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Chemical reactions are processes where substances known as reactants transform into different substances called products. In a combustion reaction, a fuel reacts with an oxidant, often oxygen, to release energy. For our specific example, we have a combustion reaction involving methane (\(\mathrm{CH}_4\)) and ethylene (\(\mathrm{C}_2\mathrm{H}_4\)) with oxygen. The reactions can be summarized as follows:

• Methane Combustion: \(\mathrm{CH}_4 + 2 \mathrm{O}_2 \rightarrow \mathrm{CO}_2 + 2\mathrm{H}_2\mathrm{O}\)
• Ethylene Combustion: \(\mathrm{C}_2\mathrm{H}_4 + 3 \mathrm{O}_2 \rightarrow 2\mathrm{CO}_2 + 2\mathrm{H}_2\mathrm{O}\)

For each of these reactions, energy is released and can be measured as the change in enthalpy (\(\Delta H\)), which is the heat absorbed or released at constant pressure. The negative sign in \(\Delta H\) values for these reactions indicates that they are exothermic, meaning they release heat.

Enthalpy change, symbolized as \(\Delta H\), measures the heat change during a chemical reaction at constant pressure. It tells us whether the reaction absorbs or releases heat:

• For exothermic reactions, like combustion, \(\Delta H\) is negative, indicating that heat is released into the surroundings.
• For endothermic reactions, \(\Delta H\) would be positive, meaning the reaction absorbs heat from the surroundings.

In the combustion of methane and ethylene, the respective enthalpy changes are \(-890\ \mathrm{kJ/mol}\) and \(-1411\ \mathrm{kJ/mol}\). These values tell us how much energy is released when one mole of each substance is combusted. In our given problem, the total energy released from the combustion reactions equals \(-520\ \mathrm{kJ}\) indicating the combined heat release from both \(\mathrm{CH}_4\) and \(\mathrm{C}_2\mathrm{H}_4\). With these values, we can set up equations relating the masses of the reactants to the total energy produced.

Mass percentage is a way to express the concentration of an element or compound in a mixture. It's calculated as the mass of the component divided by the total mass of the mixture, multiplied by 100%. To find the mass percentage of methane (\(\mathrm{CH}_4\)) in the mixture, we first determine the mass corresponding to \(\mathrm{CH}_4\). If \(x\) grams is the mass of \(\mathrm{CH}_4\), the mass percentage is given by:\[\text{Mass Percentage of } \mathrm{CH}_4 = \frac{x}{10}\times 100\%\]Using the relationships and equations of heat provided in the problem, we solve for \(x\). After working through the calculations, we find that \(x \approx 3.02\ \mathrm{g}\).Thus, the mass percentage of \(\mathrm{CH}_4\) becomes:\[\frac{3.02}{10} \times 100\% = 30.2\%\]This result tells us that 30.2% of the mixture is methane by mass. Calculating mass percentage is essential for knowing the exact composition of compounds and mixtures in chemical processes.