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A 2.5-l sample of helium gas, collected at 0.00°c and 1.00 atm, is compressed into a 0.50-l cylinder. What pressure will the gas exert in the cylinder at 34.8°c?
Accepted Answer
This problem can be solved using the combined gas law, which states: (P₁V₁)/T₁ = (P₂V₂)/T₂.
Here's how to apply it:
Identify the variables:
P₁ = 1.00 atm (initial pressure)
V₁ = 2.5 L (initial volume)
T₁ = 0.00°C = 273.15 K (initial temperature in Kelvin)
V₂ = 0.50 L (final volume)
T₂ = 34.8°C = 307.95 K (final temperature in Kelvin)
P₂ = ? (final pressure, what we need to find)
Plug the values into the combined gas law equation:
(1.00 atm
2.5 L) / 273.15 K = (P₂
0.50 L) / 307.95 K
Solve for P₂:
P₂ = (1.00 atm
2.5 L
307.95 K) / (273.15 K
0.50 L)
P₂ ≈ 5.64 atm
Therefore, the helium gas will exert a pressure of approximately 5.64 atm in the cylinder.
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