use a combustion reaction of liquid ethanol( C2H5OH) an air as a source of work, assuming T=25 celcius, air pressure is 1 atm, and all products are gases with partial pressure of 10 atm each. How high can one lift a 1000 kg weight by burning 100 g of ethanol.
note oxygen is 21% by volume of air
To determine the maximum height that can be lifted by burning 100 g of ethanol, we need to calculate the amount of energy released during the combustion reaction and then convert it to work done in lifting the weight.
First, let's calculate the moles of ethanol burned:
Molar mass of ethanol (C2H5OH) = 2(12.01 g/mol) + 6(1.01 g/mol) + 16.00 g/mol
= 46.07 g/mol
moles of ethanol = mass of ethanol / molar mass of ethanol
= 100 g / 46.07 g/mol
= 2.17 moles
Next, let's determine the heat of combustion of ethanol. The balanced chemical equation for the combustion of ethanol is:
C2H5OH + 3 O2 -> 2 CO2 + 3 H2O
The heat of combustion of ethanol is approximately -1367 kJ/mol.
The energy released during the combustion of 2.17 moles of ethanol is:
Energy released = moles of ethanol * heat of combustion of ethanol
= 2.17 moles * -1367 kJ/mol
= -2964.39 kJ
Now, let's convert the energy released to work done. Assuming no energy loss, we can equate the energy released to the work done:
work done = force * distance
We are given the weight (force) of 1000 kg and need to find the height (distance).
Since work done is the product of force and distance, we can rearrange the equation to solve for distance:
distance = work done / force
Using the weight of 1000 kg, we find the force using Newton's second law (F = mg):
force = mass * gravity
= 1000 kg * 9.8 m/s^2
= 9800 N
Substituting the known values into the equation, we can calculate the maximum height:
distance = -2964.39 kJ / 9800 N
= -0.302 m
Note that the negative sign indicates that the work is being done against gravity, so the height should be expressed as a negative value.
Therefore, in this specific scenario, involving the combustion reaction of 100 g of ethanol, the 1000 kg weight can be lifted to a maximum height of approximately 0.302 meters.
To determine the maximum height one can lift a weight by burning ethanol, we need to calculate the amount of work done by the combustion reaction. The work done can be calculated using the equation:
Work = Force x Distance
To find the force, we need to calculate the pressure exerted by the products of the combustion reaction. Since all the products are gases with a partial pressure of 10 atm each, the total pressure of the gases is 10 + 10 + 10 = 30 atm.
First, let's calculate the number of moles of ethanol burned:
1 mole of ethanol (C2H5OH) = molar mass of C2H5OH = 46.07 g/mol
Number of moles of ethanol burned = mass of ethanol burned / molar mass of ethanol
= 100 g / 46.07 g/mol
≈ 2.17 moles of ethanol
Next, let's determine the number of moles of oxygen needed for complete combustion. Ethanol reacts with oxygen in a 1:3 ratio.
Number of moles of oxygen = 3 x number of moles of ethanol
= 3 x 2.17 moles
≈ 6.51 moles of oxygen
To calculate the total volume of air required, we need to consider that oxygen is 21% by volume of air. Therefore, the total volume of air is:
Total volume of air = Volume of oxygen / (Oxygen percentage/100)
= 6.51 moles x 22.4 L/mol / (0.21)
≈ 69.39 L
Now, let's calculate the pressure exerted by the combustion products:
Pressure = Number of moles x 0.0821 x Temperature / Volume
Assuming temperature in Kelvin, T = 25°C + 273.15 = 298.15 K
Pressure = (2.17 moles + 6.51 moles) x 0.0821 x 298.15 K / (69.39 L)
≈ 2.06 atm
Since the pressure of the combustion products is 2.06 atm, the force exerted is:
Force = Pressure x Area
Assuming the area is the same as the surface area of the weight being lifted, we can calculate the force.
Area = mass x g / Pressure
Area = 1000 kg x 9.8 m/s^2 / 2.06 atm
≈ 4726 m^2
Therefore, the force exerted is:
Force = 2.06 atm x 4726 m^2
≈ 9743 N
Finally, we can calculate the work done by multiplying the force exerted by the distance traveled:
Work = Force x Distance
The distance lifted is the height we are trying to find, let's assume it is h:
Work = Force x h
Solving for h:
h = Work / Force
Since we are trying to find the maximum height, we need to use the maximum value for Work, which is achieved when the combustion reaction is complete.
Work = mass of the weight x gravitational force x height
Substituting the values:
1000 kg x 9.8 m/s^2 x h = (9743 N) x h
Simplifying and solving for h:
h = (9743 N) x h / (1000 kg x 9.8 m/s^2)
Finally, substituting the values:
h = (9743 N) x h / (1000 kg x 9.8 m/s^2)
h ≈ 49.8 meters
Therefore, one can lift a 1000 kg weight to a maximum height of approximately 49.8 meters by burning 100 g of ethanol in the given conditions.