A gas fired power plant burns methane, `CH_(4)(g)` for which standard enthalpy of combustion is -890 kJ `mol^(-1)`. How many moles of `CO_(2)` gas are produced for every `1.0 ` MJ ( mega joule) of energy produced by it ?

Explanation

To solve the problem, we need to determine how many moles of carbon dioxide (CO₂) are produced when 1.0 MJ (megajoule) of energy is generated from the combustion of methane (CH₄).

### Step-by-Step Solution:

1. **Understand the Enthalpy of Combustion**:
The standard enthalpy of combustion of methane (CH₄) is given as -890 kJ/mol. This means that when 1 mole of methane is burned, it releases 890 kJ of energy.

2. **Convert Energy Units**:
We need to convert the energy from megajoules to kilojoules since the enthalpy of combustion is given in kJ.
\[ 1 \text{ MJ} = 1000 \text{ kJ} \]

3. **Calculate Moles of Methane Required**:
To find out how many moles of methane are required to produce 1000 kJ, we use the relationship from the enthalpy of combustion:
\[ \text{Moles of } CH₄ = \frac{\text{Energy required}}{\text{Energy released per mole}} = \frac{1000 \text{ kJ}}{890 \text{ kJ/mol}} \]
\[ \text{Moles of } CH₄ = \frac{1000}{890} \approx 1.12 \text{ moles} \]

4. **Determine Moles of CO₂ Produced**:
From the balanced chemical equation for the combustion of methane:
\[ CH₄ + 2O₂ \rightarrow CO₂ + 2H₂O \]
We can see that 1 mole of CH₄ produces 1 mole of CO₂. Therefore, the moles of CO₂ produced will be equal to the moles of CH₄ burned.
\[ \text{Moles of } CO₂ = \text{Moles of } CH₄ = 1.12 \text{ moles} \]

### Final Answer:
For every 1.0 MJ of energy produced, approximately **1.12 moles of CO₂** gas are produced.

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