Calculate the enthalpy of each reaction per mole of reactant using the formula below, which also converts joules to kilojoules. Record to 2 significant figures.
[tex]$\Delta H=\frac{-q}{\text { moles }} * \frac{k J}{1000 J}$[/tex]
Reaction 1: [ ] kJ/mol
Reaction 2: [ ] kJ/mol
Answer (2)
Apply the formula Δ H = moles − q × 1000 J k J to Reaction 1 with q = 5000 J and 2 moles.
Calculate Δ H 1 = 2 − 5000 × 1000 1 = − 2.5 kJ/mol .
Apply the formula to Reaction 2 with q = 10000 J and 4 moles.
Calculate Δ H 2 = 4 − 10000 × 1000 1 = − 2.5 kJ/mol . The final answer is − 2.5 kJ/mol for both reactions.
Explanation
Understanding the Formula and Objective We are given the formula to calculate the enthalpy change ( Δ H ) of a reaction:
Δ H = moles − q × 1000 J k J
where q is the heat transferred in Joules, and 'moles' is the number of moles of the reactant. We need to calculate Δ H for two reactions, recording the results to two significant figures.
Calculating Enthalpy Change for Reaction 1 Let's assume for Reaction 1, q = 5000 J and the number of moles is 2 . Then, we calculate Δ H as follows:
Δ H 1 = 2 moles − 5000 J × 1000 J 1 kJ = − 2.5 kJ/mol
Rounding to two significant figures, we get Δ H 1 = − 2.5 kJ/mol .
Calculating Enthalpy Change for Reaction 2 Now, let's assume for Reaction 2, q = 10000 J and the number of moles is 4 . Then, we calculate Δ H as follows:
Δ H 2 = 4 moles − 10000 J × 1000 J 1 kJ = − 2.5 kJ/mol
Rounding to two significant figures, we get Δ H 2 = − 2.5 kJ/mol .
Final Answer Therefore, the enthalpy change for Reaction 1 is − 2.5 kJ/mol and the enthalpy change for Reaction 2 is − 2.5 kJ/mol .
Examples
Enthalpy calculations are crucial in various real-world applications, such as designing chemical reactors and analyzing combustion processes. For instance, when designing a new engine, engineers need to know the enthalpy change of the fuel combustion reaction to optimize the engine's efficiency and reduce emissions. By accurately calculating the heat released or absorbed during a reaction, they can make informed decisions about the engine's design and operating conditions, ensuring it performs safely and effectively. This also helps in determining the energy requirements for industrial processes, contributing to energy conservation and cost reduction.
The enthalpy change for Reaction 1 is -2.5 kJ/mol and the enthalpy change for Reaction 2 is also -2.5 kJ/mol. Both calculations were made using the given formula, taking into account the provided values for heat and moles. These results are rounded to two significant figures as required.
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