35ml sample of hydrogen peroxide gives off 500 ml of `O_2` at `27^@ C` and 1 atm pressure. Volume strength of `H_2 O_2` sample will be:

Options

A. 10 volume
B. 13 volume
C. 11 volume
D. 12 volume

Answer

To find the volume strength of the hydrogen peroxide (H₂O₂) sample, we will follow these steps:

### Step 1: Convert the given conditions to STP
We have a sample of hydrogen peroxide that produces 500 mL of oxygen at 27°C (300 K) and 1 atm pressure. We need to find out how much oxygen would be produced at standard temperature and pressure (STP), which is 0°C (273 K) and 1 atm.

### Step 2: Use the gas law to find the volume of oxygen at STP
Using the relation for gas volumes at different temperatures and pressures, we can set up the equation:

\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]

Where:
- \( V_1 = 500 \, \text{mL} \) (volume of oxygen at given conditions)
- \( T_1 = 300 \, \text{K} \) (temperature at given conditions)
- \( T_2 = 273 \, \text{K} \) (temperature at STP)
- \( V_2 \) is the volume of oxygen at STP that we need to find.

Rearranging the equation gives us:

\[ V_2 = V_1 \cdot \frac{T_2}{T_1} \]

Substituting the values:

\[ V_2 = 500 \cdot \frac{273}{300} \]

Calculating this:

\[ V_2 = 500 \cdot 0.91 = 455 \, \text{mL} \]

### Step 3: Determine the volume of oxygen produced per 1000 mL of H₂O₂
Now that we know that 35 mL of H₂O₂ produces 455 mL of oxygen at STP, we can find out how much oxygen would be produced from 1000 mL of H₂O₂.

Using the unitary method:

\[ \text{Volume of oxygen from 1000 mL of H₂O₂} = \frac{455}{35} \cdot 1000 \]

Calculating this gives:

\[ \text{Volume of oxygen} = 13,000 \, \text{mL} \, \text{or} \, 13 \, \text{L} \]

### Step 4: Determine the volume strength of H₂O₂
The volume strength of H₂O₂ is defined as the volume of oxygen produced by 1 mL of H₂O₂. Since we found that 1000 mL of H₂O₂ produces 13,000 mL of oxygen, the volume strength is:

\[ \text{Volume strength} = 13 \, \text{volumes} \]

### Final Answer
The volume strength of the H₂O₂ sample is **13 volumes**.

---