Question

A spheroidal bacterium with a diameter of 1 mm contains 2 molecules of a particular protein. What is the molar concentration?

Answer 1

Answer : The molar concentration is,
`6.35* 10^(-18)mol/L`

Explanation :

First we have to calculate the moles of protein.

`\text{Moles of protein}=\frac{\text{Number of molecules of protein}}{\text{Avogadro's number}}`

Number of molecules of protein = 2 molecules

Avogadro's number =
`6.022* 10^(23)molecules/mol`

`\text{Moles of protein}=\frac{2\text{ molecules}}{6.022* 10^(23)molecules/mol}=3.32* 10^(-24)mol`

Now we have to calculate the radius.

Radius =
`(Diameter)/(2)=(1mm)/(2)=0.5mm=5.0* 10^(-4)m`

Conversion used : (1 mm = 0.001 m)

Now we have to calculate the volume.

`V=(4)/(3)\pi r^3`

`V=(4)/(3)* 3.14* (5.0* 10^(-4)m)^3`

`V=5.23* 10^(-10)m^3=5.23* 10^(-7)L`

Conversion used : (1 m³ = 1000 L)

Now we have to calculate the molar concentration.

`Concentration=\frac{\text{Moles of protein}}{\text{Volume}}`

`Concentration=(3.32* 10^(-24)mol)/(5.23* 10^(-7)L)`

`Concentration=6.35* 10^(-18)mol/L`

Thus, the molar concentration is,
`6.35* 10^(-18)mol/L`