Answer :
Answer
The mole fraction of sulfuric acid in the solution = 0.0939.
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:
[tex]\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}[/tex]Step 2: Determine the mole fraction of H2SO4 in the solution.
The mole fraction of sulfuric acid in the solution can be calculated using:
[tex]\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}[/tex]Thus, the mole fraction of sulfuric acid in the solution made is 0.0939.