A bacterium is modelled as a sphere of radius filled with cytoplasm

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Thermal, Statistical & Complex Systems · Fluid statics and the continuum picture

Thermal Physics, Ch Chemical potential, open systems and chemical equilibrium

Problem

A bacterium is modelled as a sphere of radius

0.50\,\mathrm{\mu m}

filled with cytoplasm. Counting only the small dissolved species that are free to move as separate particles (ions, sugars, amino acids), there are about

2.0\times10^{8}

of them inside one cell; the few large molecules are so few in number that they are ignored. The cell is placed in pure fresh water at

300\,\mathrm{K}

. Treat the cytoplasm as a dilute ideal solution and the cell membrane as ideally semipermeable, passing water only; treat the outside water as pure and at atmospheric pressure. ((a)) Estimate the number density of dissolved particles inside the cell, in

\mathrm{m^{-3}}

. ((b)) Estimate the osmotic pressure of the cell contents, in bar. ((c)) What height of a column of pure water (density

1.0\times10^{3}\,\mathrm{kg\,m^{-3}}

g = 9.81\,\mathrm{m\,s^{-2}}

) would exert the same pressure at its base?

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