1. Calculate the mass, in grams, of K2SO4 needed to prepare 32.00 g of 2.000%(m/m) K2SO4 solution.
2. Calculate the mass, in grams, of KCl needed to prepare 200.0 g of 5.000%(m/m) KCl solution.
3. How many grams of water must be added to 20.0 g of NaOH in order to prepare a 6.75%(m/m) solution?
4. How many grams of water must be added to 10.0 g of Ca(NO3)2 in order to prepare a 12.0%(m/m) solution?
The Correct Answer and Explanation is :
Let’s go through each question step by step and calculate the values. We’ll start by calculating the masses and then explain how each formula works.
1. Mass of K₂SO₄ needed to prepare a 2.000% (m/m) K₂SO₄ solution (32.00 g of solution):
The formula for the mass percent is:
[
\text{mass percent} = \left( \frac{\text{mass of solute}}{\text{mass of solution}} \right) \times 100
]
Rearranging the formula to solve for the mass of the solute:
[
\text{mass of solute} = \frac{\text{mass percent} \times \text{mass of solution}}{100}
]
For this case:
- Mass percent = 2.000%
- Mass of solution = 32.00 g
[
\text{mass of K₂SO₄} = \frac{2.000 \times 32.00}{100} = 0.6400 \, \text{g}
]
So, 0.6400 g of K₂SO₄ is needed.
2. Mass of KCl needed to prepare a 5.000% (m/m) KCl solution (200.0 g of solution):
Again, use the same formula:
[
\text{mass of solute} = \frac{\text{mass percent} \times \text{mass of solution}}{100}
]
For this case:
- Mass percent = 5.000%
- Mass of solution = 200.0 g
[
\text{mass of KCl} = \frac{5.000 \times 200.0}{100} = 10.000 \, \text{g}
]
So, 10.000 g of KCl is needed.
3. Mass of water to be added to 20.0 g of NaOH to prepare a 6.75% (m/m) solution:
The mass percent formula is:
[
\text{mass percent} = \left( \frac{\text{mass of NaOH}}{\text{mass of NaOH} + \text{mass of water}} \right) \times 100
]
Rearranging to solve for the mass of water:
[
\text{mass of water} = \frac{\text{mass of NaOH} \times (100 – \text{mass percent})}{\text{mass percent}}
]
For this case:
- Mass of NaOH = 20.0 g
- Mass percent = 6.75%
[
\text{mass of water} = \frac{20.0 \times (100 – 6.75)}{6.75} = \frac{20.0 \times 93.25}{6.75} = 276.296 \, \text{g}
]
So, 276.3 g of water must be added.
4. Mass of water to be added to 10.0 g of Ca(NO₃)₂ to prepare a 12.0% (m/m) solution:
Using the same formula as before:
[
\text{mass of water} = \frac{\text{mass of Ca(NO₃)₂} \times (100 – \text{mass percent})}{\text{mass percent}}
]
For this case:
- Mass of Ca(NO₃)₂ = 10.0 g
- Mass percent = 12.0%
[
\text{mass of water} = \frac{10.0 \times (100 – 12.0)}{12.0} = \frac{10.0 \times 88.0}{12.0} = 73.33 \, \text{g}
]
So, 73.33 g of water must be added.
Explanation of the Process:
- Mass percent gives the proportion of solute in a solution by mass.
- To calculate the mass of the solute, you can rearrange the formula for mass percent. If you are given the mass of the solution, simply multiply by the percentage and divide by 100.
- When you’re working backwards to find the mass of water in a solution, you rearrange the formula to account for the difference between the solute and the total mass.
Now, I’ll create a visual representation of these calculations.
Here’s the bar chart illustrating the mass of solute and water in the different solutions. As you can see, the chart helps visualize how much solute and water are needed for each solution based on the given concentrations. Let me know if you need further clarifications or additional information!
