Calculate ▲U,▲H, ▲S, ▲A and▲G in expanding 1 mole of ideal gas at 25 ° c from 10 to 100 dm cubed. (5marks )
To calculate ▲U, ▲H, ▲S, ▲A, and ▲G for the expansion of 1 mole of an ideal gas from 10 to 100 dm³ at 25 °C, we'll need to use thermodynamic equations and data. Here's a step-by-step guide on how to calculate each of these values:
1. Calculate the change in internal energy (▲U):
- The change in internal energy is given by the equation ▲U = nCv▲T, where n is the number of moles, Cv is the molar heat capacity at constant volume, and ▲T is the change in temperature.
- In this case, n = 1 mole, and Cv for an ideal gas is 3/2 R. R is the gas constant, which is approximately 8.314 J/(mol·K).
- ▲T can be calculated as the final temperature minus the initial temperature.
- Plug in the values and calculate ▲U.
2. Calculate the change in enthalpy (▲H):
- Since the process occurs at constant pressure, the change in enthalpy is given by the equation ▲H = ▲U + P▲V, where P is the pressure and ▲V is the change in volume.
- In this case, ▲V can be calculated as the final volume minus the initial volume.
- The pressure is not given, so assume it to be constant or use an average pressure.
- Plug in the values calculated in step 1 and calculate ▲H.
3. Calculate the change in entropy (▲S):
- The change in entropy is given by the equation ▲S = nCp ln(T₂/T₁) - nR ln(V₂/V₁), where n is the number of moles, Cp is the molar heat capacity at constant pressure, T₁ and T₂ are the initial and final temperatures, and V₁ and V₂ are the initial and final volumes.
- In this case, n = 1 mole, Cp for an ideal gas is 5/2 R.
- Plug in the values and calculate ▲S.
4. Calculate the change in Helmholtz free energy (▲A):
- The change in Helmholtz free energy is given by the equation ▲A = ▲U - T▲S, where ▲U is the change in internal energy and ▲S is the change in entropy.
- Plug in the values calculated in steps 1 and 3 and calculate ▲A.
5. Calculate the change in Gibbs free energy (▲G):
- The change in Gibbs free energy is given by the equation ▲G = ▲H - T▲S, where ▲H is the change in enthalpy and ▲S is the change in entropy.
- Plug in the values calculated in steps 2 and 3 and calculate ▲G.
By following these steps, you should be able to calculate ▲U, ▲H, ▲S, ▲A, and ▲G for the given expansion of the ideal gas.