To find the percent by mass of sodium hydroxide (NaOH) in the solution, we need to calculate the mass of the solution and then use that to find the percent by mass.
-
Calculate the mass of water: The density of water is approximately 1 g/mL, so the mass of 750 mL of water is:
\[ \text{Mass of water} = \text{Volume of water} \times \text{Density of water} = 750 , \text{mL} \times 1 , \frac{\text{g}}{\text{mL}} = 750 , \text{g} \]
-
Calculate the total mass of the solution: The total mass of the solution is the mass of sodium hydroxide plus the mass of water:
\[ \text{Total mass of solution} = \text{Mass of NaOH} + \text{Mass of water} = 83 , \text{g} + 750 , \text{g} = 833 , \text{g} \]
-
Calculate the percent by mass of sodium hydroxide: The percent by mass is calculated using the formula:
\[ \text{Percent by mass} = \left( \frac{\text{Mass of solute}}{\text{Mass of solution}} \right) \times 100 \]
Plugging in the values:
\[ \text{Percent by mass} = \left( \frac{83 , \text{g}}{833 , \text{g}} \right) \times 100 \approx 9.95% \]
Thus, the percent by mass of sodium hydroxide in the solution is approximately 9.95%.