If 84 g of NaOH (aq) is present in a 3 Molar Solution, find volume of solution (in mL)

The correct answer is 700.

To find the volume of the solution, we can use the formula for molarity (M):

$\text{Molarity (M)}=\frac{\text{Moles of solute}}{\text{Volume of solution in Liters (L)}}$

Step 1: Calculate the molar mass of sodium hydroxide (NaOH)
The atomic masses of the constituent elements are:
Sodium (Na) = 23 g/mol
Oxygen (O) = 16 g/mol
Hydrogen (H) = 1 g/mol
Therefore, the molar mass of NaOH is:

$\text{Molar mass of NaOH}=23+16+1=40\text{g/mol}$

Step 2: Calculate the number of moles of NaOH
We are given that the mass of NaOH is 84 g. We calculate the number of moles using the formula:

$\text{Moles of NaOH}=\frac{\text{Given mass}}{\text{Molar mass}}$

$\text{Moles of NaOH}=\frac{84}{40}=2.1\text{moles}$

Step 3: Calculate the volume of the solution in Liters
Rearranging the molarity formula to solve for the volume of the solution in Liters:

$\text{Volume of solution (L)}=\frac{\text{Moles of solute}}{\text{Molarity (M)}}$

Given that the molarity is 3 M, we substitute the values:

$\text{Volume of solution (L)}=\frac{2.1}{3}=0.7\text{L}$

Step 4: Convert the volume to milliliters (mL)
Since 1 Liter (L) contains 1000 milliliters (mL), we multiply the volume in Liters by 1000:

$\text{Volume of solution (mL)}=0.7\times 1000=700\text{mL}$

Thus, the volume of the solution is 700 mL.