Pure water and alcohol are mixed to get a 60% (weight) alcohol solution. The densities in Kg/m3 of water, alcohol and the solution may be taken as 998, 798 and 895 respectively at 293 K. Estimate the molarity and molality??
1 Answer
Explanation:
We're asked to find
of a solution, given the percent by mass of the solution, and density values.
- Let's do the molality first
Equation for molality:
#"molality" = "mol solute"/"kg solvent"#
We're given that a solution of alcohol and water is
-
#60# #"g alcohol"# -
#40# #"g water"#
(The "alcohol" here is ethanol, which isn't given to us, but we can either assume this, or look it up based on the given density.)
Let's convert from grams of ethanol to moles, using its molar mass:
#60cancel("g ethanol")((1color(white)(l)"mol ethanol")/(46.068cancel("g ethanol"))) = color(red)(ul(1.30color(white)(l)"mol ethanol"#
And the number of kilograms of water is
#40cancel("g H"_2"O")((1color(white)(l)"kg H"_2"O")/(10^3cancel("g H"_2"O"))) = color(green)(ul(0.040color(white)(l)"kg H"_2"O"#
The molality is thus
#color(blue)("molality") = color(red)(1.30color(white)(l)"mol ethanol")/color(green)(0.040color(white)(l)"kg H"_2"O") = color(blue)(ulbar(|stackrel(" ")(" "32.6color(white)(l)"mol/kg"" ")|)#
- Now, the molarity
The equation for molarity is
#"molarity" = "mol solute"/"L solution"#
To find the volume of solution, we take the given density, and the fact that we assumed a
#"desnity" = "mass"/"volume"#
So
#"volume" = "mass"/"density"#
The density of the solution is given as
#100cancel("g soln")((1cancel("kg soln"))/(10^3cancel("g soln")))((1cancel("m"^3))/(895cancel("kg soln")))((100^3cancel("cm"^3))/(1cancel("m"^3)))((1cancel("mL soln"))/(1cancel("cm"^3)))((1color(white)(l)"L soln")/(10^3cancel("mL soln"))) = color(red)(ul(0.112color(white)(l)"L solution"#
The molarity is therefore
#color(darkblue)("molarity") = (1.30color(white)(l)"mol ethanol")/(color(red)(0.112color(white)(l)"L soln")) = color(darkblue)(ulbar(|stackrel(" ")(" "11.6color(white)(l)"mol/L"" ")|)#
