The human body consists of cells, which in turn consist of atoms. About two thirds of body mass is w — Physical Chemistry Chemistry Question
The human body
The human body consists of cells, which in turn consist of atoms. About two thirds of body mass is water, which means that about two thirds of cell mass is water.
Estimate the approximate number of atoms 10x in a human body weighing 60 kg (estimate number x.) Consider the average atomic mass of the three atoms in a water molecule. For your own information, consider the average atomic mass of atoms in other molecules such as proteins, fats, and carbohydrates.
Model Answer
The average relative atomic mass of the three atoms in a water molecule = 18 / 3 = 6, the average relative atomic masses of atoms in other molecules are about the same. For example, consider carbohydrate, C(H2O). 30 / 4 = 7.5
So, let’s assume that the human body is composed of only water.
60 kg of water = 10,000 moles of atoms = 6×1027 atoms or about 1028 atoms
A human body consists of about 100 trillion (1014) cells. Assume that all human cells are cubic and identical in size. Estimate the size of an average human cell (length of the edge of the cube) in one significant figure.
Model Answer
Assume that the density of the human body is 1 g cm–3.
Volume of body = 6×10–2 m3
Volume of a cell = 6×10–16 m3
Length of a cell = 8×10–6 m (about 10 micrometers)
Assume that all atoms in a cell are uniformly distributed. Estimate the distance between two atomic nuclei in a cell.
Model Answer
Number of atoms in a cell = 1028 / 1014 = 1014
Volume per atom in a cell = 6×10–16 m3 / 1014 = 6×10–30 m3
Distance between two atomic nuclei = 2×10–10 m = 2 Angstroms
Estimate the distance between the centers of mass of two water molecules in pure water.
Model Answer
Volume of a mole of water = 18×10–6 m3
Average volume occupied by a water molecule = 3×10–29 m3
Distance between centers of mass of two water molecules = 3×10–10 m = 3 Angstroms
Estimate the average distance between atomic nuclei in pure water. Compare your result with answers in 24.3 and 24.4.
Model Answer
Volume of a mole of water = 18×10–6 m3
Number of atoms in a mole of water = 18×1023
Average volume occupied by an atom in water = 10–29 m3
Average distance between atomic nuclei in water = 2×10–10 m = 2 Å (angstroms)