HOW DO WE CALCULATE Δ G (Second Way)?
The second way to calculate Δ G is to use a formula that involves enthalpy, temperature, and entropy. The formula is below:
Spontaneity = |
Enthalpy – (Temperature * Entropy) |
Δ G = |
Δ H – (T * Δ S) |
Δ G is in the units Joules (J). Δ H is in the units of Joules (J). T is in the units of Kelvin (K). Δ S is in the units of Joules per Kelvin (J / K). However, again because all of these are linked to chemistry and because chemistry likes to measure everything per mole all of the variables above but temperature may also have attached to them per mole ( /mol). So for example Δ H might be in the units of (J / mol) or (kJ / mol). I will do a demonstration of the two most common ways you will see the units of these problems on homework or tests.
VIDEO Calculate Δ G (DELTA G) Demonstrated Example 3: For a particular chemical reaction the Δ H is -1345 J the temperature is 300K and the Δ S is 50 J/K. What is the Gibbs free energy? Is this reaction spontaneous or non-spontaneous?
What information are we given?
Answer:
Δ H = -1345 J
T = 300K
Δ S = 50 J/K
What does the question ask for?
Answer: Δ G = ?
How do we set up the problem?
Answer: Start with the equation
Δ G = | Δ H – (T * Δ S) |
What can we fill in for the equation?
Answer: The information we are given (red).
Δ G = | -1345 J – (300 K * 50 J /K) |
How do I do the calculations?
Answer: 1345 – (300 * 50) = -13655
-13655 J = | -1345 J – (300 K * 50 J /K) |
What is the complete answer?
COMPLETE ANSWER: -16345 J…..spontaneous (because the number is negative)
VIDEO Calculate Δ G (DELTA G) Demonstrated Example 4: A chemical reaction has the Δ H of 65 kJ/mol the temperature of -100 C and the Δ S of 14 J/mol K. What is the Gibbs free energy? Is this reaction spontaneous or non-spontaneous?
What information are we given?
Answer:
Δ H = 65 kJ/mol ——> 65000 J/mol
T = -100 C ——> 173 K
Δ S = 50 J/K
What does the question ask for?
Answer: Δ G = ?
How do we set up the problem?
Answer: Start with the equation
Δ G = | Δ H – (T * Δ S) |
What can we fill in for the equation?
Answer: The information we are given (red).
Δ G = | 65000 J / mol – (173 K * 14 J / mol K) |
How do I do the calculations?
Answer: 65000 – (173 * 14) = 62578 J
62578 J = | 65000 J – (173 K * 14 J /K) |
What is the complete answer?
COMPLETE ANSWER: 62578 J…..non-spontaneous (because the number is positive)
VIDEO Calculate Δ G (DELTA G) Demonstrated Example 5: A chemical reaction has a Δ H of 3800 J and a Δ S of 26 J/K. At what temperature does the reaction become spontaneous?
What information are we given?
Answer:
Δ H = 3800 J
Δ S = 26 J/K
Δ G = 0 J (reaction become spontaneous)
What does the question ask for?
Answer: T = ?
How do we set up the problem?
Answer: Start with the equation
Δ G = | Δ H – (T * Δ S) |
1 |
What can we fill in for the equation?
Answer: The information we are given (red).
0 J = | 3800 J – (T * 26 J / K) |
1 |
How do we rearrange the equation?
Answer: Subtract 3800 J from both sides (red).
0 J = | 3800 J – (T * 26 J / K) |
– 3800 J | – 3800 J |
Cross out the 3800 J on the right side.
0 J = | 3800 J – (T * 26 J / K) |
– 3800 J | – 3800 J |
Simplify
– 3800 J = | – (T * 26 J / K) |
1 |
Remove the negative from both sides of the equation.
3800 J = | T * 26 J / K |
1 |
Divide both sides by 26 J / K (red).
3800 J = | T * 26 J / K |
26 J / K | 26 J / K |
Cross out the 26 J / K on the right side.
3800 J = | T * 26 J / K |
26 J / K | 26 J / K |
Simplify
3800 J = | T |
26 J / K |
How do I do the calculations?
Answer: (3800 / 26 ) = 146
3800 J = | T |
26 J / K |
What is the complete answer?
COMPLETE ANSWER: 146 K
PRACTICE PROBLEMS: Calculate the Δ G, Δ H, Δ S, or T for the problems below.
A chemical reaction has the Δ H of +5055 J at the temperature 273K and the Δ S is 105 J/K. What is the Gibbs free energy? Is this reaction spontaneous or non-spontaneous?
Answer: -23610 J, spontaneous……because the number is negative
If you have a reaction with a Δ S of 48 J/K the temperature of 40 C and the Δ G of 12 kJ. What is the Enthalpy of the reaction?
Answer: -1772 J
A chemical reaction has a Δ H of 14000 J and a Δ S of 44 J/K . At what temperature does the reaction become spontaneous?
Answer: 318 K……your Δ G is 0 (become spontaneous)
If you have a reaction with a temperature of 58 C and the Δ H of -7400 J. What is the entropy when the Δ G is -56 kJ?
Answer: 147 J / K