Question

Staphylococcus aureus is spherical cell approximately 1.0um in diameter. Assuming it is almost entirely water with a density of 1g/mL, compute
a) the mass of the bacterium in kg
b) the mass of the bacterium in kD
c) the numbe of water molecules it contains
d) how many s.aureus in a row would it take to circle the Earth? (Earth radius at the equater is 6378.1km)
e) the surface area in m^2
f) the number of phospholipid molecules in its plasma membrane, assuming each lipid molecule has an area of 0.50nm^2

Answer 1

a) volume of bacerium*density = (4/3)*(22/7)*(0.5x10^-6)³ m³ * 1000 kg/m³ = 5.24 x 10^-16 kg

b) 1kD is one g/mole (commonly used in polymer chemistry). Therefore, mass of the bacterium = 2.91x10-11 kD (assuming it contains mainly water)

c) 5.24x10-13 / 18 * 6.023x1023 = 1.75x10¹⁰ water molecules

d) Circumference of Earth along its equador = 2pi*r = 4x10⁴ km or 4x10¹³ micrometers. Diameter of bacterium is 1 micrometer.

No. of bacterium covering the Earth's equador =4x10¹³ /1 = 4x10¹³  

e) The surface area of bacterium = 4pi*r² = 3.14 x10^-12 m²

f) No. of phospholipid molecules = 3.14 x10^-12 m² /5.0x10^-19 m² = 6.28x10⁶ molecules