The original conditions in a container filled with gas at constant temperature are 183 mL and 310 mm Hg. The desired new volume is 90.6 mL. What pressure should be applied?
Question
The original conditions in a container filled with gas at constant temperature are 183 mL and 310 mm Hg. The desired new volume is 90.6 mL. What pressure should be applied?
Solution
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas have an inverse relationship when temperature is held constant. In mathematical terms, this is expressed as P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Here are the steps to solve the problem:
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Convert all measurements to the same units. In this case, both the initial and final volumes are given in mL and the initial pressure is given in mm Hg, so no conversion is necessary.
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Plug the given values into Boyle's Law. The initial volume V1 is 183 mL, the initial pressure P1 is 310 mm Hg, and the final volume V2 is 90.6 mL. We're solving for the final pressure P2, so the equation is 310 * 183 = P2 * 90.6.
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Solve for P2. Divide both sides of the equation by 90.6 to isolate P2 on one side of the equation. P2 = (310 * 183) / 90.6.
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Calculate the value of P2. P2 = 625.55 mm Hg.
So, the pressure that should be applied is approximately 625.55 mm Hg.
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