Methanol (CH3OH) (molar mass: of 32.042 g/mol), used as a cooking fuel, burns in oxygen to produce carbon dioxide and water.
2 CH3OH (g) + 3O2 (g) —-> 2CO2 (g) + 4H2O + heat = -726 kJ
How many grams of methanol are burnt to release 865. kJ of energy?
The Correct Answer and Explanation is:
To find how many grams of methanol (CH₃OH) are burned to release 865 kJ of energy, we can use stoichiometry based on the balanced chemical equation and the energy change:
Balanced Reaction:
2CH3OH+3O2→2CO2+4H2OΔH=−726 kJ2 \text{CH}_3\text{OH} + 3 \text{O}_2 \rightarrow 2 \text{CO}_2 + 4 \text{H}_2\text{O} \quad \Delta H = -726 \text{ kJ}
This tells us that 726 kJ of energy is released when 2 moles of methanol combust.
Step 1: Determine how many moles of methanol release 865 kJ
Use a proportion: 2 mol CH3OH726 kJ=x mol CH3OH865 kJ\frac{2 \text{ mol CH}_3\text{OH}}{726 \text{ kJ}} = \frac{x \text{ mol CH}_3\text{OH}}{865 \text{ kJ}} x=865×2726≈2.3825 mol CH3OHx = \frac{865 \times 2}{726} \approx 2.3825 \text{ mol CH}_3\text{OH}
Step 2: Convert moles to grams
Molar mass of CH₃OH = 32.042 g/mol Mass=2.3825 mol×32.042 g/mol≈76.30 g\text{Mass} = 2.3825 \text{ mol} \times 32.042 \text{ g/mol} \approx 76.30 \text{ g}
✅ Final Answer:
76.3 grams of methanol are burned to release 865 kJ of energy.
🔬 Explanation
Methanol (CH₃OH) is a simple alcohol that combusts in the presence of oxygen to produce carbon dioxide, water, and energy in the form of heat. This reaction is exothermic, meaning it releases energy. The balanced chemical equation for methanol combustion is: 2CH3OH+3O2→2CO2+4H2OΔH=−726 kJ2 \text{CH}_3\text{OH} + 3 \text{O}_2 \rightarrow 2 \text{CO}_2 + 4 \text{H}_2\text{O} \quad \Delta H = -726 \text{ kJ}
The negative enthalpy (ΔH = -726 kJ) indicates that 726 kJ of energy is released when 2 moles of methanol are burned. To find out how much methanol is needed to release a specific amount of energy—865 kJ in this case—we use a proportional relationship.
We first calculate how many moles of methanol would produce that much energy. Using the ratio of energy per mole from the balanced equation, we solve for the unknown number of moles corresponding to 865 kJ. The answer is about 2.3825 moles.
Next, we convert this amount into grams using the molar mass of methanol (32.042 g/mol). Multiplying the moles by the molar mass gives approximately 76.3 grams of methanol.
This kind of stoichiometric calculation is vital in chemistry and engineering when designing combustion processes, estimating fuel requirements, or understanding environmental impacts of fuel use.
