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What volume of gas in liters at 100.°c must be cooled to 34°c if the gas volume at constant pressure and 34°c is to be 1.8 l?
Accepted Answer
This problem involves Charles's Law, which states that the volume of an ideal gas is directly proportional to its absolute temperature (in Kelvin) at constant pressure. Here's how to solve it:
1. Convert temperatures to Kelvin:
- 100°C + 273.15 = 373.15 K
- 34°C + 273.15 = 307.15 K
2. Set up the Charles's Law equation:
V₁/T₁ = V₂/T₂
Where:
- V₁ is the initial volume (unknown)
- T₁ is the initial temperature (373.15 K)
- V₂ is the final volume (1.8 L)
- T₂ is the final temperature (307.15 K)
3. Solve for V₁:
V₁ = (T₁
V₂) / T₂
V₁ = (373.15 K
1.8 L) / 307.15 K
V₁ ≈ 2.19 L
Therefore, the initial volume of the gas must be approximately 2.19 liters.
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