Question

Assuming the human body is primarily made of water, estimate the number of molecules in it. (Note that water has a molecular mass of 18 g/mol and there are roughly 1024 atoms in a mole.)

a) 10^24 molecules
b) 10^25 molecules
c) 10^26 molecules
d) 10^27 molecules

Answer 1

To estimate the number of water molecules in the human body, we calculate the mass of water based on body weight and then use the molar mass of water and Avogadro's number to find the total number of molecules. The best estimate is 10^27 molecules.

Step-by-step explanation:

The question focuses on estimating the number of water molecules in the human body. To do this, we use the information that the molecular mass of water (H2O) is 18 g/mol and that each mole contains Avogadro's number of molecules, which is approximately 6.022 x 1023. An average adult human body consists of about 60% water, and if we assume a body weight of 70 kg (which is 70,000 g), then the mass of water in the body would be approximately 42,000 g of water.

To find the number of moles of water in the body, we divide the mass of the body's water (42,000 g) by the molar mass of water (18 g/mol), which gives us 2333.33 moles of water. Multiplying this by Avogadro's number gives us the total number of water molecules: 2333.33 moles x 6.022 x 1023 molecules/mol = 1.403 x 1027 molecules. Therefore, the best estimate for the number of molecules in the human body is option d) 1027 molecules.