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# Calculate the number of H2O molecules in a human body of mass 78.5 kg. Assume that, on average, water makes up

Calculate the number of H2O molecules in a human body of mass 78.5 kg. Assume that, on average, water makes up 62% of the mass of a human body. (Use 1.0 u for the atomic mass of hydrogen, and 16.0 u for the atomic mass of oxygen.)

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The unified atomic mass unit is equivalent to a mass of 1 g divided by Avogadro's number, or 1 g / 6.022142 x 10^23 ≈ 1.660539 x 10^-24 g, or 1.660539 x 10^-27 kg, since there are 1000 g / kg.

If 62% of the human body is made up of water, then the fraction of this body which is water is 0.62 x 78.5 kg = 48.67 kg.

To determine the total number of atomic mass units in that mass of water, we divide 48.67 kg by the weight of each mass unit in kilograms:

# amu's ≈ 48.67 kg / 1.660539 x 10^-27 kg / amu

# amu's ≈ 2.930976 x 10^28.

Since each molecule of water contains 18 amu's, then we divide the last figure above by 18:

# molecules H20 ≈ 2.930976 x 10^28 amu's / (18 amu's / H20 molecule) ≈ 1.628320 x 10^27 molecules.

So there are approximately 1.628320 x 10^27 molecules of water in a human body with a mass of 78.5 kg.

• calculate number h2o molecules human body mass 785 kg assume average water

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