To find the enthalpy change for the oxidation of sulfur dioxide (SO₂) to sulfur trioxide (SO₃), we can use Hess's Law. Hess's Law states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps, regardless of the pathway taken.
We'll first clarify the reactions given and then relate them to the reaction of interest:
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Given Reaction 1:
\( 25 \text{S} (s) + 30 \text{O}_2 (g) \rightarrow 250 \text{SO}_2 (g) \)
\( \Delta H_1 = -790 , \text{kJ} \) -
Given Reaction 2:
\( 5 \text{S} (s) + \text{O}_2 (g) \rightarrow 5 \text{SO}_3 (g) \)
\( \Delta H_2 = 297 , \text{kJ} \) -
Target Reaction:
\( 250 \text{SO}_2 (g) + 2 \text{O}_2 (g) \rightarrow 250 \text{SO}_3 (g) \)
Now we need to derive the enthalpy change for the reaction from SO₂ to SO₃.
Steps to find the enthalpy of the target reaction:
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From Reaction 1, we have the formation of SO₂: \[ 25 \text{S} (s) + 30 \text{O}_2 (g) \rightarrow 250 \text{SO}_2 (g) \quad \Delta H_1 = -790 \text{kJ} \]
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From Reaction 2, we reverse it to get the combustion of SO₃ back to SO₂: \[ 250 \text{SO}_3 (g) \rightarrow 25 \text{S} (s) + 30 \text{O}_2 (g) + \Delta H_2 \times (250/5) = -297 \text{kJ} \times 50 = -14850 \text{kJ} \]
Now, we can combine these two reactions to eliminate sulfur and obtain the target reaction. Let's write the reversed Reaction 2:
Reverse Reaction 2
\[ 250 \text{SO}_3 (g) \rightarrow 25 \text{S} (s) + 30 \text{O}_2 (g) \quad \Delta H = -14850 \text{kJ} \]
Add the two reactions:
- \( 25 \text{S} (s) + 30 \text{O}_2 (g) \rightarrow 250 \text{SO}_2 (g) \quad \Delta H = -790 \text{kJ} \)
- \( 250 \text{SO}_3 (g) \rightarrow 25 \text{S} (s) + 30 \text{O}_2 (g) \quad \Delta H = -14850 \text{kJ} \)
Combining these: \[ 250 \text{SO}_2 (g) + 30 \text{O}_2 (g) \rightarrow 250 \text{SO}_3 (g) \] Sum of \(\Delta H\): \[ \Delta H = -790 \text{kJ} + (-14850 \text{kJ}) = -15640 \text{kJ} \]
So, the enthalpy change for the reaction \( 250 \text{SO}_2 (g) + 2 \text{O}_2 (g) \rightarrow 250 \text{SO}_3 (g) \) is: \[ \Delta H = -14860 \text{kJ} \]
If we want the per mole or different coefficients, further adjustments can be done based on stoichiometry principles.