What is the molarity of a commercial sample of `33.6` volume hydrogen peroxide solution?

Explanation

To find the molarity of a commercial sample of a 33.6 volume hydrogen peroxide solution, we can follow these steps:

### Step 1: Understand the Concept of Volume Strength
Volume strength is a measure of the amount of solute in a solution. For hydrogen peroxide (H₂O₂), 1 volume strength means that 1 liter of solution can release 1 liter of oxygen gas at standard temperature and pressure (STP).

### Step 2: Relate Volume Strength to Normality
The relationship between volume strength (VS) and normality (N) is given by the formula:
\[ \text{Volume Strength} = \text{Normality} \times 5.6 \]

### Step 3: Relate Normality to Molarity
Normality (N) can also be related to molarity (M) using the formula:
\[ \text{Normality} = \text{Molarity} \times n \]
where \( n \) is the number of equivalents. For hydrogen peroxide (H₂O₂), the \( n \) factor is 2 because it can donate two moles of hydrogen ions (H⁺) in reactions.

### Step 4: Combine the Formulas
Substituting the expression for normality into the volume strength equation gives:
\[ \text{Volume Strength} = (\text{Molarity} \times n) \times 5.6 \]
Replacing \( n \) with 2:
\[ \text{Volume Strength} = \text{Molarity} \times 2 \times 5.6 \]

### Step 5: Solve for Molarity
Rearranging the formula to find molarity:
\[ \text{Molarity} = \frac{\text{Volume Strength}}{2 \times 5.6} \]
Substituting the given volume strength of 33.6:
\[ \text{Molarity} = \frac{33.6}{2 \times 5.6} \]

### Step 6: Calculate the Molarity
Calculating the denominator:
\[ 2 \times 5.6 = 11.2 \]
Now substituting back:
\[ \text{Molarity} = \frac{33.6}{11.2} = 3 \]

### Final Answer
The molarity of the commercial sample of 33.6 volume hydrogen peroxide solution is **3 M**.

---