To determine which option correctly describes the combustion of methane producing 802 kJ/mol of energy, let's analyze each option step by step:
1. Combustion Reaction Overview:
The general form of a combustion reaction involving methane ([tex]\(CH_4\)[/tex]) is:
[tex]\[
CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(g)
\][/tex]
In a combustion reaction, energy is released, meaning it is an exothermic reaction, and the energy should be on the product side of the equation.
2. Option Analysis:
- Option A:
[tex]\[
CH_4(g) + 2 O_2(g) + 802 \, \text{kJ/mol} \rightarrow CO_2(g) + 2 H_2O(g)
\][/tex]
Here, energy is added to the reactants side. This would imply an endothermic reaction, which is incorrect for combustion. Hence, this option is incorrect.
- Option B:
[tex]\[
CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(g) + 802 \, \text{kJ/mol}
\][/tex]
In this option, the energy is on the products side of the equation, indicating that energy is released during the reaction, which fits the description of an exothermic combustion process. Hence, this option is correct.
- Option C:
[tex]\[
CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(g) - 802 \, \text{kJ/mol}
\][/tex]
Here, the energy term is negative on the products side. This might imply energy absorption or incorrect notational representation. Energy should not be depicted as negative in a typical exothermic release reaction’s products. Hence, this option is incorrect.
- Option D:
[tex]\[
CH_4(g) + 2 \, O_2(g) \xrightarrow{+802 \, \text{kJ/mol}} CO_2(g) + 2 \, H_2O(g)
\][/tex]
Although this option attempts to show energy involved in the reaction, the notation used is not conventional for expressing energy released in a chemical reaction. Hence, this option is also incorrect.
3. Conclusion:
Based on the step-by-step analysis, the correct option that shows the combustion of methane producing 802 kJ/mol of energy is:
[tex]\[
\boxed{\text{B: } CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(g) + 802 \, \text{kJ/mol}}
\][/tex]
