Animated Solution for Chemistry - Basic Concepts in Chemistry: The strength of 11.2 volume solution of $H_2{O}_2$ is [Given that molar mass of $H=1{\text{ g mol}}^{-1}$ and $O=16{\text{ g mol}}^{-1}$]

Hydrogen peroxide ($H_2{O}_2$) is a fascinating chemical, often sold in pharmacies in dark brown bottles. If you look closely at the label, you might see a peculiar unit: "Volume". But what does "11.2 Volume" actually mean? It's not a measure of how loud the bottle is!

In chemistry, the volume strength of a hydrogen peroxide solution is a unique way to express its concentration. It tells us the volume of oxygen gas ($O_2$) that will be liberated at Standard Temperature and Pressure (STP) by the complete decomposition of exactly 1 litre (or 1 mL) of that solution.

So, an 11.2 volume solution means that 1 litre of this $H_2{O}_2$ solution will produce exactly 11.2 litres of $O_2$ gas at STP.

To translate this physical observation into a mathematical concentration, we must first understand the chemical reaction taking place. Hydrogen peroxide is inherently unstable and slowly decomposes into water and oxygen gas.

The balanced chemical equation is:

This equation is our master key. It tells us the exact stoichiometric ratio: 2 moles of hydrogen peroxide are required to produce 1 mole of oxygen gas.

Let's convert these moles into more tangible units like grams and litres.

The molar mass of $H_2{O}_2$ is calculated as $(2\times 1)+(2\times 16)=34\text{ g/mol}$. Therefore, 2 moles of $H_2{O}_2$ weigh $2\times 34=68\text{ g}$.

On the product side, we know from the ideal gas law that 1 mole of any ideal gas at STP occupies a volume of 22.4 litres.

Connecting these facts, we establish our fundamental stoichiometric bridge:

Now, let's bring it back to our specific bottle. Our solution doesn't produce 22.4 litres; it produces 11.2 litres of oxygen per litre of solution.

We can use a simple unitary method to find out how much $H_2{O}_2$ is hiding in our 1-litre bottle to produce this exact amount of gas:

Since 11.2 is exactly half of 22.4, the math is beautifully simple. The mass of $H_2{O}_2$ is half of 68, which is 34 grams.

This means that in every 1 litre (1000 mL) of our solution, there are exactly 34 grams of pure hydrogen peroxide.

The question asks for the percentage strength. In standard chemical contexts, unless specified otherwise, this refers to the percentage by weight ($\%w/w$) or weight by volume ($\%w/v$). For dilute aqueous solutions, the density is approximately $1\text{ g/mL}$, meaning 1000 mL of solution weighs roughly 1000 grams.

Let's calculate the percentage by weight:

Thus, the strength of the 11.2 volume $H_2{O}_2$ solution is 3.4%.

While deriving this from scratch builds great intuition, competitive exams demand speed. Here are two golden formulas you should memorize for $H_2{O}_2$ volume strength:

1. Molarity ($M$) = $\frac{\text{Volume Strength}}{11.2}$ 2. Normality ($N$) = $\frac{\text{Volume Strength}}{5.6}$

Using the first formula, the molarity of our solution is $\frac{11.2}{11.2}=1\text{ M}$. Since Molarity is moles per litre, we have 1 mole ($34\text{ g}$) in 1 litre ($1000\text{ mL}$). The percentage is simply $\frac{34}{1000}\times 100=3.4\%$. Both paths lead to the same elegant truth!