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?

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.

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