A sample of helium gas has a volume of 325L at 25C and at 5atm. At what temperature the gas can be compressed at 50atm to a volume of 125L?
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To solve this problem, we can use the combined gas law, which relates the pressure, volume, and temperature of a gas.
The combined gas law formula is:
(P₁ * V₁) / T₁ = (P₂ * V₂) / T₂
Where:
P₁ and P₂ are the initial and final pressures
V₁ and V₂ are the initial and final volumes
T₁ and T₂ are the initial and final temperatures, measured in Kelvin
Let's plug in the values from the problem into the formula:
P₁ = 5 atm
V₁ = 325 L
T₁ = 25 °C = 25 + 273.15 = 298.15 K
P₂ = 50 atm
V₂ = 125 L
We want to find T₂.
Now, we can rearrange the formula to solve for T₂:
T₂ = (P₂ * V₂ * T₁) / (P₁ * V₁)
Let's substitute the given values into the formula:
T₂ = (50 atm * 125 L * 298.15 K) / (5 atm * 325 L)
The units of atm and L cancel out, leaving us with:
T₂ = (50 * 125 * 298.15) / (5 * 325)
T₂ = 15055.625 / 1625
T₂ ≈ 9.26 K
Therefore, the gas can be compressed to a volume of 125 L at a pressure of 50 atm, at a temperature of approximately 9.26 Kelvin.