Thermochemistry: Understanding the Relationship Between ∆H, ∆E, and RT

What is the relationship between heat change (∆H), internal energy change (∆E), and the gas constant times temperature (RT) in a chemical reaction?

In the reaction C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(l), at constant temperature, what is the value of ∆H – ∆E?

(a) – RT

(b) + RT

(c) – 3 RT

(d) + 3 RT

Answer:

The correct answer to the question is (c) -3RT. This is calculated using the formula ∆H – ∆E = ∆(PV), which eventually becomes ∆H – ∆E = ∆nRT, given by substituting the difference between gaseous moles of products and reactants, ∆n = 3 - 6, hence ∆H – ∆E = -3RT.

Thermochemistry deals with the study of heat changes in chemical reactions. In the given reaction C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(l) at constant temperature, the relationship between heat change (∆H), internal energy change (∆E), and the gas constant times temperature (RT) can be expressed as ∆H – ∆E = ∆nRT.

Here's a step-by-step explanation of how the value of ∆H – ∆E is calculated:

1. Identify the number of moles of gaseous reactants and products:

In the given reaction, there are 5 moles of O₂(g) and 1 mole of C₃H₈(g) in the reactants, totaling to 6 moles. For products, there are 3 moles of CO₂(g).

2. Apply the formula ∆H – ∆E = ∆(PV) that eventually leads to ∆H – ∆E = ∆nRT:

Substitute the difference between the moles of gaseous products and reactants into the formula.

3. Calculate the value of ∆H – ∆E:

∆n = (moles of gaseous products) - (moles of gaseous reactants) = 3 - 6 = -3

Therefore, ∆H – ∆E = -3RT

Understanding the relationship between ∆H, ∆E, and RT in thermochemistry is essential in determining the heat changes in chemical reactions and analyzing the energy dynamics involved.

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