Which substances have [tex]$\Delta H_{ f }=0 kJ / mol$[/tex] by definition? Select all that apply.
[tex]$O _2(g)$[/tex]
[tex]$N ( g )$[/tex]
[tex]$H _2 O ( l )$[/tex]
[tex]$Br _2( I )$[/tex]
Fe(s)
He(g)
Answer (1)
Identify elements in their standard states.
Oxygen's standard state is O 2 ( g ) .
Bromine's standard state is B r 2 ( l ) .
Iron's standard state is F e ( s ) .
Helium's standard state is He ( g ) .
Therefore, the substances with Δ H f = 0 kJ/mol are O 2 ( g ) , B r 2 ( l ) , F e ( s ) , He ( g ) .
Explanation
Understanding the Problem The problem asks us to identify which of the given substances have a standard enthalpy of formation ( Δ H f ) equal to 0 kJ/mol by definition. The standard enthalpy of formation is defined as the change of enthalpy during the formation of 1 mole of the substance from its constituent elements in their standard states. By definition, the standard enthalpy of formation of an element in its standard state is 0 kJ/mol.
Identifying Standard States We need to identify the standard state of each element at 298 K and 1 atm.
Oxygen's standard state is diatomic gas, O 2 ( g ) .
Nitrogen's standard state is diatomic gas, N 2 ( g ) . Therefore, N ( g ) is not in its standard state.
Hydrogen and oxygen combine to form H 2 O ( l ) , which is a compound, not an element in its standard state.
Bromine's standard state is liquid, B r 2 ( l ) .
Iron's standard state is solid, F e ( s ) .
Helium's standard state is monatomic gas, He ( g ) .
Conclusion Therefore, O 2 ( g ) , B r 2 ( l ) , F e ( s ) , and He ( g ) have Δ H f = 0 kJ/mol by definition.
Examples
Understanding standard enthalpies of formation is crucial in chemical thermodynamics. For instance, when designing a chemical reaction, knowing the Δ H f values allows us to calculate the overall enthalpy change of the reaction using Hess's Law. This helps predict whether the reaction will release heat (exothermic) or require heat (endothermic), which is vital for industrial processes, such as optimizing energy consumption or ensuring safety.
