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A sample of flammable liquid is placed into an enclosed cylinder which is then fitted with a movable piston. Initially the cylinder contains a volume of 8.20 L. The sample is ignited producing gas and releasing 427.8 J of energy. To what volume will the cylinder expand to if it must expand against a pressure of 826.1 mmHg. Assume all the energy released is converted to work used to push the piston?


760 mmHg = 1 atm
101.3 J = 1 L atm

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dsdrajlin

Answer:

12.09 L

Explanation:

Step 1: Convert 826.1 mmHg to atm

We will use the conversion factor 760 mmHg = 1 atm.

826.1 mmHg × 1 atm/760 mmHg = 1.087 atm

Step 2: Convert 427.8 J to L.atm

We will use the conversion factor 101.3 J = 1 L.atm.

427.8 J × 1 L.atm/101.3 J = 4.223 L.atm

Step 3: Calculate the change in the volume

Assuming the work done (w) is 4.223 L.atm against a pressure (P) of 1.087 atm, the change in the volume is:

w = P × ΔV

ΔV = w/P

ΔV = 4.223 L.atm/1.087 atm = 3.885 L

Step 4: Calculate the final volume

V₂ = V₁ + ΔV

V₂ = 8.20 L + 3.885 L = 12.09 L

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