Manganese dioxide [tex]$\left( MnO _2(s), \Delta H_{ f }=-520.0 kJ\right)$[/tex] reacts with aluminum to form aluminum oxide [tex]$\left( Al _2 O _3(s), \Delta H_{ f }=-\right.$[/tex] [tex]$1699.8 kJ / mol$[/tex]) and manganese according to the equation below.
[tex]$3 MnO_2(s)+4 Ar(s) \rightarrow 2 Al_2 O_3(g)+3 Mn(s)$[/tex]
What is the enthalpy of the reaction?
Use [tex]$\Delta H_{r \times n}=\sum\left(\Delta H_{\text {teproducts }}\right)-\sum\left(\Delta H_{\text {tereatants }}\right)$[/tex]
Answer (1)
The problem provides a balanced chemical equation and the enthalpies of formation for the reactants and products.
We use the formula Δ H r x n = ∑ ( Δ H f products ) − ∑ ( Δ H f reactants ) to calculate the enthalpy of the reaction.
Substitute the given values into the formula and perform the calculations.
The enthalpy of the reaction is − 1839.6 kJ .
Explanation
Problem Setup and Given Data We are given the balanced chemical equation: 3 M n O 2 ( s ) + 4 A l ( s ) → 2 A l 2 O 3 ( s ) + 3 M n ( s ) We are also given the enthalpy of formation for M n O 2 ( s ) as Δ H f = − 520.0 kJ and for A l 2 O 3 ( s ) as Δ H f = − 1699.8 kJ/mol . We need to find the enthalpy of the reaction using the formula: Δ H r x n = ∑ ( Δ H f products ) − ∑ ( Δ H f reactants ) Since A l ( s ) and M n ( s ) are elements in their standard states, their enthalpy of formation is 0.
Applying the Formula Now, we can plug in the given values into the formula: Δ H r x n = [ 2 × Δ H f ( A l 2 O 3 ) + 3 × Δ H f ( M n )] − [ 3 × Δ H f ( M n O 2 ) + 4 × Δ H f ( A l )] Δ H r x n = [ 2 × ( − 1699.8 kJ/mol ) + 3 × ( 0 kJ/mol )] − [ 3 × ( − 520.0 kJ ) + 4 × ( 0 kJ/mol )]
Calculating the Enthalpy of Reaction Now, we perform the calculations: Δ H r x n = ( − 3399.6 kJ ) − ( − 1560.0 kJ ) Δ H r x n = − 3399.6 + 1560.0 kJ Δ H r x n = − 1839.6 kJ
Final Answer The enthalpy of the reaction is -1839.6 kJ.
Examples
Enthalpy calculations are crucial in various real-world applications, such as designing chemical reactors, understanding combustion processes, and developing new materials. For instance, when designing a rocket engine, engineers need to know the enthalpy change of the combustion reaction to determine the amount of fuel required and the heat released. Similarly, in the development of new drugs, chemists use enthalpy calculations to understand the stability and reactivity of different compounds, ensuring the drug's effectiveness and safety. Understanding enthalpy changes helps optimize energy production, improve industrial processes, and create innovative technologies.
