Question #cf7fe

1 Answer
Sep 14, 2017

Answer:

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

#"CaCl"_2"(s)" → "Ca"^"2+""(aq)" + "2Cl"^"-""(aq)"#
#color(white)(ll)"1 mol"color(white)(mmmll)"1 mol"color(white)(mmm)"2 mol"#

Thus,

#"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.

#"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.

#"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 #"C"_6"H"_12"O"_6#, and its molar mass is 180.16 g/mol.

#"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 #"C"_16"H"_18"N"_2"O"_4"S"#, and its molar mass is 334,4 g/mol.

#"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 #("C"_21"H"_42"N"_7"O"_12^"3+")_2, ("SO"_4^"2-")_3#, and its molar mass is 1361,32 g/mol.

Note that I mol of streptomycin sulfate is 5 Osmol.

#"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

#"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"#).

#"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"#

#"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"#

#"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.

#"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.

#bbul("Mass/g"color(white)(m)"Substance"color(white)(m)"Osmol")#
#color(white)(m)"3,87"color(white)(mmmm)"Tris"color(white)(mmm)"0,031 95"#
#color(white)(m)"2,17"color(white)(mmmm)"HCit"color(white)(mmll)"0,011 30"#
#color(white)(m)"1,56"color(white)(mmmm)"Fruct"color(white)(mml)"0,008 66"#
#color(white)(m)"0,06"color(white)(mmmm)"Pen"color(white)(mmm)"0,000 18"#

#color(white)(m)"0,1"color(white)(mmmmll)"Strep"color(white)(mml)"0,000 37"#
#color(white)(m)"20,6"color(white)(mmmm)"Yolk"color(white)(mmll)"0,008 06"#
#ul(color(white)(mmmmmmm)"α-Toco"color(white)(mll)"0,000 10")#
#color(white)(mmmmmmll)"TOTAL = 0,063 95"#

#"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.