To determine which gas is at the highest temperature among the four containers, we can use the Ideal Gas Law, which is expressed as PV = nRT. In this equation, P represents pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. Since we have the same number of moles (0.5 moles) for each gas, we can rearrange the equation to solve for temperature:
Rearranging the Ideal Gas Law
The formula can be rearranged to find temperature:
T = PV / (nR)
Since R is a constant, we can focus on the product of pressure and volume (PV) for each gas to compare their temperatures directly.
Calculating PV for Each Gas
- For Helium (A):
P = 120 kPa, V = 8.0 L
PV = 120 kPa * 8.0 L = 960 kPa·L
- For Neon (B):
P = 160 kPa, V = 6.0 L
PV = 160 kPa * 6.0 L = 960 kPa·L
- For Argon (C):
P = 250 kPa, V = 4.0 L
PV = 250 kPa * 4.0 L = 1000 kPa·L
- For Krypton (D):
P = 300 kPa, V = 3.0 L
PV = 300 kPa * 3.0 L = 900 kPa·L
Comparing the Results
Now that we have calculated the PV values for each gas, we can compare them:
- Helium: 960 kPa·L
- Neon: 960 kPa·L
- Argon: 1000 kPa·L
- Krypton: 900 kPa·L
Identifying the Highest Temperature
From our calculations, Argon has the highest PV value at 1000 kPa·L. Since temperature is directly proportional to the PV product when the number of moles is constant, Argon must be at the highest temperature among the four gases.
In summary, the gas at the highest temperature is Argon (C), with a pressure of 250 kPa and a volume of 4.0 L, resulting in a PV product of 1000 kPa·L.
