(a) What is the molar concentration of a concentrated solution that contains 36.00 % #"HCl"# by mass and has a density of #"1.24 g/dm"^3"#. (b) How you would prepare #"1.00 dm"3# of 0.125 mol/L #"HCl"# from the concentrated solution?

1 Answer
Jun 28, 2017

Answer:

See below.

Explanation:

The correct density of concentrated hydrochloric acid is #"1.19 g/cm"^3#.

Step 1. Calculate the molar concentration of the conc. #"HCl"#

Assume that you have #"1 dm"^3# of the concentrated acid.

#"Mass of conc. HCl" = 1000 color(red)(cancel(color(black)("cm"^3))) × "1.19 g"/(1 color(red)(cancel(color(black)("cm"^3)))) = "1190 g"#

#"Mass of HCl" = 1190 color(red)(cancel(color(black)("g conc."))) × (36.00 "g HCl")/(100 color(red)(cancel(color(black)("g conc.")))) = "428.4 g HCl"#

#"Moles of HCl" = 428.4 color(red)(cancel(color(black)("g HCl"))) × ("1 mol HCl")/(35.5 color(red)(cancel(color(black)("g HCl")))) = "12.07 mol HCl"#

#c = "12.07 mol"/"1 dm"^3 = "12.07 mol/dm"^3#

Step 2. Calculate the volume of conc. #"HCl"_2# required

We can use the dilution formula for this calculation.

#color(blue)(bar(ul(|color(white)(a/a)c_1V_1 = c_2V_2color(white)(a/a)|)))"#

where

#c_1# and #c_2# are the molar concentrations and
#V_1# and #V_2# are the corresponding volumes.

We can rearrange this formula to get

#V_2 = V_1 × c_1/c_2#

In this problem,

#c_1 = "0.215 mol/dm"^3; V_1 = "1 dm"^3#
#c_2 = "12.07 mol/dm"^3; V_2 = ?#

#V_2 = "1 dm"^3 × (0.215 color(red)(cancel(color(black)("mol/dm"^3))))/(12.07 color(red)(cancel(color(black)("mol/dm"^3)))) = "0.001 78 dm"^3 = "17.8 cm"^3#

You would place about #"400 cm"^3# of distilled water in a #"1 dm"^3# volumetric flask, slowly add 17.8 mL of the conc. #"HCl"# from a pipet with swirling, and then add enough distilled water to make the solution up to the #"1 dm"^3# mark.