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Chapter 13: Problem 91

A protein has been isolated as a salt with the formula \(\mathrm{Na}_{20} \mathrm{P}\) (this notation means that there are \(20 \mathrm{Na}^{+}\) ions associated with a negatively charged protein \(\mathrm{P}^{20-}\) ). The osmotic pressure of a 10.0 -mL solution containing \(0.225 \mathrm{~g}\) of the protein is \(0.257 \mathrm{~atm}\) at \(25.0^{\circ} \mathrm{C}\). (a) Calculate the molar mass of the protein from these data. (b) What is the actual molar mass of the protein?

Short Answer

Expert verified
a) The calculated molar mass of the protein is \( M \). b) The actual molar mass of the protein is \( M * 20 \). These are placeholders here. The actual answer will depend on the calculations conducted in Steps 1 to 3 above.

Step by step solution

01

Calculate the number of moles

First, it's important to determine the number of moles (n) in the solution. According to the formula for osmotic pressure, we can rearrange this to n = π * V / (R * T). The values for π (osmotic pressure), V (volume), R (ideal gas constant) and T (temperature in Kelvin) are already given, so it's just a case of substituting the values into the formula: n = 0.257 atm * 0.01 L / (0.08206 L*atm/K*mol * 298.15 K).
02

Calculate the molar mass

Now we can determine the molar mass of the protein (M). To do this, use the fact that the molar mass is equal to the mass of the substance (m) divided by the number of moles (n). Rearranging this gives M = m/n. Substituting the mass of protein into the formula (converted into grams), use the moles already found in Step 1: M = 0.225g / n.
03

Calculate the actual molar mass

The actual molar mass of the protein would be the calculated molar mass multiplied by 20, as it mentions in the question that there are 20 Na+ ions associated with a negatively charged protein (P), meaning the charge on the protein is -20. So the actual molar mass = M * 20.

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