what volume of 98% sulphuric acid(DENSITY 1.88gm/ml of solution)and what mass of water must be taken to prepare 200ml of 15% H2SO4 by weight(density=1.12gm/ml)

To prepare a solution of 15% sulfuric acid (H2SO4) by weight, we need to determine the volume of concentrated sulfuric acid and the mass of water required to achieve this concentration in a final volume of 200 mL. Let's break this down step by step.

Step 1: Calculate the Mass of the Final Solution

The first step is to find out the total mass of the final solution. Since we want a 15% solution by weight, we can use the formula:

• Mass of H2SO4 in the final solution = (Percentage by weight / 100) × Total mass of solution

Given that the total volume of the solution is 200 mL and the density of the final solution is 1.12 g/mL, we can calculate the total mass:

• Total mass of solution = Volume × Density = 200 mL × 1.12 g/mL = 224 g

Now, we can find the mass of H2SO4 in this solution:

• Mass of H2SO4 = 0.15 × 224 g = 33.6 g

Step 2: Determine the Volume of Concentrated Sulfuric Acid

Next, we need to find out how much concentrated sulfuric acid (98% solution) is needed to obtain 33.6 g of H2SO4. The mass of H2SO4 in the concentrated solution can be calculated as follows:

• Mass of H2SO4 in concentrated solution = (Percentage of H2SO4 / 100) × Mass of concentrated solution

Let’s denote the mass of the concentrated solution as \( m \). Therefore, we can set up the equation:

• 33.6 g = 0.98 × \( m \)

Solving for \( m \):

• \( m = \frac{33.6 g}{0.98} \approx 34.31 g \)

Step 3: Calculate the Volume of Concentrated Sulfuric Acid

Now that we have the mass of the concentrated sulfuric acid, we can find its volume using its density. The density of the concentrated sulfuric acid is 1.88 g/mL:

• Volume of concentrated sulfuric acid = \( \frac{Mass}{Density} = \frac{34.31 g}{1.88 g/mL} \approx 18.25 mL \)

Step 4: Calculate the Mass of Water Required

To find out how much water we need to add, we can use the total mass of the final solution and subtract the mass of the concentrated sulfuric acid:

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

We need to convert the volume of concentrated sulfuric acid to mass:

• Mass of concentrated sulfuric acid = 34.31 g

Now we can calculate the mass of water:

• Mass of water = 224 g - 34.31 g = 189.69 g

Summary of Results

To prepare 200 mL of a 15% H2SO4 solution by weight, you will need:

• Volume of 98% sulfuric acid: approximately 18.25 mL
• Mass of water: approximately 189.69 g

By following these calculations, you can accurately prepare the desired sulfuric acid solution. Always remember to handle concentrated acids with care and use appropriate safety equipment!