Thank you for visiting Calculate tex Delta H tex for the following reaction tex S s 2 SO 3 varphi rightarrow 3 SO 2 underline 0 quad Delta H. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
We are given the following reference reactions:
[tex]$$
\text{Reaction 1:} \quad S(s) + O_2(g) \rightarrow SO_2(g) \quad \Delta H_1 = -296.0\ \text{kJ/mol},
$$[/tex]
[tex]$$
\text{Reaction 2:} \quad 2\,SO_2(g) + O_2(g) \rightarrow 2\,SO_3(g) \quad \Delta H_2 = -198.2\ \text{kJ/mol}.
$$[/tex]
We need to calculate the enthalpy change for the reaction:
[tex]$$
S(s) + 2\,SO_3(g) \rightarrow 3\,SO_2(g) \quad \Delta H = ?
$$[/tex]
Step 1. Reverse Reaction 2
To obtain [tex]$2\,SO_3(g)$[/tex] on the left, we reverse Reaction 2. When a reaction is reversed, the sign of [tex]$\Delta H$[/tex] is also reversed. Thus, the reversed Reaction 2 becomes
[tex]$$
2\,SO_3(g) \rightarrow 2\,SO_2(g) + O_2(g) \quad \Delta H_{\text{rev2}} = +198.2\ \text{kJ/mol}.
$$[/tex]
Step 2. Add Reaction 1 and the Reversed Reaction 2
Now, write down the two reactions you will combine:
1. Reaction 1:
[tex]$$
S(s) + O_2(g) \rightarrow SO_2(g) \quad \Delta H_1 = -296.0\ \text{kJ/mol}
$$[/tex]
2. Reversed Reaction 2:
[tex]$$
2\,SO_3(g) \rightarrow 2\,SO_2(g) + O_2(g) \quad \Delta H_{\text{rev2}} = +198.2\ \text{kJ/mol}
$$[/tex]
Add these reactions together:
[tex]$$
\begin{array}{rcl}
S(s) + O_2(g) &\rightarrow& SO_2(g) \\
2\,SO_3(g) &\rightarrow& 2\,SO_2(g) + O_2(g)
\end{array}
$$[/tex]
When we add the left-hand sides and right-hand sides, we get:
[tex]$$
S(s) + O_2(g) + 2\,SO_3(g) \rightarrow SO_2(g) + 2\,SO_2(g) + O_2(g).
$$[/tex]
Step 3. Simplify the Overall Reaction
Notice that [tex]$O_2(g)$[/tex] appears on both sides and cancels out:
[tex]$$
S(s) + 2\,SO_3(g) \rightarrow 3\,SO_2(g).
$$[/tex]
This is exactly the reaction for which we want to find [tex]$\Delta H$[/tex].
Step 4. Calculate the Overall Enthalpy Change
The overall enthalpy change is the sum of the enthalpy changes of the individual steps:
[tex]$$
\Delta H = \Delta H_1 + \Delta H_{\text{rev2}}.
$$[/tex]
Substitute the values:
[tex]$$
\Delta H = (-296.0\ \text{kJ/mol}) + (198.2\ \text{kJ/mol}) = -97.8\ \text{kJ/mol}.
$$[/tex]
Thus, the enthalpy change for the reaction
[tex]$$
S(s) + 2\,SO_3(g) \rightarrow 3\,SO_2(g)
$$[/tex]
is
[tex]$$
\Delta H = -97.8\ \text{kJ/mol}.
$$[/tex]
[tex]$$
\text{Reaction 1:} \quad S(s) + O_2(g) \rightarrow SO_2(g) \quad \Delta H_1 = -296.0\ \text{kJ/mol},
$$[/tex]
[tex]$$
\text{Reaction 2:} \quad 2\,SO_2(g) + O_2(g) \rightarrow 2\,SO_3(g) \quad \Delta H_2 = -198.2\ \text{kJ/mol}.
$$[/tex]
We need to calculate the enthalpy change for the reaction:
[tex]$$
S(s) + 2\,SO_3(g) \rightarrow 3\,SO_2(g) \quad \Delta H = ?
$$[/tex]
Step 1. Reverse Reaction 2
To obtain [tex]$2\,SO_3(g)$[/tex] on the left, we reverse Reaction 2. When a reaction is reversed, the sign of [tex]$\Delta H$[/tex] is also reversed. Thus, the reversed Reaction 2 becomes
[tex]$$
2\,SO_3(g) \rightarrow 2\,SO_2(g) + O_2(g) \quad \Delta H_{\text{rev2}} = +198.2\ \text{kJ/mol}.
$$[/tex]
Step 2. Add Reaction 1 and the Reversed Reaction 2
Now, write down the two reactions you will combine:
1. Reaction 1:
[tex]$$
S(s) + O_2(g) \rightarrow SO_2(g) \quad \Delta H_1 = -296.0\ \text{kJ/mol}
$$[/tex]
2. Reversed Reaction 2:
[tex]$$
2\,SO_3(g) \rightarrow 2\,SO_2(g) + O_2(g) \quad \Delta H_{\text{rev2}} = +198.2\ \text{kJ/mol}
$$[/tex]
Add these reactions together:
[tex]$$
\begin{array}{rcl}
S(s) + O_2(g) &\rightarrow& SO_2(g) \\
2\,SO_3(g) &\rightarrow& 2\,SO_2(g) + O_2(g)
\end{array}
$$[/tex]
When we add the left-hand sides and right-hand sides, we get:
[tex]$$
S(s) + O_2(g) + 2\,SO_3(g) \rightarrow SO_2(g) + 2\,SO_2(g) + O_2(g).
$$[/tex]
Step 3. Simplify the Overall Reaction
Notice that [tex]$O_2(g)$[/tex] appears on both sides and cancels out:
[tex]$$
S(s) + 2\,SO_3(g) \rightarrow 3\,SO_2(g).
$$[/tex]
This is exactly the reaction for which we want to find [tex]$\Delta H$[/tex].
Step 4. Calculate the Overall Enthalpy Change
The overall enthalpy change is the sum of the enthalpy changes of the individual steps:
[tex]$$
\Delta H = \Delta H_1 + \Delta H_{\text{rev2}}.
$$[/tex]
Substitute the values:
[tex]$$
\Delta H = (-296.0\ \text{kJ/mol}) + (198.2\ \text{kJ/mol}) = -97.8\ \text{kJ/mol}.
$$[/tex]
Thus, the enthalpy change for the reaction
[tex]$$
S(s) + 2\,SO_3(g) \rightarrow 3\,SO_2(g)
$$[/tex]
is
[tex]$$
\Delta H = -97.8\ \text{kJ/mol}.
$$[/tex]
Thank you for reading the article Calculate tex Delta H tex for the following reaction tex S s 2 SO 3 varphi rightarrow 3 SO 2 underline 0 quad Delta H. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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