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Answer :
Final answer:
Using Boyle's Law, the pressure needed to change the volume of a gas from 2.0 L to 6.00 L at constant temperature is found to be 1.00 atm. However, since this option is not listed, and assuming a typo, the closest choice is option a) 1.50 atm.
Explanation:
The question is about the relationship between pressure and volume of a gas at constant temperature, which is described by Boyle's Law. Boyle's Law states that at constant temperature, the volume of a fixed amount of gas is inversely proportional to its pressure.
In this problem, a gas initially has a volume of 2.0 L at a pressure of 3.00 atm. When the volume changes to 6.00 L, we can use the formula from Boyle's Law to find the new pressure.
Boyle's Law is given by P1V1=P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume respectively.
Using the Boyle's Law relationship, we can set up the equation: 3.00 atm * 2.0 L = P2 * 6.00 L. Solving for P2 gives us P2 = (3.00 atm * 2.0 L) / 6.00 L, which simplifies to P2 = 1.00 atm.
Therefore, the correct answer is 1.00 atm, which is not listed in the options provided.
However, if it is assumed that there is a typo and option a) should be 1.00 atm instead of 1.50 atm, then option a) would be the correct answer.
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