what volume of 95percent by mass of sulphuric acid (density=1.85g/m) and what mass of water must be taken to prepare 100ml of 15percent by mass of solution of sulphuric acid (density=1.10g/ml)?

To solve the problem of preparing a 15% by mass solution of sulfuric acid from a 95% by mass sulfuric acid solution, we need to determine the volume of the concentrated solution and the mass of water required. Let's break this down step by step.

Understanding the Problem

We have two solutions:

• A concentrated sulfuric acid solution that is 95% by mass with a density of 1.85 g/mL.
• A diluted sulfuric acid solution that we want to prepare, which is 15% by mass with a density of 1.10 g/mL.

Step 1: Calculate the Mass of the Final Solution

First, we need to find the total mass of the 100 mL of the 15% solution we want to prepare. The density of the final solution is 1.10 g/mL, so:

Mass of final solution = Volume × Density

Mass of final solution = 100 mL × 1.10 g/mL = 110 g

Step 2: Calculate the Mass of Sulfuric Acid in the Final Solution

Next, we calculate how much sulfuric acid is needed in this 15% solution:

Mass of sulfuric acid = (Percentage by mass / 100) × Total mass of solution

Mass of sulfuric acid = (15 / 100) × 110 g = 16.5 g

Step 3: Calculate the Mass of Water in the Final Solution

Now, we can find out how much water is needed by subtracting the mass of sulfuric acid from the total mass of the solution:

Mass of water = Total mass of solution - Mass of sulfuric acid

Mass of water = 110 g - 16.5 g = 93.5 g

Step 4: Calculate the Volume of 95% Sulfuric Acid Required

Now we need to find out how much of the 95% sulfuric acid solution we need to obtain 16.5 g of sulfuric acid. The mass of sulfuric acid in the concentrated solution can be calculated as follows:

Mass of sulfuric acid in concentrated solution = (Percentage by mass / 100) × Mass of concentrated solution

Let m be the mass of the concentrated solution we need. Then:

0.95 × m = 16.5 g

Solving for m gives:

m = 16.5 g / 0.95 = 17.368 g

Step 5: Convert Mass of Concentrated Solution to Volume

Now, we can convert the mass of the concentrated solution to volume using its density:

Volume = Mass / Density

Volume of concentrated sulfuric acid = 17.368 g / 1.85 g/mL = 9.38 mL

Summary of Required Quantities

To prepare 100 mL of a 15% by mass sulfuric acid solution, you will need:

• Volume of 95% sulfuric acid solution: 9.38 mL
• Mass of water: 93.5 g

By following these steps, you can accurately prepare the desired solution while understanding the relationships between mass, volume, and concentration. This method can be applied to similar problems in solution preparation as well.