Up Learn – A Level Chemistry (aqa) – Thermodynamics
Finding Entropy and Enthalpy from Gibbs vs. Temperature Graph
A graph of ΔG vs T has a gradient of -ΔS and an intercept of ΔH
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Last time we saw that all graphs of delta g against temperature will have a gradient of this, and an intercept of this.
So, here’s the graph for the reaction between methane and water.
What’s the enthalpy change for this reaction?
The enthalpy change for this reaction is this, because that’s the intercept of this graph.
And when we compare our answer to the data book value, they match up well!
Next, what’s the entropy change for this reaction?
The entropy change for this reaction is related to the gradient of this graph by this equation
We find the gradient by drawing a triangle like this, finding the change in y and the change in x, dividing the change in y by the change in x, and evaluating to give this.
And so, since the entropy change for the reaction is the negative of the gradient of this line, that means it must be this.
However, this time, when we compare our answer to the data book value, they match up poorly.
The value we calculated is exactly a thousand times smaller than the data book value.
So why are they different? Have we made a mistake?
Nope, they’re different thanks to units.
This value is in joules per kelvin per mole
But this value is in kilo joules per kelvin per mole
…which explains why it’s a thousand times smaller.
So, since it’s convention to give entropy in joules per kelvin per mole, whenever we work out the entropy change from the gradient of a graph, we need to multiply our answer by one thousand.
So now, what’s the entropy change for this reaction?
The gradient of the graph is this
And that means the entropy change for the reaction is this in these units [negative of that value calculated in kJ K-1 mol-1],
But we need our answer in these units [last answer multiplied by 1000 with units of J K-1 mol-1]
And, to find that, we multiply this answer by a thousand..
So, to sum up…
If we’re given a graph of delta g against temperature for a reaction, we can find the enthalpy change – in units of kilojoules per mole – by simply reading off the intercept
However to find the entropy change – in units of joules per kelvin per mole – we need to find the gradient…
Reverse its sign
And multiply it by a thousand.