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A protein has been isolated as a salt with the formula
Chapter 13, Problem 109AP(choose chapter or problem)
A protein has been isolated as a salt with the formula \(N a_{20} P\)(this notation means that there are 20 \(\mathrm{Na}^{+}\) ions associated with a negatively charged protein \(P^{20-}\)). The osmotic pressure of a 10.0-mL solution containing 0.225 g of the protein is 0.257 atm at 25.0°C. (a) Calculate the molar mass of the protein from these data, (b) Calculate the actual molar mass of the protein.
Questions & Answers
QUESTION:
A protein has been isolated as a salt with the formula \(N a_{20} P\)(this notation means that there are 20 \(\mathrm{Na}^{+}\) ions associated with a negatively charged protein \(P^{20-}\)). The osmotic pressure of a 10.0-mL solution containing 0.225 g of the protein is 0.257 atm at 25.0°C. (a) Calculate the molar mass of the protein from these data, (b) Calculate the actual molar mass of the protein.
ANSWER:
Step 1 of 2
a.
The expression for the calculation of osmotic pressure is as follows.
Here, M is the molarity, R is the gas constant, T is the temperature and 
pressure.
Rewrite equation (1) to calculate the molarity as follows:
From the given,
The osmotic pressure = 0.257 atm
Gas constant = 0.0821L.atm/mol-K
Temperature = 298 K
Substitute these values in equation (2) as follows:
= 0.0105 mol/L
Use molarity, moles and volume to calculate the molar mass as follows:
The molarity is 0.0105 mol / L, the mass of protein is 0.225 g and the volume of the solution is 10.0 mL . So using these values, calculate the molar mass of the protein as follows:
Therefore, the molar mass of the protein is
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