A sulfuric acid solution containing 571.8gg of H2SO4 per liter of solution has a density of 1.329 g/cm3
Calculate the mole fraction of H2SO4 in this solution.
mass water per liter=1329-571.8
moles water= mass water/18
moles H2SO4=571.8/molmassH2SO4
mole fraction=molesacid/total moles
where total moles =moles water+moles acid
To calculate the mole fraction of H2SO4 in the solution, we need to first determine the moles of H2SO4 and the total moles of the solution.
Step 1: Calculate the moles of H2SO4
The mass of H2SO4 is given as 571.8 g per liter of solution. As the density of the solution is 1.329 g/cm3, we can convert the mass to volume using the density formula:
Volume of H2SO4 = mass of H2SO4 / density of the solution
= 571.8 g / 1.329 g/cm3
Since the density is given in g/cm3, we can rewrite the equation using the conversion factor 1 cm3 = 1 mL:
Volume of H2SO4 = 571.8 g / 1.329 g/mL
≈ 430.764 mL
Step 2: Convert the volume of H2SO4 to moles
The molar mass of H2SO4 is 98.09 g/mol. Using this information, we can convert the volume of H2SO4 to moles using the formula:
moles of H2SO4 = Volume of H2SO4 (in mL) × (1 mL / 1 cm3) × (1 cm3 / 1 mL) × (1 L / 1000 mL) × (1 mol / molar mass of H2SO4)
= 430.764 mL × (1 L / 1000 mL) × (1 mol / 98.09 g)
≈ 0.004374 mol
Step 3: Calculate the total moles of the solution
As the mole fraction is the moles of solute (H2SO4) divided by the total moles of the solution, we need to determine the total moles. Since the density of the solution is given as 1.329 g/cm3, we can calculate the mass of 1 liter of the solution:
Mass of the solution = Volume of the solution × density of the solution
= 1 L × 1.329 g/cm3
= 1329 g
Next, we convert the mass of the solution to moles using the molar mass of H2SO4:
moles of the solution = Mass of the solution / molar mass of H2SO4
= 1329 g / 98.09 g/mol
≈ 13.548 mol
Step 4: Calculate the mole fraction
Now that we have the moles of H2SO4 (0.004374 mol) and the total moles of the solution (13.548 mol), we can calculate the mole fraction using the formula:
mole fraction = moles of H2SO4 / moles of the solution
= 0.004374 mol / 13.548 mol
≈ 0.000323
Therefore, the mole fraction of H2SO4 in this solution is approximately 0.000323.