4. A sulfuric acid solution containing 571.6 g of H2SO4 per liter of solution has a density of
1.329 g/cm3
. Calculate
a. The mass percentage
b. The mole fraction
c. The molality
d. The molarity of H2SO4 in this solution
C.molality
To calculate the mass percentage of H2SO4 in the solution, you need to determine the mass of H2SO4 in the solution and divide it by the total mass of the solution, then multiply by 100.
a. Mass Percentage:
First, we need to find the mass of H2SO4 in one liter of the solution.
Mass of H2SO4 = 571.6 g/L
Next, we need to calculate the total mass of the solution. Since the density is given, we can find the volume of one liter of the solution.
Volume = 1000 mL = 1000 cm^3
Density = Mass / Volume
1.329 g/cm^3 = Mass / 1000 cm^3
Now, we can calculate the total mass of the solution:
Mass of Solution = 1.329 g/cm^3 * 1000 cm^3 = 1329 g
Finally, we can determine the mass percentage:
Mass Percentage = (Mass of H2SO4 / Mass of Solution) * 100
Mass Percentage = (571.6 g / 1329 g) * 100 = 42.99%
b. Mole Fraction:
To calculate the mole fraction of H2SO4 in the solution, we need to determine the moles of H2SO4 and divide it by the total moles of all components in the solution.
First, let's calculate the moles of H2SO4:
Molar mass of H2SO4 = 2(1.01 g/mol H) + 32.07 g/mol S + 4(16.00 g/mol O) = 98.09 g/mol
Moles of H2SO4 = Mass of H2SO4 / Molar mass of H2SO4
Moles of H2SO4 = 571.6 g / 98.09 g/mol = 5.82 mol
Next, let's calculate the moles of the solvent (water). Since the solution is made by adding H2SO4 to water, we can assume the mass of the solvent is the difference of the solution mass and H2SO4 mass.
Mass of Solvent = Mass of Solution - Mass of H2SO4
Mass of Solvent = 1329 g - 571.6 g = 757.4 g
Moles of Solvent = Mass of Solvent / Molar mass of H2O
Molar mass of H2O = 2(1.01 g/mol H) + 16.00 g/mol O = 18.02 g/mol
Moles of Solvent = 757.4 g / 18.02 g/mol = 42.01 mol
Finally, we can calculate the mole fraction of H2SO4:
Mole Fraction of H2SO4 = Moles of H2SO4 / Total Moles
Mole Fraction of H2SO4 = 5.82 mol / (5.82 mol + 42.01 mol) = 0.121
c. Molality:
Molality represents the number of moles of solute (H2SO4) per kilogram of solvent (water). To calculate the molality, divide the moles of solute by the mass of the solvent in kilograms.
Molality = Moles of H2SO4 / Mass of Solvent (kg)
Mass of Solvent (kg) = Mass of Solvent (g) / 1000
Molality = 5.82 mol / (757.4 g / 1000) = 7.68 mol/kg
d. Molarity:
Molarity represents the number of moles of solute (H2SO4) per liter of solution. To calculate the molarity, divide the moles of solute by the volume of the solution in liters.
Molarity = Moles of H2SO4 / Volume of Solution (L)
Volume of Solution (L) = 1 L
Molarity = 5.82 mol / 1 L = 5.82 M
Therefore, the answers are:
a. The mass percentage is 42.99%.
b. The mole fraction is 0.121.
c. The molality is 7.68 mol/kg.
d. The molarity of H2SO4 in this solution is 5.82 M.
To calculate the mass percentage, mole fraction, molality, and molarity of H2SO4 in the given sulfuric acid solution, we need to use the given information:
- Mass of H2SO4 per liter of solution: 571.6 g/L
- Density of the solution: 1.329 g/cm3
a. Mass Percentage (w/w):
Mass percentage is calculated by dividing the mass of the solute (H2SO4) by the mass of the solution and multiplying by 100.
Mass of H2SO4 = 571.6 g/L (given)
Mass of the solution = density × volume of the solution
The volume of the solution in liters can be calculated from the density:
1.329 g/cm3 = 1.329 g/mL
Density = Mass (g) / Volume (mL)
Volume (mL) = Mass (g) / Density
Since we are given the mass of the solution in grams per liter, we need to convert mL to L:
Volume (L) = (Mass (g) / Density) / 1000
Now we can calculate the mass percentage:
Mass percentage (w/w) = (Mass of H2SO4 / Mass of the solution) × 100
= (571.6 g / (Mass (g) / Density) / 1000) × 100
b. Mole Fraction (χ):
Mole fraction is calculated by dividing the moles of the solute (H2SO4) by the total moles of all components in the solution.
To calculate the moles of H2SO4, we need to know the molar mass of H2SO4:
H = 1.008 g/mol × 2 = 2.016 g/mol
S = 32.06 g/mol
O = 16.00 g/mol × 4 = 64.00 g/mol
Molar mass of H2SO4 = 2.016 g/mol + 32.06 g/mol + 64.00 g/mol = 98.08 g/mol
Moles of H2SO4 = Mass of H2SO4 / Molar mass of H2SO4
To calculate the total moles of all components, we need the molar mass of the solution, which can be calculated using the density of the solution:
Molar mass of the solution = Density (g/cm3) × 1000 (g/L) / Volume (L)
Mole fraction of H2SO4 = Moles of H2SO4 / Total moles of all components
c. Molality (m):
Molality is calculated by dividing the moles of the solute (H2SO4) by the mass of the solvent (water) in kg.
To calculate the molality, we need the moles of H2SO4 and the mass of the solvent (water).
d. Molarity (M):
Molarity is calculated by dividing the moles of the solute (H2SO4) by the volume of the solution in liters.
To calculate the molarity, we need the moles of H2SO4 and the volume of the solution.
By following these steps and using the given information, you should be able to calculate the mass percentage, mole fraction, molality, and molarity of H2SO4 in the solution.