# What is the volume of a sample of NaOH solution that contains 154 grams of NaOH and has a concentration of 0.55 M?

Nov 27, 2017

7000 $c {m}^{3}$

#### Explanation:

First we need to calculate the number of moles of NaOH in 154g. You do this using the following equation:

mol = mass / Mr

where mol = number of moles; mass = weight in grams; Mr = molecular weight

The Mr of NaOH can be calculated using the atomic weights (Ar) of sodium, oxygen, and hydrogen. These can be found on the periodic table.

Ar O = 15.999 $g m o {l}^{-} 1$
Ar Na = 22.990 $g m o {l}^{-} 1$
Ar H = 1.008 $g m o {l}^{-} 1$

Adding these all together you get the Mr of NaOH:
Mr NaOH = 39.99 $g m o {l}^{-} 1$

Then you substitute this into the equation to calculate the number of moles of NaOH:

no. mol NaOH = 154 g / 39.99 $g m o {l}^{-} 1$
no. mol NaOH = 3.85 mol

To calculate the volume you use the following equation:

v = n/c

where c = concentration; n = no. of moles; v = volume

You substitute in the moles of NaOH that you calculated before, and the concentration of the solution 0.55 M (M = $m o l {\mathrm{dm}}^{-} 3$)

v = 3.85 mol / 0.55 $m o l {\mathrm{dm}}^{-} 3$
v = 7 ${\mathrm{dm}}^{3}$ or 7000 $c {m}^{3}$