A mammalian cell nucleus contains 4.0 x 10 ^ 3 molecules of protein X (molecular weight...

A mammalian cell nucleus contains 4.0 x 10 ^ 3 molecules of protein X (molecular weight 6.0 x 10 ^4). Assume the nucleus is a sphere with diameter of 5.0 microns. Calculate the following: A) the molarity of protein X in the nucleus B) the mass (in grams) of protein X in one nucleus. Please show work.

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Expert Solution

A) The diameter of the spherical cell is 5.0 µ 5.0 µm = (5.0 µ)*(1 m/10⁶ µm)*(100 cm/1 m) = 5.0*10^-4 cm; therefore, radius of the sphere is r = ½*(5.0*10^-4 cm) = 2.5*10^-4 cm.

Volume of the spherical cell is V = 4/3*π*r³ = 4/3*(3.14)*(2.5*10^-4 cm)³ = 6.54167*10^-11 cm³ = (6.54167*10^-11 cm³)*(1 mL/1 cm³) = 6.54167*10^-11 mL = (6.54167*10^-11 mL)*(1 L/1000 mL) = 6.54167*10^-14 L.

Next, find the number of moles of protein X in the nucleus. We know that 1 mole of any substance = 6.023*10²³ molecules of that substance.

Therefore, moles of protein X = (4.0*10³ molecules)*(1 mole/6.023*10²³ molecules) = 6.64121*10^-21 mole.

Molar concentration of protein X = (moles of protein X)/(volume of cell) = (6.64121*10^-21 mole)/(6.54167*10^-14 L) = 1.0152*10^-7 mol/L = (1.0152*10^-7 mol/L)*(10⁶ µmol/1 mol) = 0.10152 µM (1 mol/L = 1 M) (ans).

B) We have 6.64121*10^-21 mole of protein X; the molecular mass of protein X = (6.64121*10^-21 mol)*(6.0*10⁴ g/mol) = 3.984726*10^-16 g ≈ 3.98*10^-16 g (ans).

queen_honey_blossom answered 1 year ago

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