High School

Synthetic diamonds can be manufactured at pressures of [tex]6.00 \times 10^4[/tex] atm. If we took 2.00 liters of gas at 775 kPa and compressed it to a pressure of [tex]6.00 \times 10^4[/tex] atm, what would the volume of that gas be?

Answer :

If we took 2.00 liters of gas at 775 kpa and compressed it to a pressure of 6.00 x 104 atm the volume of the gas would be 6.00 x 10⁻⁴atm.

The ideal gas law can be used to solve this issue:

PV = nRT

where n is the number of moles of gas, P the pressure, V the volume, R the gas constant, and T the temperature.

n = PV/RT

where (8.31 J/mol*K) is the gas constant (R). The gas must be an ideal gas, as no information is provided to indicate otherwise.

The formula for n is (775 kPa * 2.00 L) / (8.31 J/mol*K * 298 K) = 0.595 mol.

The final volume can then be determined using the revised ideal gas law equation, which is as follows:

V2 = 12 mL or 0.012 L.

Therefore, assuming constant temperature and optimal gas behavior, the volume of gas at a pressure of 6.00 x 10⁻⁴atm would be roughly 12 mL.

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