# 5.3 Enthalpy  (Page 6/25)

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## Standard enthalpy of formation

A standard enthalpy of formation $\text{Δ}{H}_{\text{f}}^{°}$ is an enthalpy change for a reaction in which exactly 1 mole of a pure substance is formed from free elements in their most stable states under standard state conditions. These values are especially useful for computing or predicting enthalpy changes for chemical reactions that are impractical or dangerous to carry out, or for processes for which it is difficult to make measurements. If we have values for the appropriate standard enthalpies of formation, we can determine the enthalpy change for any reaction, which we will practice in the next section on Hess’s law.

The standard enthalpy of formation of CO 2 ( g ) is −393.5 kJ/mol. This is the enthalpy change for the exothermic reaction:

$\text{C}\left(s\right)+{\text{O}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}{\text{CO}}_{2}\left(g\right)\phantom{\rule{3em}{0ex}}\text{Δ}{H}_{\text{f}}^{°}=\text{Δ}{H}_{298}^{°}=-393.5\phantom{\rule{0.2em}{0ex}}\text{kJ}$

starting with the reactants at a pressure of 1 atm and 25 °C (with the carbon present as graphite, the most stable form of carbon under these conditions) and ending with one mole of CO 2 , also at 1 atm and 25 °C. For nitrogen dioxide, NO 2 ( g ), $\text{Δ}{H}_{\text{f}}^{°}$ is 33.2 kJ/mol. This is the enthalpy change for the reaction:

$\frac{1}{2}{\text{N}}_{2}\left(g\right)+{\text{O}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}{\text{NO}}_{2}\left(g\right)\phantom{\rule{3em}{0ex}}\text{Δ}{H}_{\text{f}}^{°}=\text{Δ}{H}_{298}^{°}=\text{+33.2 kJ}$

A reaction equation with $\frac{1}{2}$ mole of N 2 and 1 mole of O 2 is correct in this case because the standard enthalpy of formation always refers to 1 mole of product, NO 2 ( g ).

You will find a table of standard enthalpies of formation of many common substances in Appendix G . These values indicate that formation reactions range from highly exothermic (such as −2984 kJ/mol for the formation of P 4 O 10 ) to strongly endothermic (such as +226.7 kJ/mol for the formation of acetylene, C 2 H 2 ). By definition, the standard enthalpy of formation of an element in its most stable form is equal to zero under standard conditions, which is 1 atm for gases and 1 M for solutions.

## Evaluating an enthalpy of formation

Ozone, O 3 ( g ), forms from oxygen, O 2 ( g ), by an endothermic process. Ultraviolet radiation is the source of the energy that drives this reaction in the upper atmosphere. Assuming that both the reactants and products of the reaction are in their standard states, determine the standard enthalpy of formation, $\text{Δ}{H}_{\text{f}}^{°}$ of ozone from the following information:

$3{\text{O}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}2{\text{O}}_{3}\left(g\right)\phantom{\rule{3em}{0ex}}\text{Δ}{H}_{298}^{°}=\text{+286 kJ}$

## Solution

$\text{Δ}{H}_{\text{f}}^{°}$ is the enthalpy change for the formation of one mole of a substance in its standard state from the elements in their standard states. Thus, $\text{Δ}{H}_{\text{f}}^{°}$ for O 3 ( g ) is the enthalpy change for the reaction:

$\frac{3}{2}{\text{O}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}{\text{O}}_{3}\left(g\right)$

For the formation of 2 mol of O 3 ( g ), $\text{Δ}{H}_{298}^{°}=\text{+286 kJ.}$ This ratio, $\left(\frac{286\phantom{\rule{0.2em}{0ex}}\text{kJ}}{2\phantom{\rule{0.2em}{0ex}}\text{mol}\phantom{\rule{0.2em}{0ex}}{\text{O}}_{3}}\right),$ can be used as a conversion factor to find the heat produced when 1 mole of O 3 ( g ) is formed, which is the enthalpy of formation for O 3 ( g ):

$\text{Δ}\text{H}\text{° for}\phantom{\rule{0.2em}{0ex}}1\phantom{\rule{0.2em}{0ex}}\text{mole of}\phantom{\rule{0.2em}{0ex}}{\text{O}}_{3}\left(g\right)=1\phantom{\rule{0.2em}{0ex}}\overline{)\text{mol}\phantom{\rule{0.2em}{0ex}}{\text{O}}_{3}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\frac{286\phantom{\rule{0.2em}{0ex}}\text{kJ}}{2\phantom{\rule{0.2em}{0ex}}\overline{)\text{mol}\phantom{\rule{0.2em}{0ex}}{\text{O}}_{3}}}\phantom{\rule{0.2em}{0ex}}=143\phantom{\rule{0.2em}{0ex}}\text{kJ}$

Therefore, $\text{Δ}{H}_{\text{f}}^{°}\left[{\text{O}}_{3}\left(g\right)\right]=\text{+143 kJ/mol}.$

Hydrogen gas, H 2 , reacts explosively with gaseous chlorine, Cl 2 , to form hydrogen chloride, HCl( g ). What is the enthalpy change for the reaction of 1 mole of H 2 ( g ) with 1 mole of Cl 2 ( g ) if both the reactants and products are at standard state conditions? The standard enthalpy of formation of HCl( g ) is −92.3 kJ/mol.

