What volume of `98%` sulphuric acid should be mixed with water to obtain `200mL` of `15%` solution of sulphuric acid by weight ? Given density of `H_(2)O=1.00 g cm^(-3)`, sulphuric acid `(98%)=1.88g cm^(-3)` and sulphuric acied `(15%)=1.12g cm^(-3)`.

Explanation

To solve the problem of determining the volume of 98% sulfuric acid needed to create 200 mL of a 15% sulfuric acid solution, we can follow these steps:

### Step 1: Calculate the mass of the 15% sulfuric acid solution
To find the mass of the 15% sulfuric acid solution, we can use the formula:
\[ \text{mass} = \text{volume} \times \text{density} \]
Given:
- Volume of the solution (V) = 200 mL
- Density of 15% sulfuric acid = 1.12 g/cm³

Calculating the mass:
\[ \text{mass}_{15\%} = 200 \, \text{mL} \times 1.12 \, \text{g/cm}^3 = 224 \, \text{g} \]

### Step 2: Calculate the mass of sulfuric acid in the 15% solution
The mass of sulfuric acid in the 15% solution is given by:
\[ \text{mass of } H_2SO_4 = \frac{15}{100} \times \text{mass}_{15\%} \]
Calculating:
\[ \text{mass of } H_2SO_4 = 0.15 \times 224 \, \text{g} = 33.6 \, \text{g} \]

### Step 3: Calculate the volume of 98% sulfuric acid needed
Now, we need to find out how much volume of 98% sulfuric acid is required to obtain 33.6 g of sulfuric acid.

Given:
- Density of 98% sulfuric acid = 1.88 g/cm³
- Mass of sulfuric acid in 98% solution = 98 g in 100 g of solution

First, we calculate the mass of the 98% solution needed to get 33.6 g of sulfuric acid:
\[ \text{mass of 98% solution} = \frac{33.6 \, \text{g}}{0.98} = 34.31 \, \text{g} \]

Next, we can find the volume of the 98% sulfuric acid solution:
\[ \text{volume} = \frac{\text{mass}}{\text{density}} = \frac{34.31 \, \text{g}}{1.88 \, \text{g/cm}^3} \approx 18.26 \, \text{mL} \]

### Final Answer
The volume of 98% sulfuric acid required to mix with water to obtain 200 mL of a 15% solution is approximately **18.26 mL**.

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