The enthalpy of combustion of methanol is -711 kJ/mole. What mass of methanol must be completely burned in oxygen to produce 71.1 kJ of energy?
To find the mass of methanol required to produce 71.1 kJ of energy, we can use the enthalpy change of combustion given and the molar mass of methanol.
Step 1: Calculate the number of moles of methanol needed.
According to the enthalpy of combustion, the energy released per mole of methanol is -711 kJ. Therefore, we can set up the following proportion:
-711 kJ/1 mole = 71.1 kJ/x moles
Cross-multiplying and solving for x:
-711 kJ * x moles = 71.1 kJ * 1 mole
x = (71.1 kJ * 1 mole) / (-711 kJ)
x = 0.1 moles
Step 2: Calculate the mass of methanol.
The molar mass of methanol (CH3OH) is:
C: 12.01 g/mol
H: 1.008 g/mol (3 atoms)
O: 16.00 g/mol
1 mole of methanol = 12.01 g + (1.008 g * 3) + 16.00 g = 32.04 g
To find the mass of 0.1 moles of methanol:
Mass = moles × molar mass
Mass = 0.1 moles × 32.04 g/mol
Mass = 3.204 g
Therefore, approximately 3.204 grams of methanol must be completely burned in oxygen to produce 71.1 kJ of energy.
To determine the mass of methanol required for the given energy output, you need to use the enthalpy of combustion of methanol.
The enthalpy of combustion (-711 kJ/mole) represents the energy released when one mole of methanol reacts with oxygen and completely burns. This means that for every mole of methanol burned, 711 kJ of energy is released.
To find the mass of methanol required for a specific energy output, you can use the following steps:
Step 1: Calculate the number of moles of methanol required.
Use the equation:
moles of methanol = energy output / enthalpy of combustion
In this case, the energy output is 71.1 kJ. Convert it to kJ by dividing it by 1000:
71.1 kJ = 71.1 kJ / 1
Using the enthalpy of combustion (-711 kJ/mole):
moles of methanol = 71.1 kJ / (-711 kJ/mole)
Step 2: Convert moles of methanol to grams.
To convert moles to grams, you need the molar mass of methanol. The molar mass of methanol (CH3OH) is approximately 32 g/mol.
mass of methanol = moles of methanol x molar mass of methanol
Substituting the values:
mass of methanol = (71.1 kJ / -711 kJ/mole) x 32 g/mol
Calculate the mass of methanol using the given formula.