SME
Grade 10 Science · Problem type
ΔS° from a table, then ΔG°
Use this for “The products’ standard entropies add to 214 J/(mol·K) and the reactants’ to 188; ΔH° = −50 kJ/mol. What are ΔS° and ΔG° at 298 K?”
Diagram
From 188 J/(mol·K) to 214 J/(mol·K): 26 J/(mol·K) to the right.
This is an example. Type your own values to start a new problem.
ΔS° (J/(mol·K))
=
S°ₚ (J/(mol·K))
−
S°ᵣ (J/(mol·K))
ΔG° (kJ/mol)
=
ΔH° (kJ/mol)
−
T (K)
×
ΔS° (J/(mol·K))
1,000
Formulas
ΔS° = S°ₚ − S°ᵣ
26 = 214 − 188
ΔG°
=
ΔH°
−
T
×
ΔS°/1,000
−57.7
=
−50
−
298
×
26
1,000
Assumptions
•
Each sum is over one side of the balanced equation: every S° is multiplied by its coefficient first.
•
A change is products minus reactants, so ΔS° = S°ₚ − S°ᵣ (p for products, r for reactants); ΔG°f values from a table subtract the same way.
•
ΔG° = ΔH° − TΔS°, with ΔS° divided by 1,000 to match ΔH°’s kJ; tables are for 298 K.
•
At other temperatures this treats ΔH° and ΔS° as unchanged, an estimate.
Step-by-step
WE KNOW
S°ₚ = 214 J/(mol·K), S°ᵣ = 188 J/(mol·K), ΔH° = −50 kJ/mol, T = 298 K
FIND
standard entropy change (ΔS°), standard free energy change (ΔG°)
Step 1 · Find standard entropy change (ΔS°)
Use ΔS° = S°ₚ − S°ᵣ
Products minus reactants: a positive change means the products are more spread out.
ΔS° = 214 − 188
ΔS° = 26 J/(mol·K)
Step 2 · Find standard free energy change (ΔG°)
Use ΔG° = ΔH° − T × ΔS°/1,000
Take TΔS°, in kJ, from ΔH°.
ΔG°
=
−50
−
298
×
26
1,000
ΔG° = −50 − 7.748
ΔG° = −57.7 kJ/mol (below 0: spontaneous at 298 K)
Check
Put the numbers back in. Both sides should match.
26 = 214 − 188 ✓
−57.7
≈
−50
−
298
×
26
1,000
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Related lessons
Entropy, free energy and spontaneity
Main lesson
The temperature where it turns spontaneous
Use this for “Above what temperature is a reaction with ΔH = 60 kJ/mol and ΔS = 150 J/(mol·K) spontaneous?”
Does entropy go up or down?
Use this for “Predict the sign of ΔS when a gas forms from a solid.”
When is it spontaneous?
Use this for “A reaction has ΔH > 0 and ΔS > 0. When is it spontaneous?”