Textbook Question
What is the molarity of Br- in each solution? b. 0.150 M CaBr2
6. Chemical Quantities & Aqueous Reactions
Osmolarity
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A 2.26 g sample of a protein of unknown molecular weight was dissolved in enough water to produce 21.3 mL of solution. The solution was found to have an osmotic pressure of 2.45 torr at 25 °C. What is the molecular weight of the protein?
A
100,000 g/mol
B
12,000 g/mol
C
68,000 g/mol
D
45,000 g/mol
Verified step by step guidance1
Start by understanding the concept of osmotic pressure, which is the pressure required to stop the flow of solvent into a solution through a semipermeable membrane. It is related to the concentration of solute particles in the solution.
Use the formula for osmotic pressure: \( \Pi = \frac{nRT}{V} \), where \( \Pi \) is the osmotic pressure, \( n \) is the number of moles of solute, \( R \) is the ideal gas constant, \( T \) is the temperature in Kelvin, and \( V \) is the volume of the solution in liters.
Convert the osmotic pressure from torr to atm, since the ideal gas constant \( R \) is typically used in units of atm·L/mol·K. Use the conversion factor: \( 1 \text{ atm} = 760 \text{ torr} \).
Calculate the temperature in Kelvin by converting from Celsius using the formula: \( T(K) = T(°C) + 273.15 \).
Rearrange the osmotic pressure formula to solve for the number of moles \( n \): \( n = \frac{\Pi V}{RT} \). Then, use the definition of molecular weight \( MW = \frac{\text{mass}}{n} \) to find the molecular weight of the protein, where mass is given as 2.26 g.
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