# Volume of Water and Body Density

50 kg person is immersed in a water tank for body fat testing, she has an underwater mass of 2kg. This difference in body mass is equal to the mass of water displaced by the body. The density of water 1.00g/ml.

a) what is the volume of the water displaced?

b) what is the volume in liter, of the person's body?

c) what is the body density, in g/mL of the person?

https://brainmass.com/chemistry/stoichiometry/volume-water-body-density-430889

## SOLUTION This solution is **FREE** courtesy of BrainMass!

The guidance is given in the question which is always nice. The difference in mass is 50 kg (weight on land) - 2kg (weight in water) = 48 kg. This weight (48kg) is equal to the weight of water displaced by the person.

a) what is the volume of the water displaced?

b) what is the volume in liter, of the person's body?

The volume of water displaced can be obtained bu dividing the mass of water displaced by the density of water

Density of water = 1.00 g/ml or 1.00 kg/L ( conversion obtained by multiplying 1.00 g/ml by 1000/1000)

48 kg / 1.00 kg/L = 48 L - this is the volume of water displaced which is also the volume of the person.

c) what is the body density, in g/mL of the person?

Since we know the volume of the person (48L) and the mass of the person on land (50 kg) we can calculate the density of the person which is simply the mass of the person divided by his or her volume

Density of person = 50 kg / 48L = 1.042 kg/L or (using the conversion above) 1.042 g/ml.

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