Question

Which one is more concentrated 1 molar NaOH or 1 molal NaOH aqueous solution? Explain?

Answer 1

Both solutions are dilute enough that they have the same concentrations within the uncertainty of measurement.

Explanation:

Let's calculate the percent by mass of each solution.

1 mol/kg `"NaOH(aq)"`

A 1 mol/kg `"NaOH(aq)"` solution contains `"40 g NaOH"` in 1000 g water.

`"Total mass = 1040 g"`

`"% by mass" = "mass of NaOH"/"total mass" × 100 % = (40 color(red)(cancel(color(black)("g"))))/(1040 color(red)(cancel(color(black)("g")))) × 100 % = 3.8 %`

1 mol/L `"NaOH(aq)"`

A 1 mol/L `"NaOH(aq)"` solution contains `"40 g NaOH"` in 1000 mL water.

The density of the solution is 1.04 g/mL.

Hence,

`"Total mass" = 1000 color(red)(cancel(color(black)("mL"))) × ("1.04 g")/(1 color(red)(cancel(color(black)("mL")))) = "1040 g"`

`"% by mass" = "mass of NaOH"/"total mass" × 100 % = (40 color(red)(cancel(color(black)("g"))))/(1040 color(red)(cancel(color(black)("g")))) × 100 % = 3.8 %`

Thus, both solutions have effectively the same concentration.