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Let us consider a bacterial cell that depends on chemical reactions using oxygen to produce energy. The cell needs to obtain molecular oxygen from the extra-cellular medium by diffusion through the cell membrane. We model the cell as a water-filled sphere of radius 1 um. This means that we neglect the presence of the internal structures of the cell: nucleus, nutrients, etc. The oxygen diffusion coefficient (O2) in water at 25°C is 1.0x10-5 cm².s'. Figure 1: Transmission electron microscope Reminder: The distance travelled by diffusion can be picture of a bacterium. [from Wikipedia: "Transmission Electron Microscopy"| written as L(t) = V6Dt, where D is the diffusion coefficient and t the diffusion time. People have measured the distance travelled by the oxygen molecule in water as a function of time. The results are given in the table below. | 0.1 25.5 | t(s) L (x10“m) logi0(1) logio(L) 0.001 2.45 0.005 0.01 7.7 0.05 5.4 17.3 3. Determination of the diffusion coefficient We would like to determine the diffusion coefficient of oxygen in water. To this effect we will plot the decimal logarithm of the distance travelled as a function of the decimal logarithm of time. Copy the table above on your answer sheet and complete the last two lines. • Draw the graph of log10(L) as a function of log10(t). What do you notice ? Using the diffusion equation, L(t) = \6Dt, show that the relationship between log10(L) and log10(t) is linear. Deduce the value of the slope of this linear relationship and its constant term.

Let us consider a bacterial cell that depends on chemical reactions using oxygen to produce energy. The cell needs to obtain molecular oxygen from the extra-cellular medium by diffusion through the cell membrane. We model the cell as a water-filled sphere of radius 1 um. This means that we neglect the presence of the internal structures of the cell: nucleus, nutrients, etc. The oxygen diffusion coefficient (O2) in water at 25°C is 1.0x10-5 cm².s'. Figure 1: Transmission electron microscope Reminder: The distance travelled by diffusion can be picture of a bacterium. [from Wikipedia: "Transmission Electron Microscopy"| written as L(t) = V6Dt, where D is the diffusion coefficient and t the diffusion time. People have measured the distance travelled by the oxygen molecule in water as a function of time. The results are given in the table below. | 0.1 25.5 | t(s) L (x10“m) logi0(1) logio(L) 0.001 2.45 0.005 0.01 7.7 0.05 5.4 17.3 3. Determination of the diffusion coefficient We would like to determine the diffusion coefficient of oxygen in water. To this effect we will plot the decimal logarithm of the distance travelled as a function of the decimal logarithm of time. Copy the table above on your answer sheet and complete the last two lines. • Draw the graph of log10(L) as a function of log10(t). What do you notice ? Using the diffusion equation, L(t) = \6Dt, show that the relationship between log10(L) and log10(t) is linear. Deduce the value of the slope of this linear relationship and its constant term.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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Let us consider a bacterial cell that depends on chemical reactions using oxygen to produce energy. The cell needs to obtain molecular oxygen from the extra-cellular medium by diffusion through the cell membrane. We model the cell as a water-filled sphere of radius 1 µm. This means that we neglect the presence of the internal structures of the cell: nucleus, nutrients, etc. The oxygen diffusion coefficient (O2) in water at 25°C is 1.0x10-5 cm².s'. Figure 1: Transmission electron microscope Reminder: The distance travelled by diffusion can be picture of a bacterium. [from Wikipedia: written as L(t) = v6Dt, where D is the diffusion “Transmission Electron Microscopy"] coefficient and t the diffusion time. People have measured the distance travelled by the oxygen molecule in water as a function of time. The results are given in the table below. 0.05 17.3 0.001 t(s) L (x10“m) log1o(t) log10(L) 0.005 0.01 0.1 2.45 5.4 7.7 25.5 3. Determination of the diffusion coefficient We would like to determine the diffusion coefficient of oxygen in water. To this effect we will plot the decimal logarithm of the distance travelled as a function of the decimal logarithm of time. • Copy the table above on your answer sheet and complete the last two lines. Draw the graph of log10(L) as a function of log10(t). What do you notice ? Using the diffusion equation, L(t) = V6Dt, show that the relationship between log10(L) and log1o(t) is linear. Deduce the value of the slope of this linear relationship and its constant term.
Transcribed Image Text:Let us consider a bacterial cell that depends on chemical reactions using oxygen to produce energy. The cell needs to obtain molecular oxygen from the extra-cellular medium by diffusion through the cell membrane. We model the cell as a water-filled sphere of radius 1 µm. This means that we neglect the presence of the internal structures of the cell: nucleus, nutrients, etc. The oxygen diffusion coefficient (O2) in water at 25°C is 1.0x10-5 cm².s'. Figure 1: Transmission electron microscope Reminder: The distance travelled by diffusion can be picture of a bacterium. [from Wikipedia: written as L(t) = v6Dt, where D is the diffusion “Transmission Electron Microscopy"] coefficient and t the diffusion time. People have measured the distance travelled by the oxygen molecule in water as a function of time. The results are given in the table below. 0.05 17.3 0.001 t(s) L (x10“m) log1o(t) log10(L) 0.005 0.01 0.1 2.45 5.4 7.7 25.5 3. Determination of the diffusion coefficient We would like to determine the diffusion coefficient of oxygen in water. To this effect we will plot the decimal logarithm of the distance travelled as a function of the decimal logarithm of time. • Copy the table above on your answer sheet and complete the last two lines. Draw the graph of log10(L) as a function of log10(t). What do you notice ? Using the diffusion equation, L(t) = V6Dt, show that the relationship between log10(L) and log1o(t) is linear. Deduce the value of the slope of this linear relationship and its constant term.
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