It has been determined that the body can generate 5500 kJ of energy during one hour of strenuous exercise. Perspiration is the body's mechanism for eliminating this heat. How many liters of water would have to be evaporated through perspiration to rid the body of the heat generated during two hours of exercise? (The heat of vaporization of water is 40.6 kJ/mol. Assume the density of water is 1.000 g/mL)
5500 kJ.
40.6 kJ/mol x # mol = 5500 kJ.
Solve for mols H2O
Convert mols H2O to grams.
Convert, using density, grams H2O to L H2O.
To determine the number of liters of water that would need to be evaporated through perspiration to rid the body of the heat generated during two hours of exercise, we will follow these steps:
Step 1: Convert the energy generated during exercise to Joules.
5500 kJ = 5500 * 1000 = 5,500,000 J
Step 2: Calculate the number of moles of water required to absorb this heat.
Using the heat of vaporization of water (40.6 kJ/mol), we can find the number of moles of water required by dividing the energy in Joules by the heat of vaporization.
Number of moles = Energy (J) / Heat of Vaporization (J/mol)
Number of moles = 5,500,000 J / 40.6 kJ/mol
Number of moles = 5,500,000 J / 40,600 J/mol = 135.47 mol (rounded to two decimal places)
Step 3: Convert the number of moles to grams of water.
Since the density of water is 1.000 g/mL, we know that 1 mL of water is equal to 1 g. Therefore, the number of grams of water is the same as the number of mL of water.
Number of grams = 135.47 mol * 18.015 g/mol (molar mass of water)
Number of grams = 2,440.95 g (rounded to two decimal places)
Step 4: Convert grams of water to liters.
There are 1000 g in 1 L, so we can convert the grams of water to liters by dividing by 1000.
Number of liters = 2,440.95 g / 1000
Number of liters = 2.44 L (rounded to two decimal places)
Therefore, approximately 2.44 liters of water would have to be evaporated through perspiration to rid the body of the heat generated during two hours of exercise.
To solve this problem, we need to calculate the amount of heat generated during two hours of exercise and then determine how many liters of water would have to be evaporated through perspiration to get rid of this heat.
First, let's calculate the total amount of heat generated during two hours of exercise. We know that the body can generate 5500 kJ of energy per hour, so for two hours, it would generate:
Heat generated = 5500 kJ/hour * 2 hours
Heat generated = 11000 kJ
Now, let's calculate the number of moles of water that needs to be evaporated to remove this amount of heat. We can use the equation:
q = n * ΔHvap
Where:
q is the amount of heat
n is the number of moles
ΔHvap is the heat of vaporization
Rearranging the equation, we get:
n = q / ΔHvap
Substituting the values:
n = 11000 kJ / 40.6 kJ/mol
Now we need to convert the given heat values from kilojoules (kJ) to joules (J) because the heat of vaporization (ΔHvap) is given in joules per mole (J/mol):
n = 11000 kJ * 1000 J/kJ / 40.6 kJ/mol
Simplifying the calculation:
n = 270296.08 mol
We know that the density of water is 1.000 g/mL. To convert moles to grams, we need to multiply the number of moles by the molar mass of water (18.015 g/mol):
mass = n * molar mass
mass = 270296.08 mol * 18.015 g/mol
mass = 4869641.25 g
Finally, to convert grams to liters, we need to divide the mass by the density of water:
volume = mass / density
volume = 4869641.25 g / 1.000 g/mL
volume = 4869641.25 mL
However, we need the volume in liters, so we convert:
volume = 4869641.25 mL / 1000 mL/L
volume = 4869.64 L
Therefore, approximately 4869.64 liters of water would need to be evaporated through perspiration to rid the body of the heat generated during two hours of exercise.