In this example we use Hess's law to calculate the change in enthalpy for a reaction.
Our problem reads, "Find the change in enthalpy for the reaction in kilojoules given these three reactions and their enthalpy changes."
According the Hess's law, if we can add together multiple reactions steps to get an overall reaction,
then the enthalpy change for the overall reaction is the sum of the enthalpy changes for the reactions steps.
To apply Hess's law, we must determine how we need to add together the three given reactions to get the overall reaction at the top.
To do this, we will look for substances in the overall reaction that only show up in one of the given reactions.
If a substance in the overall reaction shows up in more than one of the given reactions, we can initially skip it.
For example, solid carbon only shows up in the second reaction
so we know all of the solid carbon in the overall reaction must come from the second given reaction.
We want three moles of solid carbon as a reactant in our overall equation, but the second equation only has one mole of solid carbon as a reactant.
So we need to multiply the entire equation by three.
When we multiply all the coefficients in the equation by three, we also multiply the change in enthalpy for the reaction by three.
Now we have three moles of solid carbon as a reactant.
Our next substance in the overall equation is hydrogen gas, which only shows up in the third given equation.
We want four moles of hydrogen gas as a reactant in our overall reaction but the third equation only has two moles of hydrogen gas as a reactant.
So we need to multiply all the coefficients of the third equation by two and multiply the enthalpy of reaction by two.
This gives us four moles of hydrogen gas as a reactant.
Our last substance in our overall reaction is propane gas.
Propane only shows up in the first reaction but it shows up as a reactant instead of a product.
We want one mole a propane as a product so we need to reverse the first given equation
so that the reactans show up as products and the products show up as reactants.
This will give us one mole propane as a product.
When we reverse a reaction, we need to multiply the enthalpy of reaction by -1.
Now we can add together these reactions steps.
From the first reaction we have three moles of solid carbon and three moles of oxygen gas.
We need to distribute the three out front to all of the coefficients for both reactants and products.
From the second reaction we have four moles of hydrogen gas and two moles of oxygen gas.
And from the third reaction we have three moles of carbon dioxide gas and four moles of water vapor.
These are all of our reactants from the three steps.
For products we have three moles of carbon dioxide from the first reaction,
we have four moles of water vapor from the second reaction,
and we have one mole of propane gas and five moles of oxygen gas from the third reaction.
This should be all our products from all three reaction steps.
Now we can cancel out anything that shows up as both a reactant and product.
We have three moles plus two moles of oxygen gas as a reactant, which cancels out the five moles of oxygen gas as a product,
We have three moles of carbon dioxide as a reactant and product which cancel out.
And we have four moles of water vapor as a reactant and product which cancel.
All that's left is our overall reaction: 3 solid carbon plus 4 hydrogen gas produces propane gas.
Since we could add together these three reaction steps to get the overall reaction, according to Hess's law
the enthalpy change for the overall reaction is the sum of the enthalpy changes for the three steps.
We can plug in our numbers for the enthalpy change of each step.
Completing the calculation, the enthalpy change of our overall reaction should be -104.7 kilojoules.