Nitrogen and oxygen can react directly with one anotheer to produce nitrogen dioxide according to
N2(g) + 2O2(g) --> 2NO2(g)
The reaction may also be imagined to take place by first producing nitrogen oxide
N2(g) + O2(g) --> 2NO(g)
which then produces NO2
2NO(g) + O2(g) --> 2NO2(g)
The overall reaction is found by summing reactions and gives
N2(g) + 2O2(g) --> 2N2O(g)
How does the enthalpy change for the first reaction compare to that for the fourth reaction? Does this illustrate that enthalpy is a state function? Explain.
Calculate dH for each reaction of interest (or all of them) as
dHrxn = (n*dHf products) - (n*dHf reactants) then compare to answer the question. Yes it is a state function because the sum is equal to the individual parts and to be a state function it doesn't matter how we get there. It only matters about the initial and final states.
Calculate the enthaplychange for the following reaction.
NO(g)+1/2O2(g) =NO2(g)
To compare the enthalpy change of the first reaction to that of the fourth reaction, we need to determine the enthalpy change for each reaction.
The enthalpy change for a reaction is represented by ΔH, often known as the heat of reaction. It is a measure of the energy difference between the products and the reactants.
In the case of the first reaction:
N2(g) + 2O2(g) → 2NO2(g)
The enthalpy change for this reaction will be denoted as ΔH1.
In the case of the fourth reaction:
N2(g) + 2O2(g) → 2N2O(g)
The enthalpy change for this reaction will be denoted as ΔH4.
Now, if we add the enthalpy changes for the individual steps in the second and third reactions together, we can determine the total enthalpy change for the fourth reaction:
ΔH2 + ΔH3 = ΔH4
This implies that:
N2(g) + O2(g) → 2NO(g) ΔH2
2NO(g) + O2(g) → 2NO2(g) ΔH3
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N2(g) + 2O2(g) → 2N2O(g) ΔH4
From this, we can see that the enthalpy change for the fourth reaction, ΔH4, is equal to the sum of the enthalpy changes for the second and third reactions, ΔH2 and ΔH3, respectively.
Now, based on the conservation of energy and the principle of Hess's Law, the enthalpy change of a reaction is independent of the pathway taken. It only depends on the initial and final states of the reaction (the reactants and products). This property is what makes enthalpy a state function.
In this case, the enthalpy change for the first reaction, ΔH1, is not equal to ΔH4. However, the fact that we can achieve the same overall reaction by a different pathway (via the second and third reactions) while still obtaining the same enthalpy change (ΔH4) reaffirms that enthalpy is indeed a state function.
To compare the enthalpy change for the first reaction (N2 + 2O2 --> 2NO2) with that for the fourth reaction (N2 + 2O2 --> 2N2O), we need to consider the stoichiometric coefficients of the reactions.
The enthalpy change for a chemical reaction is given by the difference in enthalpy (ΔH) between the products and reactants. In this case, we'll use ΔHf°, which represents the enthalpy change at standard conditions (1 atm pressure, 25°C temperature).
The enthalpy change for each reaction can be determined by using the enthalpy of formation values for the individual compounds involved. The values are usually given in tables or can be looked up using a reliable source.
Considering the reactions:
1st reaction: N2(g) + 2O2(g) --> 2NO2(g)
4th reaction: N2(g) + 2O2(g) --> 2N2O(g)
We can find the enthalpy change for each reaction by subtracting the sum of the enthalpies of formation for the reactants from the sum of the enthalpies of formation for the products. The enthalpy change is given in terms of ΔHf°.
For the first reaction:
ΔH1 = (2ΔHf°(NO2)) - (ΔHf°(N2) + 2ΔHf°(O2))
For the fourth reaction:
ΔH4 = (2ΔHf°(N2O)) - (ΔHf°(N2) + 2ΔHf°(O2))
By calculating the values for ΔH1 and ΔH4 using the respective enthalpy of formation values, you can directly compare the enthalpy change between the two reactions.
If the enthalpy change (ΔH) is the same for both reactions, it would illustrate that the enthalpy change is a state function. This means that the enthalpy change only depends on the initial and final states of the reaction and is independent of the pathway taken.