# Estimate the number of H_2O molecules in a human body of mass 80.2 kg. Assume that, on average,...

## Question:

Estimate the number of {eq}H_2O {/eq} molecules in a human body of mass {eq}80.2 \ kg {/eq}. Assume that, on average, water makes up about {eq}62 \% {/eq}of the mass of a human body.

## Molar Mass:

The mass of 1 mole of atom/molecule of the element/compound gives the molar mass of the substance.

For example, the molecular mass of water is 18 g/mol. This means that the mass of 1 mole molecule of water is 18 g.

Given:

• Mass of the human body is {eq}m_h = 80.2 \ kg. {/eq}
• Water makes up about {eq}62 \% {/eq}of the mass of a human body ie {eq}m = 0.62 m_h = (0.62 \times 80.2) \ kg = 49.7 \ kg = 49.7 \times 10^3 \ g {/eq}.

Molar mass of water is M = 18 g/mol.

Thus we have the number of moles of molecule of water present in the human body is

{eq}\begin{align*} n & = \frac{m}{M} \\ & = \frac{49.7 \times 10^3}{18} \ mol \\ &= 2761 \ mol \\ & = 2761 \times 6.023 \times 10^{23} \ molecules \\ & = 1.67 \times 10^{27} \ molecules \Rightarrow(Answer) \end{align*} {/eq}