A concentrated KOH (MW = 56.105 g/mol) solution is 45.0 %wt KOH and has a density of 1.45 g/mL

A concentrated KOH (MW = 56.105 g/mol) solution is 45.0 %wt KOH and has a density of 1.45 g/mL. How many milliliters of the concentrated KOH solution must be diluted to obtain 100.0 mL of 1.20 M KOH?

The correct answer and explanation is :

To solve this problem, we can use the concept of dilution and the relationship between concentration, volume, and moles.

Given Information:

• Concentrated KOH solution:
• Mass percentage of KOH: 45.0% wt
• Density of the solution: 1.45 g/mL
• Molar mass of KOH (MW): 56.105 g/mol
• Desired diluted solution:
• Volume of diluted solution: 100.0 mL
• Desired molarity of KOH in the diluted solution: 1.20 M

Steps to Solve:

1. Calculate the mass of KOH in 100.0 mL of the diluted solution: The moles of KOH in the final solution can be calculated using the molarity equation: $$
   M = \frac{\text{moles of solute}}{\text{volume of solution (in liters)}}
   $$ Rearranging to solve for moles of KOH: $$
   \text{moles of KOH} = M \times V
   $$ Where:

• $M = 1.20 \, \text{M}$
• $V = 100.0 \, \text{mL} = 0.100 \, \text{L}$ $$
  \text{moles of KOH} = 1.20 \, \text{mol/L} \times 0.100 \, \text{L} = 0.120 \, \text{mol}
  $$ Now, convert moles of KOH to grams: $$
  \text{grams of KOH} = \text{moles of KOH} \times \text{molar mass of KOH}
  $$ $$
  \text{grams of KOH} = 0.120 \, \text{mol} \times 56.105 \, \text{g/mol} = 6.73 \, \text{g}
  $$

1. Determine the amount of concentrated solution needed: In the concentrated solution, 45.0% by mass is KOH. Therefore, for every 100 grams of solution, there are 45 grams of KOH. The mass of KOH in the concentrated solution is proportional to the mass of the solution. The amount of solution needed to obtain 6.73 g of KOH is: $$
   \frac{45.0 \, \text{g KOH}}{100.0 \, \text{g solution}} = \frac{6.73 \, \text{g KOH}}{x \, \text{g solution}}
   $$ Solving for $x$: $$
   x = \frac{6.73 \, \text{g KOH} \times 100.0 \, \text{g solution}}{45.0 \, \text{g KOH}} = 14.95 \, \text{g solution}
   $$
2. Convert the mass of concentrated solution to volume: The density of the concentrated KOH solution is 1.45 g/mL. We can use the density equation: $$
   \text{Density} = \frac{\text{mass}}{\text{volume}} \quad \Rightarrow \quad \text{volume} = \frac{\text{mass}}{\text{density}}
   $$ $$
   \text{volume} = \frac{14.95 \, \text{g}}{1.45 \, \text{g/mL}} = 10.31 \, \text{mL}
   $$

Final Answer:

To prepare 100.0 mL of a 1.20 M KOH solution, you need to dilute 10.31 mL of the concentrated KOH solution.