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

Question

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

Owen Ambrose · Accepted Answer

7000 #cm^3#

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 #gmol^-1# Ar Na = 22.990 #gmol^-1# Ar H = 1.008 #gmol^-1#

Adding these all together you get the Mr of NaOH: Mr NaOH = 39.99 #gmol^-1#

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

no. mol NaOH = 154 g / 39.99 #gmol^-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 = #moldm^-3#)

v = 3.85 mol / 0.55 #moldm^-3# v = 7 #dm^3# or 7000 #cm^3#

Jeremiah Adams · Answer

undefined To find the volume of the NaOH solution, you can use the formula for molarity:

$$ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} $$

First, calculate the number of moles of NaOH:

$$ \text{Moles of NaOH} = \frac{\text{mass of NaOH (in grams)}}{\text{molar mass of NaOH}} $$

The molar mass of NaOH (sodium hydroxide) is approximately $ 40.00 \, \text{g/mol} $ (sodium: $ 22.99 \, \text{g/mol} $, oxygen: $ 16.00 \, \text{g/mol} $, hydrogen: $ 1.01 \, \text{g/mol} $).

$$ \text{Moles of NaOH} = \frac{154 \, \text{g}}{40.00 \, \text{g/mol}} $$

$$ \text{Moles of NaOH} = 3.85 \, \text{moles} $$

Now, rearrange the molarity formula to solve for the volume of the solution:

$$ \text{Volume of solution (in liters)} = \frac{\text{moles of solute}}{\text{Molarity}} $$

Substitute the values:

$$ \text{Volume of solution} = \frac{3.85 \, \text{moles}}{0.55 \, \text{M}} $$

$$ \text{Volume of solution} = 7 \, \text{liters} $$

So, the volume of the NaOH solution is $ 7 \, \text{liters} $.