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Synthetic diamonds can be manufactured at a pressure of [tex]6.00 \times 10^4[/tex] atm. If we take 2.00 liters of gas at 1.00 atm and compress it to a pressure of [tex]6.00 \times 10^4[/tex] atm, what would the volume of the gas be?

Answer :

Final answer:

This question involves the principle of Boyle's Law in the context of gas compression during the manufacturing of synthetic diamonds. Using Boyle's Law, we find that when 2 liters of gas at 1 atm pressure is compressed to 6.00 x 10⁴ atm, the volume of the gas decreases.

Explanation:

The topic here involves the principles of gas laws, specifically Boyle's Law, which states that the pressure (P) of a given quantity of gas inversely varies with its volume (V) at constant temperature. In this case, the law can be applied to a scenario regarding the manufacturing of synthetic diamonds, where a gas is being compressed from an initial state of 1.00 atm and 2.00 liters to a final state of 6.00 x 10⁴ atm. Boyle's Law can be represented algebraically as P1V1=P2V2. If we consider P1 as 1 atm, V1 as 2 liters, and P2 as 6.00 x 10⁴ atm, we can solve for V2 (the final volume of the gas). V2=P1V1/P2 = (1 atm)(2 liters)/(6.00 x 10⁴ atm). The atm in the numerator and denominator will cancel each other out, leaving us with the final volume in liters. So, once 2 liters of the gas at 1 atm pressure would be compressed to a pressure of 6.00 x 10⁴ atm, the volume would significantly decrease according to the principles of Boyle's Law.

Learn more about Boyle's Law here:

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