For the reaction ${\text{H}}_{2}\left(g\right)+{\text{Cl}}_{2}\left(g\right)\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}2\text{HCl}\left(g\right)\phantom{\rule{3em}{0ex}}\text{Δ}{H}_{298}^{°}=-184.6\phantom{\rule{0.2em}{0ex}}\text{kJ}$

what is catenation
The property of carbon to form long chain with other atom!
Lareb
hydrocarbons can be classified as..1.Aliphatic compounds 2.cyclic compounds.under aliphatic compounds there are two types saturated hydrocarbons(alkanes) and unsaturated hydrocarbons(alkenes and alkynes).
thanks but i have also heard of aromatic hydrocarbons
emmanuel
so am kinda confused
emmanuel
hello i have big problems in understanding organic chemistry
what are the main types of hydrocarbon
emmanuel
how many elements are in the periodic table
118
daniel
please what are the main types of hydrocarbons
emmanuel
why Rutherford uses the gold foil instead of other metals?
Rutherford chose gold was because its extremely malleable. One can stretch gold foil until it is only a few atoms thick in places, which is not possible with aluminum. If the foil were too thick, there would be no transmission of particles at all; the whole point was to demonstrate that most alpha
daniel
wjat does Rutherford mean?
Asali
Ernest Rutherford was the scientist that preformed the experiment.
daniel
although other metals are also present which are more melleable!?so
Lareb
gold
daniel
what is a balanced equation 4 trioxonitrate (V)acid and sodium hydroxide?
proved ur Worth: If A is a of trioxonitrate(V)acid,HNO3' of unknown concentration .B is a standard solution of sodium hydroxide containing 4.00g per dm cube of solution.25cm cube portions solution B required an average of 24.00cm cube of solution A for neutralization,using 2 drops of methyl orange.
Marcel
calculate the concentration of solution B in moles per dm cube
Marcel
calculate the concentration of solution A and B in moles per DM cube
Marcel
finally calculate the concentration in g/dm cube of HNO3 in solution A (H=1,N=14,O=16,Na=23)
Marcel
calculate the standard enthalpy of formation for propane(C3H8) from the following data; 1), C3H8+5O2->3CO2+4H2O; -222.0kJ/mol 2), C+O2->CO2;-395.5kJ/mol 3),H2+O->H2O; 285.8kJ/mol
Josephine
let eventually of formation of propane = X X + (-222)=3×(-395.5)+4×(-286) rearrange to find X
Paul
wat is electrolysis?
it is the chemical decomposition of a substance when electric current is passed through it either in molten form or aqueous solution
Nuru
list the side effect of chemical industries
how do you ionise an atom
many ways ,but one of them is when the atom becomes heated to a certain temperature the surface electron becomes too energetic and leaves the atom because the attraction between the nucleus and the electron becomes overpowered by the energetic eletron
sunday
also hitting of two atoms can cause transfer of surface electrons
sunday
and when this transfers occur the atom becomes ionised
sunday
who is doing Cape chemistry tomorrow?
What is hybridization
the mix between different breeds of species in one
Jared
it is the blending of orbitals.
stanley
the mixing of orbital
caramel
are covalent bonds influenced by factors such as temperature and pressure?
what is catalyst used for mirror test
when an atom looses electron, what does it become?
it's oxidized and called an ion
Anora
thanks
Abdullahi
Now, I get it
Abdullahi
cation
Anora
can you give an example please, if you don't mind
Abdullahi
a positive ion,become positively charged/a cation.
Janis
sodium plus one is simple cation is exmpl
ajmal
Taking Sodium as example..... it carries a positive charge which means it is positively charged.....when it gains an electron, it is reduced cuz an electron is negatively charged.....also when an atom looses an electron, it becomes positively charged and when it gains, it becomes negatively charged.
Nuru
typically, ionization is the process where an atom looses or gains electron(s) to form ion(s) either a positively or negatively
Nuru
what is copper
just an element
Power
Cu
daniel