Ammonia $\left( NH _3(g), \Delta H_{ f }=-46.19 kJ / mol \right)$ reacts with hydrogen chloride $\left( HCl ( g ), \Delta H_{ f }=-92.30 kJ / mol \right)$ to form ammonium chloride ( $NH _4 Cl ( s ), \Delta H_{ f }=-314.4 kJ / mol$ ) according to this equation:
$NH_3(g)+HCl(g) \rightarrow NH_4 Cl(s)$
What is $\Delta H_{ rxn }$ for this reaction?
Answer (1)
The reaction is N H 3 ( g ) + H Cl ( g ) → N H 4 Cl ( s ) .
Apply the formula Δ H r x n = ∑ Δ H f ( p ro d u c t s ) − ∑ Δ H f ( re a c t an t s ) .
Substitute the given enthalpies of formation: Δ H r x n = − 314.4 − ( − 46.19 − 92.30 ) .
Calculate the enthalpy of reaction: Δ H r x n = − 175.91 kJ/mol.
Explanation
Problem Setup and Given Data We are given the reaction:
N H 3 ( g ) + H Cl ( g ) → N H 4 Cl ( s )
and the enthalpies of formation:
Δ H f ( N H 3 ( g )) = − 46.19 m o l k J Δ H f ( H Cl ( g )) = − 92.30 m o l k J Δ H f ( N H 4 Cl ( s )) = − 314.4 m o l k J
We want to find the enthalpy of reaction, Δ H r x n .
Applying the Formula To calculate the enthalpy of reaction, we use the formula:
Δ H r x n = ∑ Δ H f ( p ro d u c t s ) − ∑ Δ H f ( re a c t an t s )
In this case:
Δ H r x n = Δ H f ( N H 4 Cl ( s )) − [ Δ H f ( N H 3 ( g )) + Δ H f ( H Cl ( g ))]
Substituting Values Now, we substitute the given values:
Δ H r x n = − 314.4 − ( − 46.19 + ( − 92.30 ))
Calculating the Enthalpy of Reaction Let's calculate the value of Δ H r x n :
Δ H r x n = − 314.4 − ( − 46.19 − 92.30 ) Δ H r x n = − 314.4 − ( − 138.49 ) Δ H r x n = − 314.4 + 138.49 Δ H r x n = − 175.91
So, the enthalpy of reaction is -175.91 kJ/mol.
Final Answer The enthalpy of reaction Δ H r x n for the given reaction is − 175.91 kJ/mol.
Examples
This calculation is crucial in industrial chemistry for designing efficient processes. For example, in the production of fertilizers, understanding the heat released or absorbed during the synthesis of ammonium chloride helps engineers design reactors that can maintain optimal temperatures, ensuring the reaction proceeds efficiently and safely. By knowing the enthalpy change, they can implement appropriate cooling or heating systems to manage the heat generated or required by the reaction, leading to cost-effective and sustainable production.
