Volume Calculation Example A lysosome is a membrane bound organelle found in man
ID: 186276 • Letter: V
Question
Volume Calculation Example A lysosome is a membrane bound organelle found in many eukaryotic cells. It contains digestive enzymes that break down cellular macromolecules into their composite monomers so they can be recycled. Given a lysosome having a diameter of 0.5 m, answer the following questions. Show your work to get credit, um, g questions. Show vour work to get crr NOTE: a) Assume the lysosome is spherical and calculate its volume in me. Always convert measures of length into cm first. Then the volume calculat generate a unit of volume equal to cm3, which is me. r = d/2 = (0.5 X 10-6 m) / 2 = (2.5 X 10-7 m) X (100 cm/ m) = 2.5 X 10-5 cm -4/3m" = 4/3m(2.5 X 10-5 cm)3 = 6.54 X 10-14 cm2 = 6.54 X 10-14 ml To correct # sig, figs. 7 X 10-14 ml (Round to sig, figs. LAST) b) The enzymes in the lysosome are activated when protons are transported into the lysosome and the pH drops to pH 4. How many protons are in the lysosome at this pH? pH =-log[H+] = 4, so [H+] = 1 X 10-4 M = 1 X 10-4 moles H+ 11 (1 X 10-4 moles / ) X (6.02 X 1023 molecules/mole) = 6.02 X 1019 H+ / 1 (6.02 X 1019 H+ /) X (6.54 X 10-14 m) X (1 1 / 1 000 ml)-3925 To correct sig. figs. = 4000 H+Explanation / Answer
4) Lysosome is a membrane-bound organelle present in eukaryotes that break down cellular macromolecules into smaller particles.
a) As the question says, lysosome is spherical.
Volume of a sphere = 4/3(r3)
where value of = 3.14
and r is the radius of a sphere
Diameter of the sphere is given as 0.5 m
Radius is half of the diameter
So, r = d/2 = 0.5/2 = 0.25 m
In order to calculate volume in ml, we have to convert m (micrometer) into m (meter) and then to cm
We know that, 1 m = 1000000 m or 106m
which means 1 m = 10-6 m
Therefore, 0.25 m = 0.25 x 10-6 m = 2.5 x 10-7 m
We know that 1m = 100 cm
so, 2.5 x 10-7 m = 2.5 x 10-7 x 100 = 2.5 x 10-5 cm
Now we obtained the value of radius in cm.
Calculating the volume using the equation
V = 4/3(r3)
we get
V = 4/3()(2.5 x 10-5)3
= 4/3(3.14)(15.625 x 10-15)
= 4/3(53.125 x 10-15)
= (215.5 x 10-15)/3
= 70.83 x 10-15
= 7.083 x 10-14
which can be rounded to 7 x 10-14
Hence, the volume of lysosome is 7 x 10-14 ml.
b) According to the question, pH of the lysosome drops to 4, when protons are transported into it.
pH of a solution is calculated by
pH = -log [H+]
where [H+] is the hydrogen ion concentration.
In order to calculate the number of protons, first we should know the value of concentration of protons.
Here, pH = 4, hence from the equation above, we can calculate [H+]
pH = -log [H+]
4 = -log [H+]
So, [H+] = Antilog (-4)
= 1 x 10-4 M
Molarity is defined as the number of moles of solute per liter of the solution.
So, this means that there are 1 x 10-4 moles of H+ per liter of the solution.
This can be expressed as 1 x 10-4 moles of H+/l.
Amount of a substance is expressed in moles.
A mole can be defined as the amount of a substance that contain as many constitutive particles as there are in 12 grams of carbon-12.
This number is expressed by Avogadro constant. It is the number of constituent particles that are contained in the amount of substance given by a mole.
Value of Avogadro constant according to SI unit is
6.02 x 1023 molecules/mole.
Calculating the number of H+ in 1 x 10-4 moles/l, we get
No: of protons = 1 x 10-4 moles/l x 6.02 x 1023 molecules/mole
= 6.02 x 1019
Now we need to calculate the number of protons contained in 7 x 10-14 ml of lysosome.
As we calculated earlier, volume of lysosome is 7 x 10-14 ml
We need to convert this to liter (l).
1 l = 1000 ml
i.e, 1ml = 1/1000 l
So, 7 x 10-14 ml = (7 x 10-14)/1000 = 7 x 10-17 l
Number of protons contained in 7 x 10-17 l = (6.02 x 1019) x (7 x 10-17)
= 42.14 x 102 = 4214
which can be rounded to 4000.
Therefore, the number of protons contained in lysosome at pH 4 is 4000 H+.
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