Answer to Question #148294 in General Chemistry for kim

Question

An E. coli cell has ~72,000 ribosomes at 37'C. How many ribosomes are in a single 10 microLitres E. coli cell-free reaction in a test-tube?

Use the following numbers and show calculations:
(approximations are permitted, e.g. Naa = 6e23)

• Total protein concentration = 10 mg/mL
• Ribosomal fraction of total protein concentration = 1/3
• Molecular weight of E. coli ribosome = 2.7 MDa
• Avogadro constant = 6.02214086 × 1023 mol-1

Answer 1

no. of ribosomes in 1 E. Coli cell = 72,000

no. of ribosomes in 10mL of E. Coli = ?

Total protein concentration = 10mg/mL =

10mg of Protein in 1mL of E. Coli

Ribosome

Ribosomal fraction of protein concentration = 1/3 of protein concentration

Therefore, ribosomal concentration = 3.3mg/mL

This means that 3.3mg of ribosomes are in 1mL of E. Coli.

In 10mL of E.Coli, there are 33mg of ribosomes.

Molecular weight of ribosome = 2.7MDa = 2.7 × 10⁶ amu = 2,700,000amu

Therefore, 1 mol of ribosomes = 2,700,000g

6.022 × 10²³ molecules = 2,700,000g

x = 0.033 g

x = 0.033×6.022×10^23/2,700,000 = 7.36 × 10¹⁵ molecules

Therefore, there are 7.36 × 10¹⁵ ribosomes in 10 microLitres E. coli.