The gas in a balloon occupies 3.50 L at 300 K. At which temperature will the balloon expand to 8.50 L?
Question
The gas in a balloon occupies 3.50 L at 300 K. At which temperature will the balloon expand to 8.50 L?
Solution
This problem can be solved using the ideal gas law, which states that the volume of a gas is directly proportional to its temperature, assuming pressure and the amount of gas are constant. This relationship can be expressed as V1/T1 = V2/T2, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.
Here are the steps to solve the problem:
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Convert all temperatures to Kelvin. In this case, the initial temperature is already given in Kelvin (300 K), so no conversion is necessary.
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Plug the given values into the equation. V1 is 3.50 L, T1 is 300 K, and V2 is 8.50 L. We're solving for T2, the final temperature.
3.50 L / 300 K = 8.50 L / T2
- Solve for T2. Cross-multiply and divide to get T2 by itself:
T2 = (8.50 L * 300 K) / 3.50 L
- Calculate the value of T2. This will give you the final temperature in Kelvin at which the balloon will expand to 8.50 L.
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