Question

An aqueous solution of sulfuric acid has a composition of 25.0 wt% sulfuric acid and a specific gravity of 1.22. Calculate the volume of solution that contains 245 kg of sulfuric acid.

Answer 1

Answer: The volume of solution is
`8.03* 10^5mL`

Step-by-step explanation:

The relationship between specific gravity and density of a substance is given as:

`\text{Specific gravity}=\frac{\text{Density of a substance}}{\text{Density of water}}`

Specific gravity of sulfuric acid solution = 1.22

Density of water = 1.00 g/mL

Putting values in above equation we get:

`1.22=\frac{\text{Density of sulfuric acid solution}}{1.00g/mL}\\\\\text{Density of sulfuric acid solution}=(1.22* 1.00g/mL)=1.22g/mL`

We are given:

25% (m/m) sulfuric acid solution. This means that 25 g of sulfuric acid is present in 100 g of solution

Conversion factor: 1 kg = 1000 g

Mass of solution having 254 kg or 245000 g of sulfuric acid is calculated by using unitary method:

If 25 grams of sulfuric acid is present in 100 g of solution.

So, 245000 grams of sulfuric acid will be present in =
`(100)/(25)* 245000=980000g`

To calculate volume of a substance, we use the equation:

`\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}`

Density of solution = 1.22 g/mL

Mass of Solution = 980000 g

Putting values in above equation, we get:

`1.22g/mL=\frac{980000g}{\text{Volume of solution}}\\\\\text{Volume of solution}=(980000g)/(1.22g/mL)=8.03* 10^5mL`

Hence, the volume of solution is
`8.03* 10^5mL`