The balanced chemical equation for the combustion of methane (CH4) in oxygen (O2) is:

CH4 + 2O2 --> CO2 + 2H2O

According to the balanced equation, 1 mole of methane (CH4) reacts with 2 moles of oxygen (O2) to produce 1 mole of carbon dioxide (CO2) and 2 moles of water (H2O).

To calculate the heat released when 50.0 grams of methane burns completely, we need to use the molar mass of methane and the enthalpy of combustion.

The molar mass of methane (CH4) is calculated as follows:
1 carbon atom (C) --> atomic mass = 12.01 g/mol
4 hydrogen atoms (H) --> atomic mass = 1.008 g/mol (x 4)

Molar mass of methane (CH4) = 12.01 g/mol + (1.008 g/mol x 4) = 16.04 g/mol

Next, we need to calculate the moles of methane (CH4) in 50.0 grams:
Moles = mass / molar mass
Moles of methane (CH4) = 50.0 g / 16.04 g/mol = 3.116 moles

Since the stoichiometric ratio of methane to carbon dioxide in the balanced equation is 1:1, we can say that 3.116 moles of methane will produce 3.116 moles of carbon dioxide.

Now, we need to calculate the heat released using the enthalpy of combustion of methane. The enthalpy of combustion for methane is -890.36 kJ/mol.
Heat released = moles of methane x enthalpy of combustion

Heat released = 3.116 mol x -890.36 kJ/mol = -2777.68 kJ

Therefore, the heat released when 50.0 grams of methane (CH4) burns completely in oxygen is approximately -2777.68 kJ. Note that the negative sign indicates that the reaction is exothermic and releases heat.

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