An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Apply the formula: Δ H ∘ = ∑ n Δ H f ∘ ( p ro d u c t s ) − ∑ m Δ H f ∘ ( re a c t an t s ) .
Substitute the given values: − 1234.7 = [ 2 ( − 393.5 ) + 3 ( − 241.8 )] − [ Δ H f ∘ ( C 2 H 5 O H ) + 3 ( 0 )] .
Solve for Δ H f ∘ ( C 2 H 5 O H ) : Δ H f ∘ ( C 2 H 5 O H ) = 2 ( − 393.5 ) + 3 ( − 241.8 ) + 1234.7 .
Calculate the result: Δ H f ∘ ( C 2 H 5 O H ) = − 277.7 k J
Explanation
Problem Setup and Given Data We are given the thermochemical equation: C 2 H 5 O H ( l ) + 3 O 2 ( g ) r i g h t a rro w 2 C O 2 ( g ) + 3 H 2 O ( g ) \tquad \tDelta H ∘ = − 1234.7 k J We also know the standard enthalpies of formation for C O 2 ( g ) and H 2 O ( g ) :
Δ H ∘ f ( C O 2 ( g )) = − 393.5 k J / m o l Δ H ∘ f ( H 2 O ( g )) = − 241.8 k J / m o Our goal is to calculate the standard enthalpy of formation for C 2 H 5 O H ( l ) .
Enthalpy Change Formula Recall that the standard enthalpy change of a reaction is given by: Δ H ∘ = ∑ n Δ H f ∘ ( p ro d u c t s ) − ∑ m Δ H f ∘ ( re a c t an t s ) where n and m are the stoichiometric coefficients.
Applying the Formula to the Reaction In this specific reaction, we have: Δ H ∘ = [ 2Δ H f ∘ ( C O 2 ) + 3Δ H f ∘ ( H 2 O )] − [ Δ H f ∘ ( C 2 H 5 O H ) + 3Δ H f ∘ ( O 2 )]
Standard State of Oxygen Since O 2 is in its standard state, its standard enthalpy of formation is zero: Δ H f ∘ ( O 2 ) = 0
Substituting Known Values Now we can plug in the given values: − 1234.7 = [ 2 ( − 393.5 ) + 3 ( − 241.8 )] − [ Δ H f ∘ ( C 2 H 5 O H ) + 3 ( 0 )]
Isolating the Unknown Solve for Δ H f ∘ ( C 2 H 5 O H ) :
Δ H f ∘ ( C 2 H 5 O H ) = 2 ( − 393.5 ) + 3 ( − 241.8 ) + 1234.7
Calculating the Enthalpy of Formation Calculate the value: Δ H f ∘ ( C 2 H 5 O H ) = − 787 − 725.4 + 1234.7 = − 277.7 k J / m o l
Final Answer Therefore, the standard enthalpy of formation of C 2 H 5 O H ( l ) is − 277.7 k J / m o l .
Examples
Understanding enthalpy of formation is crucial in many real-world applications. For instance, when designing chemical reactors, engineers need to know the heat released or absorbed during a reaction to maintain optimal operating conditions and prevent dangerous temperature excursions. In the automotive industry, knowing the enthalpy of formation of fuels like ethanol helps in calculating the energy released during combustion, which is essential for improving engine efficiency and reducing emissions. Moreover, in environmental science, these values are used to assess the impact of various chemical processes on climate change and pollution.
Approximately 2.81 × 1 0 21 electrons flow through the electric device when a current of 15.0 A is delivered for 30 seconds. This is calculated by finding the total charge using the current and time, then dividing that charge by the charge of a single electron. The steps include using basic formulas in electrical theory to arrive at the final number of electrons.
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