Lysine is an amino acid that is an essential part of nutrition but which is not synthesized by the human body. What is the molar mass of lysine if 750.0 mL of a solution containing 8.60 g of lysine has an osmotic pressure of 1.918 atm? Temperature = 25.0$\degree$C
A) 110. g/mol
B) 146 g/mol
C) 220. g/mol
D) 1340 g/mol
E) 1780 g/mol

Question

Quizplus · Accepted Answer

First, we need to convert the volume of the solution to liters:
750.0 mL = 0.750 L

Next, we need to calculate the molarity of the lysine solution:
Molarity = moles of solute / liters of solution

We can find moles of lysine using its mass and its molar mass:
moles of lysine = mass of lysine / molar mass of lysine
mass of lysine = 8.60 g
molar mass of lysine = 2(14.01 g/mol) + 2(12.01 g/mol) + 4(1.01 g/mol) + 1(2.02 g/mol) + 1(4.04 g/mol) = 146.19 g/mol

moles of lysine = 8.60 g / 146.19 g/mol = 0.0588 mol

Now we can calculate the molarity:
Molarity = 0.0588 mol / 0.750 L = 0.0784 M

Finally, we can use the van't Hoff factor (i = 1 for lysine) and the formula for osmotic pressure to find the molar mass of lysine:
π = iMRT
π = 1.918 atm
R = 0.0821 L·atm/mol·K (gas constant)
T = 25.0°C = 298 K (temperature)

Rearranging the formula and solving for molar mass:
M = π / iRT = (1.918 atm) / (1 mol/L)(0.0821 L·atm/mol·K)(298 K) = 146 g/mol

Therefore, the molar mass of lysine is 146 g/mol.

Lysine Is an Amino Acid That Is an Essential Part °\degree°

Lysine Is an Amino Acid That Is an Essential Part $\degree$