# Question cf7fe

Sep 14, 2017

WARNING! Very long answer! The osmolarity of the solution is 0,640 Osmol/L.

#### Explanation:

An osmole (Osmol) is 1 mol of particles that contribute to the osmotic pressure of a solution.

For example

$\text{CaCl"_2"(s)" → "Ca"^"2+""(aq)" + "2Cl"^"-""(aq)}$
$\textcolor{w h i t e}{l l} \text{1 mol"color(white)(mmmll)"1 mol"color(white)(mmm)"2 mol}$

Thus,

$\text{1 mol CaCl"_2 ≡ "3 Osmol}$

Tris osmoles

Tris is 2-amino-2-(hydroxymethyl)propane-1,3-diol.

Its formula is ("HOCH"_2)_3"C-NH"_2, and its molar mass is 121,13 g/mol.

$\text{Tris osmoles" = "3,87" color(red)(cancel(color(black)("g"))) × {1 color(red)(cancel(color(black)("mol"))))/("121,13" color(red)(cancel(color(black)("g")))) × "1 Osmol"/(1 color(red)(cancel(color(black)("mol")))) = "0,031 95 Osmol}$

Citric acid osmoles

The formula of citric acid is "HOC(COOH)"("CH"_2"COOH")_2, and its molar mass is 192,12 g/mol.

$\text{Citric acid osmoles" = "2,17" color(red)(cancel(color(black)("g"))) × (1 color(red)(cancel(color(black)("mol"))))/("192,12" color(red)(cancel(color(black)("g")))) × "1 Osmol"/(1 color(red)(cancel(color(black)("mol")))) = "0,011 30 Osmol/L}$

Fructose osmoles

The formula of fructose is ${\text{C"_6"H"_12"O}}_{6}$, and its molar mass is 180.16 g/mol.

$\text{Fructose osmolarity" = "1,56" color(red)(cancel(color(black)("g"))) × (1color(red)(cancel(color(black)("mol"))))/("180,16" color(red)(cancel(color(black)("g")))) × "1 Osmol"/(1color(red)(cancel(color(black)("mol")))) = "0,008 66 Osmol/L}$

Penicillin osmoles

I will assume that your penicillin is Penicillin G.

Its formula is $\text{C"_16"H"_18"N"_2"O"_4"S}$, and its molar mass is 334,4 g/mol.

$\text{Penicillin G osmoles" = "0,06"color(red)(cancel(color(black)("g"))) × (1color(red)(cancel(color(black)("mol"))))/("334,4" color(red)(cancel(color(black)("g")))) × "1 Osmol"/(1color(red)(cancel(color(black)("mol")))) = "0,000 18 Osmol/L}$

Solubilized streptomycin osmoles

I assume that your solubilized streptomycin is streptomycin sulfate.

Its formula is ${\left(\text{C"_21"H"_42"N"_7"O"_12^"3+")_2, ("SO"_4^"2-}\right)}_{3}$, and its molar mass is 1361,32 g/mol.

Note that I mol of streptomycin sulfate is 5 Osmol.

$\text{Streptomycin sulfate osmolarity" = "0,1"color(red)(cancel(color(black)("g")))× (1color(red)(cancel(color(black)("mol"))))/(1361,32 color(red)(cancel(color(black)("g")))) × "5 Osmol"/(1color(red)(cancel(color(black)("mol")))) = "0,000 37 Osmol}$

Egg yolk osmoles

$\text{Mass of yolk" = 20 color(red)(cancel(color(black)("mL"))) × "1.028 g"/(1 color(red)(cancel(color(black)("mL")))) = "20.6 g}$

The yolk contains about 31 % lipids (M_text(r) ≈800) and 17 % proteins (M_text(r) ≈ "45 000"#).

$\text{Osmoles of lipid" = 20.6 color(red)(cancel(color(black)("g yolk"))) × (31 color(red)(cancel(color(black)("g lipid"))))/(100 color(red)(cancel(color(black)("g yolk")))) × (1 color(red)(cancel(color(black)("mol lipid"))))/(800 color(red)(cancel(color(black)("g lipid")))) × "1 Osmol"/(1 color(red)(cancel(color(black)("mol lipid")))) = "0,007 98 Osmol}$

$\text{Osmoles of protein" = 20.6 color(red)(cancel(color(black)("g yolk"))) × (17 color(red)(cancel(color(black)("g protein"))))/(100 color(red)(cancel(color(black)("g protein")))) × (1 color(red)(cancel(color(black)("mol protein"))))/("45 000" color(red)(cancel(color(black)("g protein")))) × "1 Osmol"/(1 color(red)(cancel(color(black)("mol protein")))) = "0,000 078 Osmol}$

$\text{Total osmoles" = "(0,007 98 + 0,000 078) Osmol" = "0,008 06 Osmol}$

α-Tocopherol osmoles

I assume that the concentration of α-tocopherol in the solution is 1 mmol/L.

$\text{Osmoles of α-tocopherol" = "0,100" color(red)(cancel(color(black)("L"))) × (1 × 10^"-3" color(red)(cancel(color(black)("mol"))))/(1 color(red)(cancel(color(black)("L")))) × "1 Osmol"/(1 color(red)(cancel(color(black)("mol")))) = "0,000 10 Osmol}$

Now, we can set up a table for easy calculation.

$\boldsymbol{\underline{\text{Mass/g"color(white)(m)"Substance"color(white)(m)"Osmol}}}$
$\textcolor{w h i t e}{m} \text{3,87"color(white)(mmmm)"Tris"color(white)(mmm)"0,031 95}$
$\textcolor{w h i t e}{m} \text{2,17"color(white)(mmmm)"HCit"color(white)(mmll)"0,011 30}$
$\textcolor{w h i t e}{m} \text{1,56"color(white)(mmmm)"Fruct"color(white)(mml)"0,008 66}$
$\textcolor{w h i t e}{m} \text{0,06"color(white)(mmmm)"Pen"color(white)(mmm)"0,000 18}$

$\textcolor{w h i t e}{m} \text{0,1"color(white)(mmmmll)"Strep"color(white)(mml)"0,000 37}$
$\textcolor{w h i t e}{m} \text{20,6"color(white)(mmmm)"Yolk"color(white)(mmll)"0,008 06}$
$\underline{\textcolor{w h i t e}{m m m m m m m} \text{α-Toco"color(white)(mll)"0,000 10}}$
$\textcolor{w h i t e}{m m m m m m l l} \text{TOTAL = 0,063 95}$

$\text{Osmolarity" = "0,063 95 Osmol"/"0,100 L" = "0.640 Osmol/L}$

Effect of temperature

The osmolarity will decrease by about 0,3 % on cooling from 25 °C to 5 °C, because the volume increases. However, this is probably less than your experimental uncertainty.

The mixture will be solid at -196 °C, and the concept of osmolarity does not apply to solids.