3
,an absolute pressure of 1.8 atm, and a temperature of 35.0 °C. The pressure is 0.90 atm when the volume of
the container is decreased to 0.012 m3 . What is the final temperature of the gas?
A) 77 K
B) 85 K
C) 170 K
D) 154 K
E) 282 K
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The ideal gas law states that the pressure of a gas times its volume is proportional to the number of gas molecules times the temperature of the gas. This can be written as P1V1/T1 = P2V2/T2, where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures.
First, we need to convert the temperatures from Celsius to Kelvin. The conversion is T(K) = T(C) + 273.15. So, T1 = 35.0 + 273.15 = 308.15 K.
Next, we can plug the given values into the ideal gas law equation and solve for T2:
(1.8 atm)(0.024 m^3) / 308.15 K = (0.90 atm)(0.012 m^3) / T2
Solving for T2 gives T2 = (0.90 atm)(0.012 m^3) * 308.15 K / (1.8 atm)(0.024 m^3) = 154 K.
So, the final temperature of the gas is 154 K, which is answer choice D.
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