Warning! Long Answer!
An osmole is 1 mol of particles that contribute to the osmotic pressure of a solution.
For example, #"NaCl""# dissociates completely in water to form #"Na"^+# ions and #"Cl"^"-"# ions.
Thus, each mole of #"NaCl"# becomes two osmoles in solution: one mole of #"Na"^+# and one mole of #"Cl"^"-"#.
A solution of 1 mol/L #"NaCl"# has an osmolarity of 2 Osmol/L.
A solution of 1 mol/L #"CaCl"_2# has an osmolarity of 3 Osmol/L (1 mol #"Ca"^"2+"#
and 2 mol #"Cl"^"-"#).
To calculate the osmolarity of a solution, we add up the osmolarities of all the solutes.
Tris osmolarity
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 osmolarity" = (2.4 color(red)(cancel(color(black)("g"))))/(100 color(red)(cancel(color(black)("mL")))) × (1000 color(red)(cancel(color(black)("mL"))))/"1 L" × {1 color(red)(cancel(color(black)("mol"))))/(121.13 color(red)(cancel(color(black)("g")))) × "1 Osmol"/(1 color(red)(cancel(color(black)("mol")))) = "0.1981 Osmol/L"#
Citric acid osmolarity
The formula of citric acid is #"HOC(COOH)"("CH"_2"COOH")_2#, and its molar mass is 192.12 g/mol.
#"Citric acid osmolarity" = (1.4 color(red)(cancel(color(black)("g"))))/(100 color(red)(cancel(color(black)("mL")))) × (1000 color(red)(cancel(color(black)("mL"))))/"1 L" × (1 color(red)(cancel(color(black)("mol"))))/(192.12 color(red)(cancel(color(black)("g")))) × "1 Osmol"/(1 color(red)(cancel(color(black)("mol")))) = "0.0729 Osmol/L"#
Glucose osmolarity
The formula of glucose is #"C"_6"H"_12"O"_6#, and its molar mass is 180.16 g/mol.
#"Glucose osmolarity" = (0.8 color(red)(cancel(color(black)("g"))))/(100color(red)(cancel(color(black)("mL")))) × (1000color(red)(cancel(color(black)("mL"))))/"1 L" × (1color(red)(cancel(color(black)("mol"))))/(180.16 color(red)(cancel(color(black)("g")))) × "1 Osmol"/(1color(red)(cancel(color(black)("mol")))) = "0.0444 Osmol/L"#
Na-benzylpenicillin osmolarity
The formula of sodium benzylpenicillin is #"C"_16"H"_17"N"_2"O"_4"S"^"-", "Na"^+#, and its molar mass is 356.37 g/mol.
Note that 1 mol of benzylpenicillin is 2 Osmol.
#"Na-benzylpenicillin osmolarity ="#
#(0.06color(red)(cancel(color(black)("g"))))/(100color(red)(cancel(color(black)("mL")))) × (1000color(red)(cancel(color(black)("mL"))))/"1 L" × (1color(red)(cancel(color(black)("mol"))))/(356.37 color(red)(cancel(color(black)("g")))) × "2 Osmol"/(1color(red)(cancel(color(black)("mol")))) = "0.0034 Osmol/L"#
Streptomycin sulfate osmolarity
The formula of streptomycin sulfate 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 ="#
#(0.1color(red)(cancel(color(black)("g"))))/(100color(red)(cancel(color(black)("mL")))) × (1000color(red)(cancel(color(black)("mL"))))/"1 L"× (1color(red)(cancel(color(black)("mol"))))/(1361.32 color(red)(cancel(color(black)("g")))) × "5 Osmol"/(1color(red)(cancel(color(black)("mol")))) = "0.0037 Osmol/L"#
Osmolarity of the buffer
Now we add up the individual osmolarities to get the total osmolarity of the buffer.
#"Compound" color(white)(mmmmll)"Osmolarity"#
#stackrel(——————————————)("Tris" color(white)(mmmmmmmmml)0.1981)#
#"Citric Acid" color(white)(mmmmmm)0.0729#
#"Glucose"color(white)(mmmmmmmll) 0.0444#
#"Na-penicillin"color(white)(mmmmml)0.0034#
#"Streptomycin sulfate" color(white)(ml)0.0037#
#stackrel(——————————————)(color(white)(mmmmm)"TOTAL =" color(white)(ml)0.3225)#
The osmolarity of your buffer is 0.3225 Osmol/L or 322.5 mOsmol/L.
Dilution calculation
You must now dilute this buffer to get a concentration of 290 mOsmol/L.
You can use the dilution fofrmula
#color(blue)(|bar(ul(color(white)(a/a) c_1V_1 = c_2V_2color(white)(a/a)|)))" "#
You can rearrange this to
#V_2 = V_1 × c_1/c_2#
#V_2 = "100 mL" × (322.5 color(red)(cancel(color(black)("mOsmol/L"))))/(290 color(red)(cancel(color(black)("mOsmol/L")))) = "111 mL"#
You need to dilute the buffer to 111 mL.
∴ Add 11 mL of distilled, deionized water to the buffer, and you will have a 290 mOsmol/L buffer.
