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P5B.7 The molar mass of a protein was determined by dissolving it in water, and measuring the height, h, of the resulting solution drawn up a capillary tube at 20°C. The following data were obtained. c/(mg cm) 3.221 4.618 5.112 6.722 h/cm 5.746 8.238 9.119 11.990

P5B.7 The molar mass of a protein was determined by dissolving it in water, and measuring the height, h, of the resulting solution drawn up a capillary tube at 20°C. The following data were obtained. c/(mg cm) 3.221 4.618 5.112 6.722 h/cm 5.746 8.238 9.119 11.990

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ISBN:9781305957404
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Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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**PSB.7: Determination of Molar Mass of a Protein** To determine the molar mass of a protein, it was dissolved in water and the height, \( h \), of the resulting solution drawn up a capillary tube at 20°C was measured. Below is the data obtained from the experiment: | \( c \)/(\( \text{mg cm}^{-3} \)) | Height, \( h \)/(cm) | |-------------------------------|----------------------| | 3.221 | 5.746 | | 4.618 | 8.238 | | 5.112 | 9.119 | | 6.722 | 11.990 | Each row in the table represents a different concentration of the protein solution and the corresponding height to which the solution rises in the capillary tube. The variables \( c \) and \( h \) denote concentration and height respectively. The experiment was conducted at a constant temperature of 20°C.
Transcribed Image Text:**PSB.7: Determination of Molar Mass of a Protein** To determine the molar mass of a protein, it was dissolved in water and the height, \( h \), of the resulting solution drawn up a capillary tube at 20°C was measured. Below is the data obtained from the experiment: | \( c \)/(\( \text{mg cm}^{-3} \)) | Height, \( h \)/(cm) | |-------------------------------|----------------------| | 3.221 | 5.746 | | 4.618 | 8.238 | | 5.112 | 9.119 | | 6.722 | 11.990 | Each row in the table represents a different concentration of the protein solution and the corresponding height to which the solution rises in the capillary tube. The variables \( c \) and \( h \) denote concentration and height respectively. The experiment was conducted at a constant temperature of 20°C.
### Understanding Osmotic Pressure and Calculating Molar Mass of a Protein **Osmotic Pressure Calculation:** The osmotic pressure (\(\Pi\)) of a solution can be determined using the height (h) of the column it creates, based on the following formula: \[ \Pi = h \rho g \] where: - \(h\) is the height of the column. - \(\rho\) (rho) is the mass density of the solution. - \(g\) is the acceleration due to gravity. **Given Data:** - The mass density of the solution (\(\rho\)) is \(1.000 \, \text{g} \, \text{cm}^{-3}\). - The acceleration due to gravity (\(g\)) is \(9.81 \, \text{m} \, \text{s}^{-2}\). **Objective:** Determine the molar mass of the protein using the above parameters. **Explanation of Terms:** - **Osmotic Pressure (\(\Pi\))**: The pressure required to stop the flow of solvent molecules through a semipermeable membrane that separates a solution from pure solvent. - **Height (h)**: The vertical distance measured in the column of solution. - **Mass Density (\(\rho\))**: The mass of the substance per unit volume. - **Acceleration due to Gravity (g)**: The rate at which an object accelerates due to the Earth's gravitational pull. ### Steps to Determine Molar Mass: 1. Measure the height \(h\) of the column created by the solution. 2. Insert the given values into the formula to calculate the osmotic pressure (\(\Pi\)). 3. Use the calculated osmotic pressure, along with the van 't Hoff equation for osmotic pressure, to determine the molar mass of the protein. This method provides a practical approach to understanding osmotic pressure and its applications in determining the properties of solutes, such as proteins, in a solution.
Transcribed Image Text:### Understanding Osmotic Pressure and Calculating Molar Mass of a Protein **Osmotic Pressure Calculation:** The osmotic pressure (\(\Pi\)) of a solution can be determined using the height (h) of the column it creates, based on the following formula: \[ \Pi = h \rho g \] where: - \(h\) is the height of the column. - \(\rho\) (rho) is the mass density of the solution. - \(g\) is the acceleration due to gravity. **Given Data:** - The mass density of the solution (\(\rho\)) is \(1.000 \, \text{g} \, \text{cm}^{-3}\). - The acceleration due to gravity (\(g\)) is \(9.81 \, \text{m} \, \text{s}^{-2}\). **Objective:** Determine the molar mass of the protein using the above parameters. **Explanation of Terms:** - **Osmotic Pressure (\(\Pi\))**: The pressure required to stop the flow of solvent molecules through a semipermeable membrane that separates a solution from pure solvent. - **Height (h)**: The vertical distance measured in the column of solution. - **Mass Density (\(\rho\))**: The mass of the substance per unit volume. - **Acceleration due to Gravity (g)**: The rate at which an object accelerates due to the Earth's gravitational pull. ### Steps to Determine Molar Mass: 1. Measure the height \(h\) of the column created by the solution. 2. Insert the given values into the formula to calculate the osmotic pressure (\(\Pi\)). 3. Use the calculated osmotic pressure, along with the van 't Hoff equation for osmotic pressure, to determine the molar mass of the protein. This method provides a practical approach to understanding osmotic pressure and its applications in determining the properties of solutes, such as proteins, in a solution.
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