How many kilojoules of heat are released when 38.5 g of CH4(g) reacts completely with O2(g) to form CH3OH(g) at constant pressure?
Express heat to three significant digits with the appropriate units.
To calculate the heat released, we need to find the moles of CH4 reactant and use the balanced chemical equation to determine the heat released per mole of CH4.
Step 1: Calculate the moles of CH4.
Moles = mass / molar mass
Molar mass of CH4 = 12.01 g/mol (C) + 4 * 1.01 g/mol (H)
Molar mass of CH4 = 16.05 g/mol
Moles of CH4 = 38.5 g / 16.05 g/mol
Step 2: Balance the chemical equation.
CH4(g) + 2O2(g) -> CH3OH(g)
Step 3: Determine the heat released per mole of CH4.
According to the balanced chemical equation, the stoichiometric coefficient of CH4 is 1, which means that 1 mole of CH4 reacts to produce 1 mole of CH3OH.
According to thermochemical data, the molar enthalpy change of the reaction is -726 kJ/mol.
Step 4: Calculate the heat released.
Heat released = Moles of CH4 x Molar heat of reaction
Heat released = (moles of CH4) x (-726 kJ/mol)
Now let's calculate the values:
Step 1:
Moles CH4 = 38.5 g / 16.05 g/mol
Moles CH4 ≈ 2.399 moles
Step 4:
Heat released = (2.399 moles) x (-726 kJ/mol)
Calculating the heat released:
Heat released ≈ -1745.87 kJ
Therefore, approximately 1745.87 kJ of heat is released when 38.5 g of CH4(g) reacts completely with O2(g) to form CH3OH(g) at constant pressure.
To determine the amount of heat released when 38.5 g of CH4(g) reacts completely with O2(g) to form CH3OH(g), we need to use the concept of molar stoichiometry and the enthalpy of reaction.
Step 1: Write and balance the chemical equation for the reaction:
CH4(g) + O2(g) → CH3OH(g)
Step 2: Calculate the moles of CH4(g) using its molar mass:
Molar mass of CH4 = 12.01 g/mol (C) + 4 * 1.01 g/mol (H) = 16.05 g/mol
Moles of CH4(g) = mass / molar mass = 38.5 g / 16.05 g/mol = 2.398 mol
Step 3: Use the balanced equation to determine the stoichiometric relationship between CH4(g) and CH3OH(g):
From the balanced equation, we see that the stoichiometric ratio of CH4(g) to CH3OH(g) is 1:1.
Step 4: Calculate the amount of heat released using the molar enthalpy of reaction (ΔHrxn):
The molar enthalpy of reaction is given as -890.3 kJ/mol. Since the stoichiometric ratio between CH4(g) and CH3OH(g) is 1:1, the amount of heat released can be calculated as follows:
Heat released = moles of CH4(g) * ΔHrxn
Heat released = 2.398 mol * -890.3 kJ/mol = -2132.97 kJ
Step 5: Round the answer to three significant digits:
The result, after rounding to three significant digits, is -2133 kJ.
Therefore, 38.5 g of CH4(g) reacting completely with O2(g) to form CH3OH(g) at constant pressure releases -2133 kJ of heat.