Consider the reaction
Ni(s) + 4CO(g) ! Ni(CO)4(g)
Assuming the gases are ideal, calculate the
work done on the system at a constant pres-
sure of 1 atm at 75�C for the conversion of
1.00 mole of Ni to Ni(CO)4.
0.008759J
I would convert 4 mols CO to volume using PV = nRT and the conditions listed.
After conversion, the volume is 1/4 that (because mols is 1/4 the original).
Work = p*delta V. P is 1 atm.
The unit is L*atm. That should be converted to J. Multiply by 101.325 to do that. You will need to add the correct sign also.
To calculate the work done on the system for this reaction, we can use the ideal gas law and the equation for work done on a gas at constant pressure.
The ideal gas law states:
PV = nRT
Where:
P = Pressure (in atm)
V = Volume (in liters)
n = Number of moles
R = Ideal gas constant
T = Temperature (in Kelvin)
To calculate the work done, we need to calculate the change in volume (ΔV) when 1.00 mole of Ni is converted to Ni(CO)4. Since the reaction occurs at a constant pressure, the work done is equal to -PΔV, where P is the pressure.
First, let's calculate the change in volume.
1. Convert the temperature from Celsius to Kelvin:
T = 75 + 273 = 348 K
2. Calculate the initial and final volumes using the ideal gas law. Since the reaction occurs at 1 atm pressure, we can assume that the initial and final pressures are also 1 atm.
Initial volume:
P1V1 = nRT
V1 = (1 mole)(0.0821 L.atm/K.mol)(348 K) / (1 atm) = 28.5696 L
Final volume:
Since 1 mole of Ni reacts to form 1 mole of Ni(CO)4, the change in moles is 1 - 1 = 0 moles.
P2V2 = nRT
V2 = (0 moles)(0.0821 L.atm/K.mol)(348 K) / (1 atm) = 0 L
3. Calculate the change in volume:
ΔV = V2 - V1 = 0 L - 28.5696 L = -28.5696 L
Finally, calculate the work done using the formula:
Work = -PΔV
Work = -(1 atm)(-28.5696 L) = 28.5696 L.atm
Therefore, the work done on the system for the conversion of 1.00 mole of Ni to Ni(CO)4 at a constant pressure of 1 atm and 75°C is 28.5696 L.atm.