Calculate ΔHºrxn for the reaction
3 O2(g) ==> 2 O3(g)
This is the information I am given:
2H2S(g) + SO2g) ==> 3S(s) + 2H2O(l)
ugh my bad the information I'm given is:
O2 ==> 2 O(g)ΔHºrxn=498kJ/mol
O(g) + O2(g) ==> O3ΔHºrxn = /106kJ/mol
I think what I'm supposed to do is change the two reactions I'm given by either reversing them or multiplying by a coefficient, then doing the same thing to the enthalpy, but I'm confused about how i go about doing that
Multiply equation 1 by 1 and equation 2 by 2, add them together and add the delta H for each. (When you add the two multiplied equations, check to make sure the items you don't want cancel and leaves the equation desired.)
1 *(O2 ==> 2 O(g)ΔHºrxn=498kJ/mol)
2 * (O(g) + O2(g) ==> O3ΔHºrxn = -106kJ/mol)
O2 + 2O + 2O2 ==> 2O + 2O3
3O2 ==> 2O3
498-212=286ΔHºrxn
is that right? and if so, how did you know which numbers to multiply each equation by?
1 *(O2 ==> 2 O(g)ΔHºrxn=498kJ/mol)
2 * (O(g) + O2(g) ==> O3ΔHºrxn = -106kJ/mol)
O2 + 2O + 2O2 ==> 2O + 2O3
3O2 ==> 2O3
498-212=286ΔHºrxn
is that right? and if so, how did you know which numbers to multiply each equation by?
Yes, that number is correct.
How to know what to multiply by.
Look at the final equation. We MUST have 2O3 on the right side and the ONLY way to get that is to multiply the second equation by 2. So I did that, added the two equations to see what I had; lo and behold, the final equation added up to what I wanted. (To emphasize the point, I should point out that wasn't my first try. FIRST, I said I needed 3 O2 and 2O3 so I FIRST multiplied equation 1 by 3 and equation 2 by 2 and added. Of course, I had too many O2 (because some comes from both 1 and 2) AND I didn't cancel all the O atoms. So I regrouped and tried the next approach. It worked. :)]
To calculate ΔHºrxn for the given reaction, we can use Hess's Law, which states that the enthalpy change of a reaction depends only on the initial and final states and is independent of the pathway taken.
First, let's examine the information given and identify any relevant reactions that can help us. We have the reaction:
2H2S(g) + SO2(g) ==> 3S(s) + 2H2O(l)
From this reaction, we can see that formation of sulfur (S) and water (H2O) are involved. However, the reaction we are interested in is the formation of ozone (O3).
To obtain the desired reaction, we can manipulate the given reaction to change sulfur to oxygen. Since we are looking for 3 moles of oxygen (O2), we need to multiply the given reaction by three:
6H2S(g) + 3SO2(g) ==> 9S(s) + 6H2O(l)
Now, it is clear to see that to go from 6 moles of sulfur (S) to 3 moles of oxygen (O2), we can cancel out the sulfur in the given reaction and rewrite it as:
3O2(g) ==> 2O3(g)
The coefficients in this reaction indicate that 3 moles of oxygen (O2) form 2 moles of ozone (O3).
Now that we have the desired reaction, we can calculate ΔHºrxn. Hess's Law tells us that we can add the enthalpy changes of the individual reactions to obtain the enthalpy change of the overall reaction.
We need to find the enthalpy change for the reaction:
3O2(g) ==> 2O3(g)
We can express this reaction as a combination of the given reaction and its reverse reaction (flipping the reaction and changing the signs of the enthalpies):
2O3(g) ==> 3O2(g)
Now, we can write the relevant enthalpy changes of these reactions:
2H2S(g) + SO2(g) ==> 3S(s) + 2H2O(l)ΔH1º = ? (given)
2O3(g) ==> 3O2(g)ΔH2º = ? (unknown)
3O2(g) ==> 2O3(g)ΔH3º = ΔHºrxn (what we are solving for)
To find ΔH2º, we need to rearrange the equation:
2O3(g) ==> 3O2(g)
So that it matches the given reaction:
2H2S(g) + SO2(g) ==> 3S(s) + 2H2O(l)
By flipping the given reaction and changing the signs of the enthalpies, we have:
3S(s) + 2H2O(l) ==> 2H2S(g) + SO2(g)
Now, we can see that:
2H2S(g) + SO2(g) + 2O3(g) ==> 3S(s) + 2H2O(l) + 3O2(g)ΔHºrxn = ΔH1º - ΔH2º
Therefore, to find ΔHºrxn, you subtract the enthalpy change of the reaction 2O3(g) ==> 3O2(g) from the enthalpy change of the given reaction 2H2S(g) + SO2(g) ==> 3S(s) + 2H2O(l).
In conclusion, to calculate ΔHºrxn for the reaction 3O2(g) ==> 2O3(g), you need to use Hess's Law and subtract the enthalpy change of the reaction 2O3(g) ==> 3O2(g) from the enthalpy change of the given reaction 2H2S(g) + SO2(g) ==> 3S(s) + 2H2O(l).