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Aqueous environment in a spherical endosome—a closed vesicle of 100 nm diameter, is at a pH 5.0, in order to denature and hydrolyze the material internalized by a cell. Assuming Avogadro’s number to be 6 × 1023, the number of free protons in an endosome is closed to
- a)24
- b)3
- c)2400
- d)300
Correct answer is option 'B'. Can you explain this answer?
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Aqueous environment in a spherical endosomea closed vesicle of 100 nm ...
Given:
- Diameter of endosome = 100 nm
- pH of aqueous environment in endosome = 5.0
- Avogadro's number = 6 x 10^23
To Find:
Number of free protons in the endosome
Solution:
To find the number of free protons in the endosome, we need to calculate the concentration of protons in the aqueous environment and then multiply it by the volume of the endosome.
Step 1: Calculate the Concentration of Protons
The pH of a solution is defined as the negative logarithm of the concentration of protons (H+) in moles per liter (M). The formula to calculate the concentration of protons is:
[H+] = 10^(-pH)
Substituting the given pH value of 5.0 into the formula:
[H+] = 10^(-5.0) = 1 x 10^(-5) M
So, the concentration of protons in the aqueous environment of the endosome is 1 x 10^(-5) M.
Step 2: Calculate the Volume of the Endosome
The volume of a sphere can be calculated using the formula:
V = (4/3)πr^3
Where r is the radius of the sphere. Since the diameter of the endosome is given as 100 nm, the radius can be calculated as half of the diameter:
r = 100 nm / 2 = 50 nm = 50 x 10^(-9) m
Substituting the radius into the volume formula:
V = (4/3)π(50 x 10^(-9))^3 = 4.19 x 10^(-22) m^3
Step 3: Calculate the Number of Free Protons
The number of moles can be calculated using the formula:
n = C x V
Where n is the number of moles, C is the concentration in moles per liter, and V is the volume in liters.
Converting the volume from cubic meters to liters:
V = 4.19 x 10^(-22) m^3 x (1 L / 10^3 m^3) = 4.19 x 10^(-25) L
Substituting the values into the formula:
n = (1 x 10^(-5) M) x (4.19 x 10^(-25) L) = 4.19 x 10^(-30) mol
Finally, to calculate the number of free protons, we can multiply the number of moles by Avogadro's number:
Number of free protons = (4.19 x 10^(-30) mol) x (6 x 10^23) ≈ 2.514 x 10^(-6)
Approximating the value to the nearest whole number, the number of free protons in the endosome is approximately 3.
Therefore, the correct answer is option B) 3.
- Diameter of endosome = 100 nm
- pH of aqueous environment in endosome = 5.0
- Avogadro's number = 6 x 10^23
To Find:
Number of free protons in the endosome
Solution:
To find the number of free protons in the endosome, we need to calculate the concentration of protons in the aqueous environment and then multiply it by the volume of the endosome.
Step 1: Calculate the Concentration of Protons
The pH of a solution is defined as the negative logarithm of the concentration of protons (H+) in moles per liter (M). The formula to calculate the concentration of protons is:
[H+] = 10^(-pH)
Substituting the given pH value of 5.0 into the formula:
[H+] = 10^(-5.0) = 1 x 10^(-5) M
So, the concentration of protons in the aqueous environment of the endosome is 1 x 10^(-5) M.
Step 2: Calculate the Volume of the Endosome
The volume of a sphere can be calculated using the formula:
V = (4/3)πr^3
Where r is the radius of the sphere. Since the diameter of the endosome is given as 100 nm, the radius can be calculated as half of the diameter:
r = 100 nm / 2 = 50 nm = 50 x 10^(-9) m
Substituting the radius into the volume formula:
V = (4/3)π(50 x 10^(-9))^3 = 4.19 x 10^(-22) m^3
Step 3: Calculate the Number of Free Protons
The number of moles can be calculated using the formula:
n = C x V
Where n is the number of moles, C is the concentration in moles per liter, and V is the volume in liters.
Converting the volume from cubic meters to liters:
V = 4.19 x 10^(-22) m^3 x (1 L / 10^3 m^3) = 4.19 x 10^(-25) L
Substituting the values into the formula:
n = (1 x 10^(-5) M) x (4.19 x 10^(-25) L) = 4.19 x 10^(-30) mol
Finally, to calculate the number of free protons, we can multiply the number of moles by Avogadro's number:
Number of free protons = (4.19 x 10^(-30) mol) x (6 x 10^23) ≈ 2.514 x 10^(-6)
Approximating the value to the nearest whole number, the number of free protons in the endosome is approximately 3.
Therefore, the correct answer is option B) 3.
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Aqueous environment in a spherical endosomea closed vesicle of 100 nm diameter, is at a pH 5.0, in order to denature and hydrolyze the material internalized by a cell. Assuming Avogadros number to be 6 1023, the number of free protons in an endosome is closed toa)24b)3c)2400d)300Correct answer is option 'B'. Can you explain this answer?
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Solutions for Aqueous environment in a spherical endosomea closed vesicle of 100 nm diameter, is at a pH 5.0, in order to denature and hydrolyze the material internalized by a cell. Assuming Avogadros number to be 6 1023, the number of free protons in an endosome is closed toa)24b)3c)2400d)300Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for IIT JAM.
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