A mixture of nitrogen and argon gas is compressed from a volume of 70.0 L to a volume of 61.0 L, while the pressure is held constant at 14.0 atm. Calculate the work done on the gas mixture. Provide your answer is kJ
To calculate the work done on the gas mixture, we can use the equation:
Work = -PΔV
where P is the pressure and ΔV is the change in volume.
Given:
Initial volume (V1) = 70.0 L
Final volume (V2) = 61.0 L
Pressure (P) = 14.0 atm
To calculate the change in volume, we use the formula:
ΔV = V2 - V1
ΔV = 61.0 L - 70.0 L
ΔV = -9.0 L
Note: The negative sign indicates a decrease in volume.
Now, we can substitute the given values into the equation:
Work = -PΔV
Work = -14.0 atm (-9.0 L)
Work = 126.0 L⋅atm
To convert L⋅atm to kJ, we need to use the conversion factor 101.3 J = 1 L⋅atm:
Work = 126.0 L⋅atm x (101.3 J / 1 L⋅atm) x (1 kJ / 1000 J)
Work = 12,752.2 kJ
Therefore, the work done on the gas mixture is 12,752.2 kJ.