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What is the molar mass of a protein if a 0. 30 l of solution containing 0. 45 g of the protein has an osmotic pressure of 0. 80 torr at 25∘c?

Sagot :

The molar mass of a protein if a 0. 30 l of solution containing 0. 45 g of the protein has an osmotic pressure of 0. 80 torr at 25∘c is 0.348 g/mol

Here we can apply the formula ∏ = iMRT, where ∏ = osmotic pressure = 0.80 - ( given ). This is only one part of the information we are given / can conclude in this case ....

i = van’t Hoff factor = 1 for a protein molecule,

R = gas constant = 62.36 L torr / K-mol,

T ( temperature in Kelvin ) = 25 + 273 - conversion factor C° + 273 = 298K

( Known initially ) ∏ = osmotic pressure = 0.80 torr

besides the part " M " in the formula, which we have no information on whatsoever, as we have to determine it's value.

_____

Substitute derived / known values to solve for M ( moles / liter ) -

∏ = iMRT

⇒ 0.80 = ( 1 )( M )( 62.36 )( 298 )

⇒ 0.80 = M( 18583.28 )

⇒ M = 0.80 / 18583.28 ≈ 4.3049 ....

_____

We know that M = moles / liter, so we can use this to solve for moles, and hence calculate the molar mass by the formula molar mass = g / mol -

M = mol / l

⇒ 4.3049 = 0.045 / 25 mL ( 0.030 L ),

0.045 / 0.030 = 1.5 g / L

⇒ 1.5 g = 4.3049 moles,

molar mass = 1.5 g = 4.3049 moles = 0.348 g / mol

Thus the concluded that the molar mass of protein is 0.348 g / mol.

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