What will be the mass of oxygen liberated by decomposition of 200 mL hydrogen peroxide solution with a strength of 34 g per litre ?

Options

A. `25.5 g`
B. `3.0 g`
C. `3.2 g`
D. `4.2 g`

Explanation

To solve the problem of finding the mass of oxygen liberated by the decomposition of 200 mL of hydrogen peroxide solution with a strength of 34 g per liter, we can follow these steps:

### Step 1: Calculate the mass of hydrogen peroxide in 200 mL of solution.
The strength of the solution is given as 34 g per liter. Since 1 liter is equal to 1000 mL, we can find the mass of hydrogen peroxide in 200 mL.

\[ \text{Mass of } H_2O_2 = \left(\frac{34 \text{ g}}{1000 \text{ mL}}\right) \times 200 \text{ mL} = 6.8 \text{ g} \]

### Step 2: Write the balanced chemical equation for the decomposition of hydrogen peroxide.
The decomposition of hydrogen peroxide can be represented by the following balanced equation:

\[ 2H_2O_2 \rightarrow 2H_2O + O_2 \]

From the equation, we see that 2 moles of hydrogen peroxide produce 1 mole of oxygen gas.

### Step 3: Determine the molar mass of hydrogen peroxide.
The molar mass of hydrogen peroxide (H2O2) can be calculated as follows:

\[ \text{Molar mass of } H_2O_2 = (2 \times 1) + (2 \times 16) = 2 + 32 = 34 \text{ g/mol} \]

### Step 4: Calculate the number of moles of hydrogen peroxide in 6.8 g.
Using the molar mass, we can calculate the number of moles of hydrogen peroxide:

\[ \text{Number of moles of } H_2O_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{6.8 \text{ g}}{34 \text{ g/mol}} = 0.2 \text{ moles} \]

### Step 5: Use the stoichiometry of the reaction to find the moles of oxygen produced.
From the balanced equation, we know that 2 moles of H2O2 produce 1 mole of O2. Therefore, the moles of O2 produced from 0.2 moles of H2O2 can be calculated as follows:

\[ \text{Moles of } O_2 = \frac{0.2 \text{ moles } H_2O_2}{2} = 0.1 \text{ moles } O_2 \]

### Step 6: Calculate the mass of oxygen produced.
The molar mass of oxygen (O2) is:

\[ \text{Molar mass of } O_2 = 2 \times 16 = 32 \text{ g/mol} \]

Now we can calculate the mass of oxygen produced:

\[ \text{Mass of } O_2 = \text{moles} \times \text{molar mass} = 0.1 \text{ moles} \times 32 \text{ g/mol} = 3.2 \text{ g} \]

### Final Answer:
The mass of oxygen liberated by the decomposition of 200 mL of hydrogen peroxide solution is **3.2 g**.

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