A Solution Of Hydrogen Peroxide Is 15.2% By Mass. What Is The Molarity Of The Solution? Assume That The Solution Has A Density Of 1.01g/Ml. Density Of 1.01g/ML.
The correct answer and explanation is :
To find the molarity of the hydrogen peroxide (H₂O₂) solution, we need to follow these steps:
Given:
- Mass percentage of H₂O₂ = 15.2% by mass
- Density of the solution = 1.01 g/mL
- Molar mass of H₂O₂ = 34.01 g/mol (approx.)
Step 1: Understanding the mass percentage
The mass percentage indicates that in 100 g of solution, there are 15.2 g of H₂O₂. Therefore, the amount of hydrogen peroxide in 100 g of solution is:
[
\text{Mass of H₂O₂} = 15.2 \, \text{g}
]
The remaining mass of the solution (100 g – 15.2 g) is water, which is 84.8 g.
Step 2: Find the volume of the solution
The density of the solution is given as 1.01 g/mL. Density is defined as:
[
\text{Density} = \frac{\text{Mass of solution}}{\text{Volume of solution}}
]
Rearranging to find the volume:
[
\text{Volume of solution} = \frac{\text{Mass of solution}}{\text{Density}} = \frac{100 \, \text{g}}{1.01 \, \text{g/mL}} \approx 99.01 \, \text{mL} = 0.09901 \, \text{L}
]
Step 3: Calculate moles of H₂O₂
Next, we calculate the moles of H₂O₂ in the solution. Using the molar mass of H₂O₂ (34.01 g/mol), the moles of H₂O₂ in 15.2 g of the solution is:
[
\text{Moles of H₂O₂} = \frac{\text{Mass of H₂O₂}}{\text{Molar mass of H₂O₂}} = \frac{15.2 \, \text{g}}{34.01 \, \text{g/mol}} \approx 0.447 \, \text{mol}
]
Step 4: Calculate the molarity
Finally, molarity (M) is defined as the number of moles of solute per liter of solution. Using the volume of the solution from Step 2:
[
\text{Molarity} = \frac{\text{Moles of H₂O₂}}{\text{Volume of solution in liters}} = \frac{0.447 \, \text{mol}}{0.09901 \, \text{L}} \approx 4.51 \, \text{M}
]
Conclusion:
The molarity of the hydrogen peroxide solution is approximately 4.51 M.
This process involves several steps to ensure accurate conversion of mass to moles, then using the solution’s volume to determine molarity. We used the density to find the volume of the solution and used the molar mass to convert the mass of hydrogen peroxide into moles.