By using the data in this question, estimate how much oxygen a person requires on average in a life time and how far a motor can go using the same amount of oxygen. the typical daily food requirement of a person can be considered to be 1.2 kg of carbohydrate. The person obtains energy by the oxidation of the carbohydrate, which can be represented by the formula (CH2O)n.
a) Construct an equation for the complete combustion of the carbohydrate formula (CH2O)n.
b)The empirical relative formula mass of the carbohydrate is 30. Use your equation above to calculate the number of moles of oxygen required by the person each day.
0.04 moles
a) To construct an equation for the complete combustion of the carbohydrate formula (CH2O)n, we need to remember that combustion involves combining the carbohydrate with oxygen to produce carbon dioxide and water.
The balanced equation for the combustion of (CH2O)n can be written as:
(CH2O)n + O2 → CO2 + H2O
b) The empirical relative formula mass of the carbohydrate is 30, indicating that the molecular formula of the carbohydrate must be (CH2O)6. This means that n = 6 in our equation.
Considering that the person requires 1.2 kg of carbohydrates each day, we need to convert this mass to moles to determine the amount of oxygen required.
First, we convert the mass of carbohydrate to grams:
1.2 kg = 1200 grams
Next, we calculate the number of moles of carbohydrate:
Number of moles = mass / molar mass
Number of moles = 1200 g / 30 g/mol
Number of moles = 40 moles
According to the balanced equation, for each mole of (CH2O)6, 6 moles of oxygen (O2) are required. Therefore, the number of moles of oxygen required each day is:
Number of moles of oxygen = Number of moles of carbohydrate x 6
Number of moles of oxygen = 40 moles x 6
Number of moles of oxygen = 240 moles
Therefore, a person requires 240 moles of oxygen each day when consuming 1.2 kg of carbohydrates.
Now let's move on to the second part of your question concerning how far a motor can go using the same amount of oxygen.
The distance a motor can go depends on various factors such as the fuel efficiency of the motor and the power it produces. Without knowing those specific details, it is difficult to provide an exact answer. However, we can consider a hypothetical scenario for estimation purposes.
Let's assume that the motor uses the same complete combustion reaction as the human body, where 240 moles of oxygen are consumed. We will also assume that this combustion provides energy and power to propel the motor.
To estimate the distance the motor can go, we need to consider the fuel efficiency, which is typically measured in miles per gallon (MPG) for internal combustion engines.
Let's assume a hypothetical fuel efficiency of 30 MPG (miles per gallon). This means that the motor can travel 30 miles using one gallon of fuel.
Now, we need to determine the amount of fuel (gasoline) that can be burned by the motor to consume 240 moles of oxygen.
The stoichiometric ratio states that for each mole of oxygen consumed, one mole of fuel is required. Therefore, the number of moles of fuel required is also 240.
One mole of a hydrocarbon fuel (like gasoline) typically has a mass of around 114 grams. Since the molar mass of gasoline varies, we will use 114 g/mol as an approximation.
So, the mass of fuel required is:
Mass of fuel = Number of moles of fuel x molar mass
Mass of fuel = 240 moles x 114 g/mol
Mass of fuel = 27360 grams
Now, we need to convert this mass to gallons. Assuming that one gallon of gasoline has a mass of approximately 3785 grams, we can calculate the required volume of fuel:
Volume of fuel (in gallons) = Mass of fuel / Mass of one gallon
Volume of fuel = 27360 g / 3785 g/gallon
Volume of fuel ≈ 7.23 gallons
Finally, if the motor has a fuel efficiency of 30 MPG, and 7.23 gallons of fuel are used:
Distance traveled = Volume of fuel x Fuel efficiency
Distance traveled = 7.23 gallons x 30 MPG
Distance traveled ≈ 217 miles
In this hypothetical scenario, a motor using the same amount of oxygen as a person consuming 1.2 kg of carbohydrates each day could potentially travel around 217 miles.