StepWorking
01Given
Temperature T=300 K.
Process A: ΔH=−25 kJ mol−1, ΔS=−80 J K−1mol−1
Process B: ΔH=−22 kJ mol−1, ΔS=40 J K−1mol−1
Process C: ΔH=25 kJ mol−1, ΔS=−50 J K−1mol−1
Process D: ΔH=22 kJ mol−1, ΔS=20 J K−1mol−1
02Find
The number of non-spontaneous processes at 300 K (processes where ΔG>0).
03Strategise
Use the Gibbs-Helmholtz equation ΔG=ΔH−TΔS. Ensure consistent units by converting ΔH to J mol−1 (multiply by 103) or ΔS to kJ K−1mol−1 (divide by 103). A process is non-spontaneous if ΔG>0.
04Execute
For Process A:
ΔGA=−25000−300(−80)=−25000+24000=−1000 J mol−1<0 (Spontaneous).
For Process B:
ΔGB=−22000−300(40)=−22000−12000=−34000 J mol−1<0 (Spontaneous).
For Process C:
ΔGC=25000−300(−50)=25000+15000=+40000 J mol−1>0 (Non-spontaneous).
For Process D:
ΔGD=22000−300(20)=22000−6000=+16000 J mol−1>0 (Non-spontaneous).
Total non-spontaneous processes = 2 (Processes C and D).
✓Verify
Processes B and C can be checked by inspection: for B, ΔH<0 and ΔS>0, always spontaneous at all T. For C, ΔH>0 and ΔS<0, always non-spontaneous at all T. For A, TΔS=−24 kJ, so ΔH−TΔS=−25−(−24)=−1 kJ<0 (spontaneous). For D, TΔS=6 kJ, so ΔH−TΔS=22−6=16 kJ>0 (non-spontaneous). Exactly 2 processes are non-spontaneous.
