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Answer :
Final answer:
The new molarity of glycerol after the evaporation of the solvent from 913 mL to 11.1 mL is 6.69 × 10^6 µM, calculated using the conservation of moles and by adjusting the concentration for the reduced volume.
Explanation:
The molarity of a solution is defined as the number of moles of solute per liter of solution. When the solvent evaporates from a solution and the volume decreases, the molarity of the solute increases because the same amount of solute is now present in a smaller volume of solvent. The original volume of the photobacterium cell growth medium is 913 mL with a glycerol concentration of 81.3 µM (micro molar). The new volume of the cell growth medium after evaporation is 11.1 mL. To find the new molarity, we can use the concept of conservation of moles of solute, which states that the number of moles in the solution before and after evaporation are the same.
First, we convert the original volume from milliliters to liters:
913 mL = 0.913 L
Then we calculate the moles of glycerol originally in the solution:
moles of glycerol = (81.3 µM) × (0.913 L) = 0.0000813 moles/L × 0.913 L = 7.42449 × [tex]10^{-5}[/tex] moles
Since the amount of glycerol remains the same, and only the volume has changed, we can find the new molarity by dividing the moles of glycerol by the new volume in liters:
New volume in liters: 11.1 mL = 0.0111 L
New molarity = moles of glycerol / new volume
= 7.42449 × [tex]10^{-5}[/tex] moles / 0.0111 L
Performing the calculation gives us:
New molarity = 6.68873 M (rounded to three significant digits). However, this result is not in micro molarity. So to convert this to µM,
1 M = 1,000,000 µM
New molarity in µM = 6.68873 × 1,000,000 µM = 6.69 × 106 µM (or 6,690,000 µM, rounded to three significant digits)
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Answer : The new molarity of glycerol in the photobacterium cell growth medium is, [tex]6.69\times 10^3\mu M[/tex]
Explanation :
Formula used :
[tex]M_1V_1=M_2V_2[/tex]
where,
[tex]M_1\text{ and }V_1[/tex] are the initial molarity and volume of glycerol.
[tex]M_2\text{ and }V_2[/tex] are the new molarity and volume of glycerol .
We are given:
[tex]M_1=81.3\mu M\\V_1=913mL\\M_2=?\\V_2=11.1mL[/tex]
Putting values in above equation, we get:
[tex]81.3\mu M\times 913mL=M_2\times 11.1mL\\\\M_2=6.69\times 10^3\mu M[/tex]
Hence, the new molarity of glycerol in the photobacterium cell growth medium is, [tex]6.69\times 10^3\mu M[/tex]
