How do I solve these problems
You have 2000. g of aqueous NaOH solution. The percent by mass of the solute is 4.25%. How many grams of NaOH are in the solution?
If you have 100.0 mL of a 25.0% aqueous solution of ethanol, what volumes of ethanol and water are in the solution?
4.25% NaOH by mass means 4.25 g NaOH/100 g solution. In 2000 g of the solution we will have
4.25 x (2000/100) =
To solve these problems, we need to use the concept of percent composition. The percent composition is the ratio of the mass of the solute to the mass of the solution, multiplied by 100%.
Let's start with the first problem:
1. The given percent by mass of NaOH is 4.25%. This means that in 100 g (or 100 mL) of the solution, there are 4.25 grams of NaOH.
2. To find the mass of NaOH in the given 2000 g of solution, we can set up a proportion based on the percent composition:
- (4.25 g NaOH) / (100 g solution) = (x g NaOH) / (2000 g solution)
3. Cross-multiplying and solving for x, we get:
- x = (4.25 g NaOH) * (2000 g solution) / (100 g solution)
- x = 85 g NaOH
Therefore, there are 85 grams of NaOH in the 2000 g aqueous NaOH solution.
Moving on to the second problem:
1. The given percentage of ethanol is 25%. This means that in 100 mL of the solution, there are 25 mL of ethanol.
2. We need to find the volumes of ethanol and water in the 100.0 mL solution. Let's call the volume of ethanol "Vethanol" and the volume of water "Vwater".
3. Since ethanol and water make up the entire volume of the solution, we have the equation:
- Vethanol + Vwater = 100.0 mL
4. The percentage of ethanol also gives us the ratio of ethanol to the total volume of the solution:
- (Vethanol / 100 mL) = (25 mL ethanol / 100 mL solution)
5. Rearranging the equation, we find:
- Vethanol = (25 mL ethanol) * (100 mL solution) / (100 mL ethanol)
- Vethanol = 25 mL
6. Substituting this value back into the equation from step 3, we find:
- 25 mL + Vwater = 100.0 mL
- Vwater = 100.0 mL - 25 mL
- Vwater = 75 mL
Therefore, in the 100.0 mL aqueous solution of ethanol, there are 25 mL of ethanol and 75 mL of water.