a gas expands from 266 mL to 983 mL at constant temperature. calc the work done (in joules) by the gas if it expands against a vacuum. also call the work done (in joules) by the gas if it expands against a constant pressure of 4.09 atm.

w₁ = 0 J

w₂ = -297 J

Explanation:

Step 1: Given data

Initial volume: 266 mL (0.266 L)

Final volume: 983 mL (0.983 L)

Step 2: Calculate the work done (in joules) by the gas if it expands against a vacuum

We will use the following expression.

w₁ = -P₁ × ΔV

Since the gas expands against a vacuum, P₁ = 0. Thus, w₁ = 0 J

Step 3:  Calculate the work done (in joules) by the gas if it expands against a constant pressure of 4.09 atm

We will use the following expression.

w₂ = -P₂ × ΔV

w₂ = -4.09 atm × (0.983 L-0.266 L) = -2.93 atm.L

Then, we convert w₂ to Joule using the conversion factor 1 atm.L = 101.325 J.

-2.93 atm.L × 101.325 J/1 atm.L = -297 J