Nitrogen dioxide, $NO _2(g)$ ( $\triangle H_{ t }=33.84 kJ / mol$ ), is decomposed according to the following reaction:
$2 NO_2(g) \rightarrow N_2(g)+2 O_2(g)$
What is the enthalpy change when 2.50 mol of nitrogen dioxide decomposes?
Use $\Delta H_{p x D}=\sum(\Delta H_{\text {f, products }})-\sum(\Delta H_{f, \text { reactants }})$.
A. 13.5 kJ of energy released
B. 13.5 kJ of energy absorbed
C. 84.6 kJ of energy released
D. 84.6 kJ of energy absorbed
Answer (1)
Calculate the enthalpy change for the reaction: Δ H r x n = [ 1 × 0 + 2 × 0 ] − [ 2 × 33.84 ] = − 67.68 k J for 2 moles of N O 2 .
Determine the enthalpy change for 2.50 moles of N O 2 : Δ H = ( 2.50/2 ) × − 67.68 k J = − 84.6 k J .
Since the enthalpy change is negative, the energy is released.
The enthalpy change when 2.50 mol of nitrogen dioxide decomposes is 84.6 k J o f e n er g yre l e a se d .
Explanation
Problem Setup We are given the reaction 2 N O 2 ( g ) i g h t ha r p oo n u p N 2 ( g ) + 2 O 2 ( g ) and the enthalpy of formation of N O 2 ( g ) is △ H f = 33.84 k J / m o l . We need to find the enthalpy change when 2.50 mol of N O 2 decomposes.
Enthalpy of Formation The enthalpy change for the reaction is given by Δ H r x n = ∑ △ H f , p ro d u c t s − ∑ △ H f , re a c t an t s . The enthalpy of formation of elements in their standard state is zero, so △ H f ( N 2 ( g )) = 0 and △ H f ( O 2 ( g )) = 0 .
Calculating Enthalpy Change Therefore, the enthalpy change for the reaction is: Δ H r x n = [ 1 × △ H f ( N 2 ( g )) + 2 × △ H f ( O 2 ( g ))] − [ 2 × △ H f ( N O 2 ( g ))] Δ H r x n = [ 1 × 0 + 2 × 0 ] − [ 2 × 33.84 k J / m o l ] Δ H r x n = − 67.68 k J This is the enthalpy change for the decomposition of 2 moles of N O 2 .
Enthalpy Change for 2.50 mol Now we need to find the enthalpy change for the decomposition of 2.50 moles of N O 2 . We can set up a proportion: 2.50 m o lN O 2 Δ H = 2 m o lN O 2 − 67.68 k J Δ H = 2 m o lN O 2 2.50 m o lN O 2 × − 67.68 k J Δ H = 1.25 × − 67.68 k J Δ H = − 84.6 k J The negative sign indicates that the reaction is exothermic, meaning energy is released.
Final Answer The enthalpy change when 2.50 mol of nitrogen dioxide decomposes is -84.6 kJ. Since the value is negative, the energy is released.
Examples
Enthalpy changes are crucial in various real-world applications, such as designing efficient combustion engines or optimizing chemical reactions in industrial processes. For instance, understanding the heat released or absorbed during a reaction helps engineers create safer and more effective systems. In the case of nitrogen dioxide decomposition, knowing the enthalpy change allows for better control and management of emissions in industrial settings, contributing to environmental sustainability.
