The strength of $11.2$ volume solution of $H_2O_2$ is : [Given that molar mass of $H = 1\, g$ $mol^{-1}$ and $O = 16\, g\, mol^{-1}]$
- $13.6\%$
- $3.4\%$
- $34\%$
- $1.7\%$
The Correct Option is B
Solution and Explanation
To solve this problem, we need to determine the strength (percentage concentration by weight/volume) of the $H_2O_2$ solution when it is given as an $11.2$ volume solution.
The term "volume strength" refers to the volume of oxygen gas (at standard temperature and pressure) that can be liberated from one volume of hydrogen peroxide solution. In this problem, an $11.2$ volume solution of $H_2O_2$ means that $1\, \text{L}$ of this solution releases $11.2\, \text{L}$ of oxygen gas on decomposition.
The balanced equation for the decomposition of hydrogen peroxide is:
\(2 H_2O_2 \rightarrow 2 H_2O + O_2\)
From this equation, we can infer that $68\, \text{g}$ of $H_2O_2$ produces $22.4\, \text{L}$ of $O_2$ at standard temperature and pressure because $2 \times 1 + 2 \times 16 = 34\, \text{g/mol}$, and the molar volume of a gas is $22.4\, \text{L}$ at STP.
Since $11.2\, \text{L}$ of $O_2$ is produced by $1\, \text{L}$ of the solution, we can write:
Step 1: Calculate the weight of $H_2O_2$ required to produce this volume:
\(\frac{68\, \text{g}}{22.4\, \text{L}} \times 11.2\, \text{L} = 34\, \text{g}\)
This implies that there are $34\, \text{g}$ of $H_2O_2$ in $1\, \text{L}$ of the solution.
Step 2: Calculate the percentage strength of the $H_2O_2$ solution:
The solution has $34\, \text{g}$ of $H_2O_2$ in $1000\, \text{ml}$, thus the percentage weight/volume ($w/v\%$) is:
\(\left(\frac{34}{1000}\right) \times 100 = 3.4\%\)
Therefore, the strength of the $11.2$ volume solution of $H_2O_2$ is $3.4\%$.
Conclusion: Option $3.4\%$ is the correct answer.
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Concepts Used:
Solutions
A solution is a homogeneous mixture of two or more components in which the particle size is smaller than 1 nm.
For example, salt and sugar is a good illustration of a solution. A solution can be categorized into several components.
Types of Solutions:
The solutions can be classified into three types:
- Solid Solutions - In these solutions, the solvent is in a Solid-state.
- Liquid Solutions- In these solutions, the solvent is in a Liquid state.
- Gaseous Solutions - In these solutions, the solvent is in a Gaseous state.
On the basis of the amount of solute dissolved in a solvent, solutions are divided into the following types:
- Unsaturated Solution- A solution in which more solute can be dissolved without raising the temperature of the solution is known as an unsaturated solution.
- Saturated Solution- A solution in which no solute can be dissolved after reaching a certain amount of temperature is known as an unsaturated saturated solution.
- Supersaturated Solution- A solution that contains more solute than the maximum amount at a certain temperature is known as a supersaturated solution.