Calculate the amount of energy a woman takes in during a year on a 2200kcal a day diet (1 calorie = 4.18J). Calculate the amount of energy she spends in driving 5000 miles a year at 40 miles to the gallon of octane, given 1 gallon of octane weighs 3.12 kg, and standard enthalpy of combustion (octane-C8H18 ) = -5512kJ/mol.
To calculate the amount of energy a woman takes in during a year on a 2200 kcal/day diet, we need to first convert the calories to joules.
1 calorie is equal to 4.18 joules. Therefore, 2200 kcal is equal to 2200 * 4.18 = 9184 joules.
Now, let's calculate the energy she spends in driving 5000 miles a year at 40 miles per gallon of octane.
First, let's calculate the amount of octane (C8H18) consumed for 5000 miles:
Since 40 miles are covered by 1 gallon of octane, the woman would consume 5000 / 40 = 125 gallons of octane in a year.
To convert this to kilograms, we need to know the weight of 1 gallon of octane. According to the information provided, 1 gallon of octane weighs 3.12 kg.
Therefore, the total weight of octane consumed in a year is 125 * 3.12 = 390 kg.
Now, let's calculate the energy released from the combustion of octane.
The standard enthalpy of combustion for octane (C8H18) is given as -5512 kJ/mol.
To convert this to joules, we need to multiply it by 1000: -5512 * 1000 = -5,512,000 J/mol.
The molar mass of octane (C8H18) can be calculated as follows:
8 carbon atoms (atomic mass = 12.01 g/mol) = 8 * 12.01 = 96.08 g
18 hydrogen atoms (atomic mass = 1.01 g/mol) = 18 * 1.01 = 18.18 g
Total molar mass = 96.08 + 18.18 = 114.26 g/mol
Now, let's calculate the moles of octane consumed:
390 kg * 1000 = 390,000 g
390,000 g / 114.26 g/mol = 3410.65 mol
Finally, let's calculate the energy spent in driving 5000 miles:
Energy spent = -5,512,000 J/mol * 3410.65 mol = -1.882 * 10^10 J
Note: The negative value indicates the released energy from the combustion process.
Therefore, the woman spends approximately 1.882 * 10^10 joules of energy in driving 5000 miles a year.