Question

Osmosis Through a Cell Membrane A cell constantly gains or loses small molecules to its environment because the small molecules are able to diffuse through the cell membrane. We will build a model for this process. Suppose a molecule is present in the cell at a concentration C(t), and present in its environment at a concentration C_(infty ) (you may assume C_(infty ) is a constant). One model for the diffusion of molecules across the cell membrane is that the rate at which molecules travel through the membrane is proportional to the difference in concentration between the cell and its surroundings. That is: Rate at which molecules flow out =k(C-C_(infty )) of cell The constant k is known as the permeability of the membrane; k>0, and k depends on the surface area of the cell and the chemistry of the membrane, as well as the type of molecule. a. Starting with a word equation for the amount of small molecules in the cell, show, if the cell volume is V, then: (dC)/(dt)=-(k)/(V)(C-C_(infty )) b. Find the equilibrium of (8.53) and use a graphical analysis to determine whether it is stable or unstable. c. Suppose that the molecule we are studying is produced within the cell. The cell produces the molecule at a rate r; that is, a quantity r is produced (added to the cell) in unit time. Explain why the differential equation for the concentration of molecules in the cell should be modified to: (dC)/(dt)=-(k)/(V)(C-C_(infty ))+(r)/(V) d. Analyze Equation (8.54) to find the equilibrium value of the cell concentration. Is this equilibrium stable or unstable? You may use a graphical argument or calculate the eigenvalue to determine the equilibrium's stability. 5.Osmosis Through a Cell Membrane A cell constantly gains or loses small molecules to its environment because the small molecules are able to diffuse through the cell membrane.We will build a model for this process. Suppose a molecule is present in the cell at a concentration C(t), and present in its environment at a concentration C..you may assume C.. is a proportional to the difference in concentration between the cell and its surroundings.That is: Rate at which molecules flow out = k(C - C) of cell The constant k is known as the permeability of the membrane;k >0,and k depends on the surface area of the cell and the chemistry of the membrane,as well as the type of molecule a. Starting with a word equation for the amount of small molecules in the cell, show, if the cell volume is V, then: dC dt C -C) (8.53) b. Find the equilibrium of (8.53) and use a graphical analysis to determine whether it is stable or unstable C. Suppose that the molecule we are studying is produced within the cell.The cell produces the molecule at a rate r; that is,a quantity r is produced (added to the cell) in unit time.Explain why the differential equation for the concentration of molecules in the cell should be modified to: dC C-C)+ (8.54) at d.Analyze Equation (8.54 to find the equilibrium value of the cell concentration.Is this eguilibrium stable or unstable? You may use a graphical argument or calculate the eigenvalue to determine the equilibrium's stability.

Name: osmosis through a cell membrane a cell constantly gains or loses small molecules to its environment because the small molecules are able to diffuse through the cell membrane we will build a 50364
Uploaded: 2023-12-09T21:05:58-08:00
Duration: 1 min 59 s
Channel: Supreeta N
Description: osmosis through a cell membrane a cell constantly gains or loses small molecules to its environment because the small molecules are able to diffuse through the cell membrane we will build a 50364

          Osmosis Through a Cell Membrane A cell constantly gains or loses small molecules to its environment because the small molecules are able to
diffuse through the cell membrane. We will build a model for this process.
Suppose a molecule is present in the cell at a concentration C(t), and present in its environment at a concentration C_(infty ) (you may assume C_(infty ) is a
constant). One model for the diffusion of molecules across the cell membrane is that the rate at which molecules travel through the membrane is
proportional to the difference in concentration between the cell and its surroundings. That is:
Rate at which
molecules flow out =k(C-C_(infty ))
of cell
The constant k is known as the permeability of the membrane; k>0, and k depends on the surface area of the cell and the chemistry of the
membrane, as well as the type of molecule.
a. Starting with a word equation for the amount of small molecules in the cell, show, if the cell volume is V, then:
(dC)/(dt)=-(k)/(V)(C-C_(infty ))
b. Find the equilibrium of (8.53) and use a graphical analysis to determine whether it is stable or unstable.
c. Suppose that the molecule we are studying is produced within the cell. The cell produces the molecule at a rate r; that is, a quantity r
is produced (added to the cell) in unit time. Explain why the differential equation for the concentration of molecules in the cell should be
modified to:
(dC)/(dt)=-(k)/(V)(C-C_(infty ))+(r)/(V)
d. Analyze Equation (8.54) to find the equilibrium value of the cell concentration. Is this equilibrium stable or unstable? You may use a
graphical argument or calculate the eigenvalue to determine the equilibrium's stability.
5.Osmosis Through a Cell Membrane A cell constantly gains or loses small molecules to its environment because the small molecules are able to
diffuse through the cell membrane.We will build a model for this process.
Suppose a molecule is present in the cell at a concentration C(t), and present in its environment at a concentration C..you may assume C.. is a
proportional to the difference in concentration between the cell and its surroundings.That is:
Rate at which
molecules flow out = k(C - C) of cell
The constant k is known as the permeability of the membrane;k >0,and k depends on the surface area of the cell and the chemistry of the
membrane,as well as the type of molecule
a.
Starting with a word equation for the amount of small molecules in the cell, show, if the cell volume is V, then:
dC dt
C -C)
(8.53)
b.
Find the equilibrium of (8.53) and use a graphical analysis to determine whether it is stable or unstable
C.
Suppose that the molecule we are studying is produced within the cell.The cell produces the molecule at a rate r; that is,a quantity r is produced (added to the cell) in unit time.Explain why the differential equation for the concentration of molecules in the cell should be
modified to:
dC
C-C)+
(8.54)
at
d.Analyze Equation (8.54 to find the equilibrium value of the cell concentration.Is this eguilibrium stable or unstable? You may use a graphical argument or calculate the eigenvalue to determine the equilibrium's stability.

