BIO How Many Atoms Are You? ?Estimate the number of atoms in the body of a 50-kg physics student. Note that the human body is mostly water, which has molar mass 18.0 g/mol, and that each water molecule contains three atoms.

Solution 67P We have to first calculate the number of moles of water in human body. The mass of the student is 50.0 kg . Since it is given that human body is mostly water, hence the amount of water will also be approximately 50.0 kg. Molar mass of water = 18.0 g/mol = 0.018 kg/mol Therefore, the number of moles of water in human body is = 50.0/0.018 moles = 2777 moles 23 Now, 1 mole of water has = 6.02 × 10 molecules 23 27 So, 2777 moles of water has = 6.02 × 10 × 2777 molecules = 1.67 × 10 molecules Given in the question that each water molecule has three atoms. Therefore, the number of 27 27 27 atoms in 1.67 × 10 molecules is = 3 × 1.67 × 10 atoms = 5.0 × 10 atoms 27 Therefore, the approximate number of atoms in the student’s body is 5.0 × 10 .