Use a combustion reaction of liquid ethanol in air as a source of work, assuming temperature is 25 deg C, air pressure is 1atm and all products are gases with partial pressures of 10atm each. How high can one lift a 1000kg weight by burning 100g of ethanol? *oxygen is 21% (by volume) of air.
To calculate the maximum height to which a weight can be lifted using the combustion of ethanol, we need to consider the energy released during the combustion reaction.
First, let's calculate the moles of ethanol burned:
100g of ethanol / molar mass of ethanol = moles of ethanol
The molar mass of ethanol (C2H5OH) is:
2(12.01 g/mol) + 6(1.01 g/mol) + 16.00 g/mol = 46.07 g/mol
So, moles of ethanol = 100g / 46.07 g/mol.
Next, let's calculate the energy released during the combustion of ethanol. The chemical equation for the combustion of ethanol is:
C2H5OH + 3O2 -> 2CO2 + 3H2O
The balanced equation indicates that 1 mole of ethanol reacts with 3 moles of oxygen to produce 2 moles of carbon dioxide and 3 moles of water.
The energy released during the combustion of 1 mole of ethanol is approximately -1367 kJ/mol.
Now, let's calculate the energy released from burning 100g of ethanol:
Energy released = (-1367 kJ/mol) * (moles of ethanol)
To find the maximum height to which a weight can be lifted, we'll convert the energy released into work done. Work is calculated as the force exerted multiplied by the distance lifted.
Work done = force * distance
The force is equal to the weight being lifted, which is given as 1000kg. The distance lifted is what we need to determine.
The work done can be calculated as the difference in potential energy:
Work done = mgh
Here, m is the mass of the weight, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height lifted.
Therefore, we can calculate the maximum height lifted by rearranging the equation as:
h = Work done / (mg)
Now, let's substitute the values into the equation to find the maximum height.
Step 1: Calculate the moles of ethanol burned
moles of ethanol = 100g / 46.07 g/mol
Step 2: Calculate the energy released during the combustion of ethanol
Energy released = (-1367 kJ/mol) * (moles of ethanol)
Step 3: Convert energy to work done
Work done = Energy released
Step 4: Calculate the maximum height lifted
h = Work done / (mg)
Substitute the values into the equation and perform the calculations to find the maximum height lifted.