Question

What is the mole fraction of sulfuric acid (H2SO4=98 g/mol)in a solution made by adding 84 g of sulfuric acid to 150 g of water (H2O=18 g/mol)?

Answer 1

The mole fraction of sulfuric acid in the solution = 0.0939.

Step-by-step explanation

Given that:

The mass of sulfuric acid in the solution = 84 g

The molar mass of sulfuric acid = 98 g/mol

The mass of water in the solution made = 150 g

The molar mass of water = 18 g/mol

What to find:

To find the mole fraction of sulfuric acid in the solution.

Step-by-step solution:

Step 1: Determine the moles of H2SO4 and H2O in the solution.

Using the mole formula, the moles of both the H2SO4 and H2O in the solution can be calculated as follows:

`\begin{gathered} Moles=\frac{Mass}{Molar\text{ }mass} \\ \\ Moles\text{ }of\text{ }H_2SO_4=\frac{84g}{98g\text{/}mol}=0.86\text{ }mol \\ \\ Moles\text{ }of\text{ }H_2O=\frac{150g}{18g\text{/}mol}=8.3\text{ }mol \end{gathered}`

Step 2: Determine the mole fraction of H2SO4 in the solution.

The mole fraction of sulfuric acid in the solution can be calculated using:

`\begin{gathered} Moles\text{ }fraction\text{ }of\text{ }H_2SO_4=\frac{Moles\text{ }of\text{ }H_2SO_4}{Total\text{ }moles} \\ \\ Moles\text{ }fraction\text{ }of\text{ }H_2SO_4=\frac{0.86\text{ }mol}{8.3\text{ }mol+0.86\text{ }mol}=\frac{0.86\text{ }mol}{9.16\text{ }mol} \\ \\ Moles\text{ }fraction\text{ }of\text{ }H_2SO_4=0.0939 \end{gathered}`

Thus, the mole fraction of sulfuric acid in the solution made is 0.0939.