Respuesta :
Answer:
a) 36,051.81 g/mol is the molar mass of the protein.
b) The actual molar mass of the protein is 757,087.96 g/mol.
Explanation:
Osmotic pressure of the solution = [tex]\pi = 0.295 atm[/tex]
Temperature of the solution , T= 25.0°C=25.0+273 K=298 K
Concentration of solution = C
van't Hoff factor = 20 +1 = 21
[tex]\pi =iCRT[/tex]
[tex]C=\frac{\pi }{iRT}=\frac{0.295 atm}{21\times 0.0821 atm L/mol K\times 298 K}[/tex]
[tex]C=0.0005742 M[/tex]
Moles of protein = n
Volume of solution = V = 10.0 mL = 0.010 L
[tex]C=\frac{n}{V(L)}[/tex]
[tex]n=0.0005742 M\times 0.010 L=5.742\times 10^{-6}mol[/tex]
Mass of protein = 0.207 g
Molar mass of protein = M
Moles of protein(n) = [tex]\frac{0.207 g}{M}[/tex]
[tex]M=\frac{0.207 g}{5.742\times 10^{-6}mol}=36,051.81 g/mol[/tex]
36,051.81 g/mol is the molar mass of the protein.
b)
Actual molar mass of protein = M'
van't hoff factor = 21
[tex]i=\frac{M'}{M}[/tex]
[tex]M'=21\times 36,051.81 g/mol=757,087.96 g/mol[/tex]
The actual molar mass of the protein is 757,087.96 g/mol.
A) The molar mass of the protein from these data is; 1725 g/mol
B) The actual molar mass of the protein is; 36225 g/mol
Molar Mass Calculations
We are given;
- Osmotic pressure; π = 0.295 atm
- Mass of protein = 0.207 g
- Volume of solution = 10.0 mL = 0.01 L
- Temperature = 25.0 °C = 298.15 K
A) Formula for osmotic pressure is;
π = MRT
Where;
π is osmotic pressure
M is the molarity
R is the gas constant = 0.08206 L.atm/k/mol
T is the temperature.
Thus;
M = π/RT
M = 0.295/(0.08206 * 298.15)
M = 0.012 M
Molar mass = mass/(molarity * volume)
Molar mass = 0.207/(0.012 * 0.01)
Molar mass = 1725 g/mol
B) Since we are given 20 sodium ions, then Van't Hoff factor will be; i = 20 + 1 = 21
Formula for i is;
i = actual molar mass/observed molar mass
actual molar mass = 21 * 1725
Actual molar mass = 36225 g/mol
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