To determine the amount of energy released when 59.7 grams of methane (CH[tex]\(_4\)[/tex]) reacts with oxygen, follow these steps:
1. Calculate the number of moles of methane:
The molecular weight of methane (CH[tex]\(_4\)[/tex]) is given as 16.04 g/mol. We can calculate the number of moles of methane by dividing the mass of methane by its molecular weight:
[tex]\[
\text{moles of CH}_4 = \frac{\text{mass of CH}_4}{\text{molecular weight of CH}_4} = \frac{59.7 \, \text{g}}{16.04 \, \text{g/mol}} = 3.7219451371571077 \, \text{moles}
\][/tex]
2. Calculate the energy released:
Given that the heat released per mole of methane is -890 kJ/mol, the total energy released can be calculated by multiplying the number of moles of methane by the heat released per mole:
[tex]\[
\text{energy released} = \text{moles of CH}_4 \times \Delta H = 3.7219451371571077 \, \text{moles} \times -890 \, \text{kJ/mol} = -3312.531 \, \text{kJ}
\][/tex]
3. Express the answer to three significant figures:
The energy released when 59.7 grams of methane reacts with oxygen is:
[tex]\[
\boxed{-3312.531 \, \text{kJ}}
\][/tex]
Therefore, the combustion of 59.7 grams of methane releases [tex]\(-3312.531 \, \text{kJ}\)[/tex] of energy, expressed to three significant figures.
