Question

In the chapter, we worked out a general statement of the free energy for two large objects in solution and in the presence of small depletant molecules, which was based upon the osmotic pressure of the molecules and the volume excluded by the objects when at distance $D$. Repeat that derivation leading up to the formula $G(D)=\Pi_{\mathrm{o}} V_{\mathrm{ex}}(D)$ where $\Pi_{\mathrm{o}}=N k_{\mathrm{B}} T / V$ is the osmotic pressure of the depletant molecules. Estimate the force between two beads whose radius is $1 \mu \mathrm{m}$ in a concentrated protein solution, when the concentration is equal to the value characteristic of an $E .$ coli cell. Use $r=3$ nm for the typical radius of a protein.

Name: Problem 5, Chapter 14: Physical Biology of the Cell
Uploaded: 2021-11-24T06:33:23-08:00
Duration: 3 min 20 s
Channel: Sana Riaz

   In the chapter, we worked out a general statement of the free energy for two large objects in solution and in the presence of small depletant molecules, which was based upon the osmotic pressure of the molecules and the volume excluded by the objects when at distance $D$. Repeat that derivation leading up to the formula 
$G(D)=\Pi_{\mathrm{o}} V_{\mathrm{ex}}(D)$
where $\Pi_{\mathrm{o}}=N k_{\mathrm{B}} T / V$ is the osmotic pressure of the depletant molecules. Estimate the force between two beads whose radius is $1 \mu \mathrm{m}$ in a concentrated protein solution, when the concentration is equal to the value characteristic of an $E .$ coli cell. Use $r=3$ nm for the typical radius of a protein.

Physical Biology of the Cell

Rob Phillips, Jane… 2nd Edition

Chapter 14, Problem 5

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Solved by Expert Sana Riaz

11/24/2021

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This is a collective property of solutions that depends only on the concentration of dissolved particles, not on their chemical identity. Show more…

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In the chapter, we worked out a general statement of the free energy for two large objects in solution and in the presence of small depletant molecules, which was based upon the osmotic pressure of the molecules and the volume excluded by the objects when at distance $D$. Repeat that derivation leading up to the formula $G(D)=\Pi_{\mathrm{o}} V_{\mathrm{ex}}(D)$ where $\Pi_{\mathrm{o}}=N k_{\mathrm{B}} T / V$ is the osmotic pressure of the depletant molecules. Estimate the force between two beads whose radius is $1 \mu \mathrm{m}$ in a concentrated protein solution, when the concentration is equal to the value characteristic of an $E .$ coli cell. Use $r=3$ nm for the typical radius of a protein.