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

Apr 22, 2017

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 $\text{NaOH(aq)}$

A 1 mol/kg $\text{NaOH(aq)}$ solution contains $\text{40 g NaOH}$ in 1000 g water.

$\text{Total mass = 1040 g}$

"% 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 $\text{NaOH(aq)}$

A 1 mol/L $\text{NaOH(aq)}$ solution contains $\text{40 g NaOH}$ in 1000 mL water.

The density of the solution is 1.04 g/mL.

Hence,

$\text{Total mass" = 1000 color(red)(cancel(color(black)("mL"))) × ("1.04 g")/(1 color(red)(cancel(color(black)("mL")))) = "1040 g}$

"% 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.