calculate the mole fraction of H2O2 hydrogen petoxide in a 1.15 M aqueous solution ,if the density of the solution is 1.11 g/cm3
The correct answer and explanation is :
To calculate the mole fraction of hydrogen peroxide (H₂O₂) in a 1.15 M aqueous solution, we will follow these steps:
Step 1: Calculate the mass of the solution.
Given:
- Molarity (M) of H₂O₂ solution = 1.15 M (mol/L)
- Density of the solution = 1.11 g/cm³
Molarity is defined as moles of solute per liter of solution, so:
[ \text{Moles of H₂O₂} = 1.15 \, \text{mol/L} \times 1 \, \text{L} = 1.15 \, \text{mol} ]
Next, we calculate the mass of the solution using its density:
Density is given as 1.11 g/cm³, and since 1 L = 1000 cm³, we find the mass of 1 L of solution:
[ \text{Mass of solution} = 1.11 \, \text{g/cm³} \times 1000 \, \text{cm³} = 1110 \, \text{g} ]
Step 2: Calculate the mass of H₂O₂ in the solution.
To do this, we need to know the molar mass of H₂O₂:
[ \text{Molar mass of H₂O₂} = 2 \times 1.008 + 2 \times 15.999 = 34.014 \, \text{g/mol} ]
The mass of H₂O₂ in the solution is:
[ \text{Mass of H₂O₂} = 1.15 \, \text{mol} \times 34.014 \, \text{g/mol} = 39.1 \, \text{g} ]
Step 3: Calculate the mass of water (solvent).
Since the total mass of the solution is the mass of H₂O₂ plus the mass of water, we can calculate the mass of water:
[ \text{Mass of water} = 1110 \, \text{g} – 39.1 \, \text{g} = 1070.9 \, \text{g} ]
Step 4: Calculate the moles of water.
The molar mass of water (H₂O) is:
[ \text{Molar mass of H₂O} = 2 \times 1.008 + 15.999 = 18.015 \, \text{g/mol} ]
The moles of water in the solution are:
[ \text{Moles of H₂O} = \frac{1070.9 \, \text{g}}{18.015 \, \text{g/mol}} = 59.4 \, \text{mol} ]
Step 5: Calculate the mole fraction of H₂O₂.
Mole fraction is defined as the ratio of the moles of solute to the total moles in the solution. The total moles in the solution are:
[ \text{Total moles} = 59.4 \, \text{mol of H₂O} + 1.15 \, \text{mol of H₂O₂} = 60.55 \, \text{mol} ]
The mole fraction of H₂O₂ is:
[
\text{Mole fraction of H₂O₂} = \frac{\text{Moles of H₂O₂}}{\text{Total moles}} = \frac{1.15 \, \text{mol}}{60.55 \, \text{mol}} = 0.0190
]
Conclusion:
The mole fraction of H₂O₂ in the 1.15 M aqueous solution is 0.0190.
Explanation:
The mole fraction represents the proportion of the total number of moles in the solution that is due to the solute (H₂O₂). In this case, the molarity of the solution gives us the moles of H₂O₂ in 1 liter of solution, which is 1.15 mol. By using the density of the solution, we can calculate the total mass of the solution, then determine the mass of H₂O₂ and subtract it from the total mass to find the mass of water. This allows us to find the moles of water and, ultimately, the mole fraction of H₂O₂. The mole fraction of H₂O₂ is very small, reflecting the fact that the solution is dilute, with water being the dominant component.