<< Chapter < Page Chapter >> Page >

We also can use Hess’s law    to determine the enthalpy change of any reaction if the corresponding enthalpies of formation of the reactants and products are available. The stepwise reactions we consider are: (i) decompositions of the reactants into their component elements (for which the enthalpy changes are proportional to the negative of the enthalpies of formation of the reactants), followed by (ii) re-combinations of the elements to give the products (with the enthalpy changes proportional to the enthalpies of formation of the products). The standard enthalpy change of the overall reaction is therefore equal to: (ii) the sum of the standard enthalpies of formation of all the products plus (i) the sum of the negatives of the standard enthalpies of formation of the reactants. This is usually rearranged slightly to be written as follows, with ∑ representing “the sum of” and n standing for the stoichiometric coefficients:

Δ H reaction ° = n × Δ H f ° ( products ) n × Δ H f ° ( reactants )

The following example shows in detail why this equation is valid, and how to use it to calculate the enthalpy change for a reaction of interest.

Using hess’s law

What is the standard enthalpy change for the reaction:

3 NO 2 ( g ) + H 2 O ( l ) 2 HNO 3 ( a q ) + NO ( g ) Δ H ° = ?

Solution: using the equation

Use the special form of Hess’s law given previously:

Δ H reaction ° = n × Δ H f ° (products) n × Δ H f ° ( reactants )
= [ 2 mol HNO 3 × −207.4 kJ mol HNO 3 ( a q ) + 1 mol NO ( g ) × +90.2 kJ mol NO ( g ) ] [ 3 mol NO 2 ( g ) × +33.2 kJ mol NO 2 ( g ) + 1 mol H 2 O ( l ) × −285.8 kJ mol H 2 O ( l ) ] = 2 ( −207.4 kJ ) + 1 ( +90.2 kJ ) 3 ( +33.2 kJ ) 1 ( −285.8 kJ ) = −138.4 kJ

Solution: supporting why the general equation is valid

Alternatively, we can write this reaction as the sum of the decompositions of 3NO 2 ( g ) and 1H 2 O( l ) into their constituent elements, and the formation of 2HNO 3 ( aq ) and 1NO( g ) from their constituent elements. Writing out these reactions, and noting their relationships to the Δ H f ° values for these compounds (from Appendix G ), we have:

3 NO 2 ( g ) 3/2N 2 ( g ) + 3O 2 ( g ) Δ H 1 ° = −99.6 kJ
H 2 O ( l ) H 2 ( g ) + 1 2 O 2 ( g ) Δ H 2 ° = +285.8 kJ [−1 × Δ H f ° ( H 2 O ) ]
H 2 ( g ) + N 2 ( g ) + 1 2 O 2 ( g ) 2 HNO 3 ( a q ) Δ H 3 ° = −414.8 kJ [ 2 × Δ H f ° ( HNO 3 ) ]
1 2 N 2 ( g ) + 1 2 O 2 ( g ) NO ( g ) Δ H 4 ° = +90.2 kJ [ 1 × ( NO ) ]

Summing these reaction equations gives the reaction we are interested in:

3NO 2 ( g ) + H 2 O ( l ) 2 HNO 3 ( a q ) + NO ( g )

Summing their enthalpy changes gives the value we want to determine:

Δ H rxn ° = Δ H 1 ° + Δ H 2 ° + Δ H 3 ° + Δ H 4 ° = ( −99.6 kJ ) + ( +285.8 kJ ) + ( −414.8 kJ ) + ( +90.2 kJ ) = −138.4 kJ

So the standard enthalpy change for this reaction is Δ H ° = −138.4 kJ.

Note that this result was obtained by (1) multiplying the Δ H f ° of each product by its stoichiometric coefficient and summing those values, (2) multiplying the Δ H f ° of each reactant by its stoichiometric coefficient and summing those values, and then (3) subtracting the result found in (2) from the result found in (1). This is also the procedure in using the general equation, as shown.

Check your learning

Calculate the heat of combustion of 1 mole of ethanol, C 2 H 5 OH( l ), when H 2 O( l ) and CO 2 ( g ) are formed. Use the following enthalpies of formation: C 2 H 5 OH( l ), −278 kJ/mol; H 2 O( l ), −286 kJ/mol; and CO 2 ( g ), −394 kJ/mol.

Answer:

−1368 kJ/mol

Got questions? Get instant answers now!

Questions & Answers

Modern Electronic Theory
Levi Reply
find the volume of oxygen produced from the electrolysis of acidified water of a current of a 2A was passed through the electrolysis of acidified water for 2 hours
Ngwu Reply
A group of atoms that are connected by chemical bounds
Valerie Reply
molecule
NARCOS_
the atoms are found in the shell, it is called atomic bond.
Andrew
what is molecules
Kelly Reply
what atoms
Simon
Moecules are groups of atoms
Adewole
What is collision theory
Isah Reply
hello guys am new here
Andrew Reply
what is the si unit for energy
enow Reply
joules
udoh
what is Charles law
Ogbu
how do mass of solvent be gram or kilogram ?
Yussuf Reply
by converting
Andrew
its a force a gas exerts on the wall of the container
udoh Reply
compressed it is
Andrew
what is gas pressure
Sandra Reply
the pressure is the amount of Gas that is compressed in the container. in other words because of the gas that is compressed in the container there is pressure on it.
Andrew
write the electron configuration for probium
Magano Reply
what is an accuracy
amadi Reply
what is it
Nhagn
accuracy has to do with speed
Emmanuel
accuracy is the movement of an object in a particular direction without any obstructions.
Andrew
what is titration curve
johnson Reply
a titration curve is the separation of a solvent in a curved direction.
Andrew
explain gaslaws
Felix Reply
explain accuracy
amadi
gas law states that the amount of molecule in the container is inversely proportional to the pressure.
Andrew
what is the functional group in this compound:CH3COCH2CH2-O-CH2
Obafemi Reply
this belongs to the Akane family. after going through this, I noticed the structural formula you gave was wrong. The answer to this is C5H10 heptane.
Andrew

Get the best Chemistry course in your pocket!





Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Chemistry' conversation and receive update notifications?

Ask