Question

Determine a reasonable estimate for the number of atoms in an average adult human. Make the following assumptions in your estimate: A human is mostly made up of water (H₂O). For simplicity's sake, assume that this is the main make-up of the human body since you are only providing an estimate. Assume the average weight of an adult human is 170 lbs. (Hint: Think about what you need to know in order to count by weighing.)

Answer 1

To estimate the number of atoms in a human body, calculate the mass of water in the body, convert it to moles, and then use Avogadro's number to determine the number of water molecules. Finally, multiply by three (since each water molecule contains three atoms) to estimate the total number of atoms.

Step-by-step explanation:

To estimate the number of atoms in an average adult human, we can begin by calculating the number of water molecules, since the human body is primarily composed of water. If we assume that an average adult weighs 170 pounds (approximately 77 kilograms), and considering that up to 70 percent of an adult's body weight is water, we get a total water mass of approximately 54 kilograms.

Since the molecular mass of water (H₂O) is 18 g/mol, we can find the number of moles of water in the body by dividing the total mass of water by the molecular mass. This gives us 54,000 grams / 18 g/mol = 3000 moles of water. With Avogadro's number, which is approximately 6.022 x 10²³ molecules per mole, we can then estimate the number of water molecules by multiplying 3000 moles x 6.022 x 10²³ molecules/mol.

To find the number of atoms, we need to consider that each molecule of water contains three atoms (two hydrogen and one oxygen). Therefore, the total number of atoms in the body would be 3 times the number of water molecules. Upon calculation, we end up with a ballpark figure of approximately 5.4 x 10²· atoms.