Question

Consider the following reaction: `"P"_(4(s)) + 10"Cl"_(2(g)) -> 4"PCl"_(5(g))`, `DeltaH =-"1776 kJ"`, what is the standard enthalpy of formation for `"PCl"_5`?

Give the standard enthalpy of formation for PCl5(g).

Answer 1

`DeltaH_f^@ = -"444 kJ mol"^(-1)`

Explanation:

The most important thing to remember about standard enthalpies of formation is that they represent the enthalpy change of reaction when one mole of a compound is formed from its constituent elements in their standard state.

This means that in order to expresses the standard enthalpy of formation, `DeltaH_f^@`, of a given compound, a thermochemical equation must always have one mole of that compound on the products' side.

In your case, the thermochemical equation that describes the synthesis of phosphorus pentachloride, `"PCl"_5`, from white phosphorus, `"P"_4` and chlorine gas, `"Cl"_2`, looks like this

`"P"_ (4(s)) + 10"Cl"_ (2(g)) -> color(red)(4)"PCl"_ (5(g))" " DeltaH_"rxn"^@ = -"1776 kJ"`

This thermochemical equation tells you that when `1` mole of white phosphorus reacts with `10` moles of chlorine gas, `color(red)(4)` moles of phosphorus pentachloride are formed and `"1776 kJ"` of heat are being released.

In order to have a thermochemical equation that expresses the enthalpy change that occurs when `1` mole of `"PCl"_5` is formed, i.e. `DeltaH_f^@`, divide all the stoichiometric coefficients by `color(red)(4)`

`1/color(red)(4)"P"_ (4(s)) + 5/2"Cl"_ (2(g)) -> "PCl"_ (5(g))" " DeltaH_f^@ = ?`

So, if you give off `"1776 kJ"` of heat when `color(red)(4)` moles of phosphorus pentachloride are formed, it follows that you will give off

`1 color(red)(cancel(color(black)("mole PCl"_5))) * "1776 kJ"/(color(red)(4)color(red)(cancel(color(black)("moles PCl"_5)))) = "444 kJ"`

when one mole of phosphorus pentachloride is formed. This means that the standard enthalpy change of formation for this compound will be

`color(green)(|bar(ul(color(white)(a/a)color(black)(DeltaH_f^@ = -"444 kJ mol"^(-1))color(white)(a/a)|)))`

Remember, the minus sign is used to symbolize heat lost.