Question

) How many cells can be grown in a 5 mL culture using minimal medium before the medium exhausts the carbon?

Answer 1

`5 * 10^(10)`

Step-by-step explanation:

The question is not complete. Remaining part of the question is as follows - Minimal growth medium for bacteria such as E. coli includes various salts with characteristic concentrations in the mM range and a carbon source. The carbon source is typically glucose and it is used at 0.5% (a concentration of 0.5 g/100 mL). For nitrogen, minimal medium contains ammonium chloride (NH4Cl) with a concentration of 0.1 g/100 mL

How many cells can be grown in a 5 mL culture using minimal medium before the medium exhausts the carbon?

Solution -

We will first find the mass concentration of 0.5 g/100 mL of solution.

`(0.5)/(100)` gram per ml of glucose

The chemical formula of glucose is
`C_6H_(12)O_6`

The molecular weight of glucose molecule is
`180` grams per mole

Now, we will find the number of moles of glucose in a 5 ml medium -

`((0.5)/(100) * 5)/(180) \\1.39 * 10^(-4)` mole

The number of carbon atom in each glucose molecule is equal to six, thus, number of minimal carbon mole is equal to

`1.39 * 10^(-4) * 6\\= 8.34* 10^(-4)`mole

Number of carbon atoms is equal to

`8.34* 10^(-4) * 6.023 * 10^(23)\\= 5 * 10^(20)\\` Carbons

One bacteria has
`10^(10)` carbon molecule.Thus,
`5` ml medium will have
`5 * 10^(10)` bacteria