To determine the standard enthalpy of the reaction \(2 \text{H}_2 + \text{O}_2 \rightarrow 2 \text{H}_2\text{O}\), you need to understand that this reaction involves the formation of water molecules from hydrogen and oxygen. Let's discuss how to approach this problem.
1. Reaction Understanding:
The given chemical reaction is:
[tex]\[
2 \text{H}_2 + \text{O}_2 \rightarrow 2 \text{H}_2\text{O}
\][/tex]
This is a formation reaction where hydrogen gas (H_2) reacts with oxygen gas (O_2) to form water (H_2O).
2. Nature of the Reaction:
- The formation of water from hydrogen and oxygen is an exothermic reaction. This means that energy is released when water is formed.
- In an exothermic reaction, the standard enthalpy change (\(\Delta H\)) is negative, indicating that energy is released to the surroundings.
3. Correct Value of Enthalpy Change:
- Based on our understanding of exothermic reactions and the specific reaction given, the standard enthalpy change for the formation of water (H_2O) from its elements in their standard states is known.
4. Choosing the Correct Answer:
- Among the options provided:
- \(a. \quad 285.8 \text{ kJ/mol}\)
- \(b. \quad -285.8 \text{ kJ/mol}\)
- \(c. \quad 258.5 \text{ kJ/mol}\)
- \(d. \quad -258.5 \text{ kJ/mol}\)
- The correct value, considering the exothermic nature of the reaction and the energy released during the formation of water, is \(-285.8 \text{ kJ/mol}\).
Therefore, the standard enthalpy of the reaction \(2 \text{H}_2 + \text{O}_2 \rightarrow 2 \text{H}_2\text{O}\) is:
[tex]\[
\boxed{-285.8 \text{ kJ/mol}}
\][/tex]
Thus, the correct answer is [tex]\( \text{b.} \quad -285.8 \text{ kJ/mol} \)[/tex].
