Question

A solution with a weight percentage of sodium hydroxide of 9% is prepared by adding the following mass of water (in grams) to 300 grams of that solution with a weight percent of NaOH of 15%.
(A) 100g
(B) 150g
(C) 200g
(D) 250g

Answer 1

Hint: The two conditions given have different weight percentages of sodium hydroxide, and as per the question, the concentration or weight NaOH will be the same for both the conditions. Weight percent is a measurement of concentration of solution.

Complete step by step answer: Solutions can be represented in terms of relative percent concentration of solute in a solution. To determine the weight percent of a solution, the mass of solute is divided by mass of the solution (Solvent and solute together) and multiplied by 100 to obtain it.
The formula of percent by weight is given as follows:
\[\text{Percent by weight=}\dfrac{\text{gram of solute}}{\text{gram of solution}}\times 100\]
In the given question, we are provided with two percent by weight values. The initial percent by weight value is 15% and to this solution some grams were added to make the percent by weight value to 9%.
The initial mass of water is given as 300 grams, to this quantity some grams lets say x grams of water is added to make the solution to 9%.
Therefore, for 15% solution the formula will be,
\[\begin{align}
  & 15\text{ }=~\dfrac{NaOHweight}{totalweight}\times 100 \\
 & NaOHweight=\dfrac{15\times 300}{100}=45gram \\
 & \\
\end{align}\]
Therefore, grams of NaOH will be 45grams. It will remain the same for both the conditions.
Now, for 9% solution, the formula will be,
 \[\begin{align}
& 9\text{ }=\dfrac{45}{300+x}\times 100 \\
& 300+x=\dfrac{45}{9}\times 100 \\
& x=200 \\
\end{align}\]\[\]

Therefore, the grams of water added is 200g, (C) option is the correct answer.

Note: Percentage w/v is a measurement of the concentration of a solution. Solubilities are sometimes given in units of grams of solute per 100mL of water. Solutions can be described in other concentrations besides molarity, molality or normality.