osmosis through a cell membrane a cell constantly gains or loses small molecules to its environment because the small molecules are able to diffuse through the cell membrane we will build a 50364

Added by Anthony S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Supreeta N

12/09/2023

Step 1

Step 1: Starting with a word equation for the amount of small molecules in the cell, we can write: Rate of change of molecules in the cell = Rate at which molecules flow in - Rate at which molecules flow out This can be represented as: (dC)/(dt) = k(C_(\infty ) - Show more…

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Osmosis Through a Cell Membrane A cell constantly gains or loses small molecules to its environment because the small molecules are able to diffuse through the cell membrane. We will build a model for this process. Suppose a molecule is present in the cell at a concentration C(t), and present in its environment at a concentration C_(infty ) (you may assume C_(infty ) is a constant). One model for the diffusion of molecules across the cell membrane is that the rate at which molecules travel through the membrane is proportional to the difference in concentration between the cell and its surroundings. That is: Rate at which molecules flow out =k(C-C_(infty )) of cell The constant k is known as the permeability of the membrane; k>0, and k depends on the surface area of the cell and the chemistry of the membrane, as well as the type of molecule. a. Starting with a word equation for the amount of small molecules in the cell, show, if the cell volume is V, then: (dC)/(dt)=-(k)/(V)(C-C_(infty )) b. Find the equilibrium of (8.53) and use a graphical analysis to determine whether it is stable or unstable. c. Suppose that the molecule we are studying is produced within the cell. The cell produces the molecule at a rate r; that is, a quantity r is produced (added to the cell) in unit time. Explain why the differential equation for the concentration of molecules in the cell should be modified to: (dC)/(dt)=-(k)/(V)(C-C_(infty ))+(r)/(V) d. Analyze Equation (8.54) to find the equilibrium value of the cell concentration. Is this equilibrium stable or unstable? You may use a graphical argument or calculate the eigenvalue to determine the equilibrium's stability. 5.Osmosis Through a Cell Membrane A cell constantly gains or loses small molecules to its environment because the small molecules are able to diffuse through the cell membrane.We will build a model for this process. Suppose a molecule is present in the cell at a concentration C(t), and present in its environment at a concentration C..you may assume C.. is a proportional to the difference in concentration between the cell and its surroundings.That is: Rate at which molecules flow out = k(C - C) of cell The constant k is known as the permeability of the membrane;k >0,and k depends on the surface area of the cell and the chemistry of the membrane,as well as the type of molecule a. Starting with a word equation for the amount of small molecules in the cell, show, if the cell volume is V, then: dC dt C -C) (8.53) b. Find the equilibrium of (8.53) and use a graphical analysis to determine whether it is stable or unstable C. Suppose that the molecule we are studying is produced within the cell.The cell produces the molecule at a rate r; that is,a quantity r is produced (added to the cell) in unit time.Explain why the differential equation for the concentration of molecules in the cell should be modified to: dC C-C)+ (8.54) at d.Analyze Equation (8.54 to find the equilibrium value of the cell concentration.Is this eguilibrium stable or unstable? You may use a graphical argument or calculate the eigenvalue to determine the equilibrium's stability.