Which reaction shows that the enthalpy of formation of $CS _2$ is $\Delta H_f=89.4$ $kJ / mol$?
A. $C (s)+2 S(s) \rightarrow CS _2(1)$
B. $C (s)+2 S(s)+894 kJ \rightarrow CS _2(t)+89.4 kJ$
c. $C (s)+2 S(s)+89.4 kJ \rightarrow CS _2(t)$
D. $C (s)+2 S(s) \rightarrow CS _2(\jmath)+89.4 kJ$
Answer (1)
The enthalpy of formation Δ H f is the heat change when one mole of a substance is formed from its elements in their standard states.
For C S 2 , the formation reaction is C ( s ) + 2 S ( s ) → C S 2 ( l ) with Δ H f = 89.4 kJ/mol.
Since the reaction is endothermic ( Δ H f is positive), heat is absorbed, so the correct representation is C ( s ) + 2 S ( s ) + 89.4 k J → C S 2 ( l ) .
Therefore, the correct answer is C .
Explanation
Understanding Enthalpy of Formation The enthalpy of formation, denoted as Δ H f , represents the change in enthalpy when one mole of a substance is formed from its constituent elements in their standard states. In this problem, we are given that the enthalpy of formation of C S 2 is Δ H f = 89.4 kJ/mol. This means that when one mole of C S 2 is formed from carbon and sulfur in their standard states, 89.4 kJ of energy is absorbed (since the value is positive).
Writing the Formation Reaction The standard state of carbon is solid, C ( s ) , and the standard state of sulfur is solid, S ( s ) . Therefore, the formation reaction for C S 2 can be written as: C ( s ) + 2 S ( s ) → C S 2 ( l ) Since the enthalpy of formation is positive, the reaction is endothermic, meaning heat is absorbed during the reaction. We can represent this by adding the enthalpy change to the reactants side: C ( s ) + 2 S ( s ) + 89.4 kJ → C S 2 ( l ) Alternatively, we can write: C ( s ) + 2 S ( s ) → C S 2 ( l ) Δ H f = + 89.4 kJ/mol
Analyzing the Options Now, let's examine the given options to find the one that correctly represents the enthalpy of formation of C S 2 :
A. C ( s ) + 2 S ( s ) → C S 2 ( l ) B. C ( s ) + 2 S ( s ) + 894 kJ → C S 2 ( t ) + 89.4 kJ C. C ( s ) + 2 S ( s ) + 89.4 kJ → C S 2 ( t ) D. C ( s ) + 2 S ( s ) → C S 2 ( j ) + 89.4 kJ
Identifying the Correct Option Comparing the options with the correct representation, we can see that option C matches the correct representation of the enthalpy of formation: C ( s ) + 2 S ( s ) + 89.4 kJ → C S 2 ( t ) Therefore, the correct answer is C.
Final Answer The reaction that shows the enthalpy of formation of C S 2 is: C ( s ) + 2 S ( s ) + 89.4 kJ → C S 2 ( t ) This indicates that 89.4 kJ of energy is absorbed when one mole of C S 2 is formed from its elements in their standard states.
Examples
Understanding enthalpy of formation is crucial in various fields, such as chemical engineering and materials science. For instance, when designing a chemical plant, engineers need to know the enthalpy changes of reactions to determine the energy requirements for heating or cooling processes. In materials science, knowing the enthalpy of formation helps in predicting the stability of compounds and designing new materials with desired properties. For example, if you're designing a process to create carbon disulfide ( C S 2 ), knowing its enthalpy of formation helps you calculate how much energy you need to input to make the reaction happen: C ( s ) + 2 S ( s ) + 89.4 k J → C S 2 ( g ) .
