Calculate the work in kilojoules done during a reaction in which the volume expands from 10.0 L to 95.9 L against an external pressure of 2.5 atm.
what is Pressure*volume?
85.9*2.5*101kPa*dm^3== 21689750e-6 Pa*L^3
but what is a Pa? force/m^2=N/m^2
so Pa*m^3=Joules
PV=21.7Joules
To calculate the work done during the reaction, we can use the formula:
Work = -P_ext * ΔV
Where P_ext is the external pressure and ΔV is the change in volume.
In this case, we are given the following values:
P_ext = 2.5 atm
ΔV = V_final - V_initial
We can substitute these values into the formula to calculate the work done:
Work = -2.5 atm * (95.9 L - 10.0 L)
First, we need to calculate the change in volume (ΔV):
ΔV = 95.9 L - 10.0 L = 85.9 L
Now we can substitute the values into the formula to find the work done:
Work = -2.5 atm * 85.9 L
To convert the units to kilojoules (kJ), we need to use the conversion factor:
1 L⋅atm = 101.325 J
To convert from joules to kilojoules, we divide by 1000:
1 kJ = 1000 J
Multiplying the work by the conversion factor, we get:
Work = (-2.5 atm * 85.9 L) * (101.325 J / 1 L⋅atm) * (1 kJ / 1000 J)
Work = - 21957.9 J
Finally, we convert the work from joules to kilojoules by dividing by 1000:
Work = -21957.9 J / 1000
Work = -21.96 kJ
Therefore, the work done during the reaction is approximately -21.96 kilojoules. The negative sign indicates that work has been done on the system (compression) rather than by the system (expansion).