Final answer:
To calculate the work done by 1.1 mol of an ideal gas during isothermal expansion to double its volume at 322 K and 4.1 atm, we use the formula W = nRTln(Vf/Vi). After converting pressure to the correct units and performing the calculations, the work done is found to be approximately 2004 J.
Step-by-step explanation:
Calculating Work Done by an Ideal Gas During Isothermal Expansion
To calculate the work done by 1.1 mol of an ideal gas as it expands isothermally to double its volume at 322 K and 4.1 atm, we use the formula for work in an isothermal process, which is:
W = nRTln(Vf/Vi)
Here:
n is the number of moles (1.1 mol)
R is the ideal gas constant (0.08206 L·atm/K·mol)
T is the absolute temperature (322 K)
Vf is the final volume (double the initial volume, so the ratio Vf/Vi = 2).
Before calculating, the pressure needs to be converted to the proper units, using the conversion 1 atm = 101.3 J/L. Now we can substitute the values:
W = 1.1 mol × 0.08206 L·atm/K·mol × 322 K × ln(2)
First, calculate the natural logarithm of 2, and then do the multiplication:
W = 1.1 × 0.08206 × 322 × 0.693 = 19.8 L·atm
Now, convert L·atm to joules:
W = 19.8 L·atm × 101.3 J/L·atm = 2004.14 J
Therefore, the work done by the ideal gas is approximately 2004 J when it expands isothermally to double its volume.