What will be the strength of 20 vol of `H_(2)O_(2)` in terms of gram per litre?

Options

A. `60.71 gL^(-1)`
B. `5.6 gL^(-1)`
C. `30.62 gL^(-1)`
D. `17 gL^(-1)`

Explanation

To find the strength of 20 volume of \( H_2O_2 \) in terms of grams per liter, we can follow these steps:

### Step 1: Understand the meaning of 20 volume \( H_2O_2 \)
20 volume \( H_2O_2 \) means that 1 liter of hydrogen peroxide will produce 20 liters of oxygen gas at standard temperature and pressure (STP).

### Step 2: Write the balanced chemical equation
The decomposition of hydrogen peroxide can be represented by the following balanced equation:
\[ 2 H_2O_2 \rightarrow 2 H_2O + O_2 \]
This shows that 2 moles of \( H_2O_2 \) produce 1 mole of \( O_2 \).

### Step 3: Relate moles of \( H_2O_2 \) to volume of \( O_2 \)
At STP, 1 mole of any gas occupies 22.4 liters. Therefore, 2 moles of \( H_2O_2 \) will produce:
\[ 2 \text{ moles } H_2O_2 \rightarrow 22.4 \text{ liters } O_2 \]

### Step 4: Calculate the mass of \( H_2O_2 \) needed to produce 20 liters of \( O_2 \)
Since 1 liter of \( H_2O_2 \) produces 20 liters of \( O_2 \), we can find how much \( H_2O_2 \) is needed to produce 22.4 liters of \( O_2 \):
\[ \text{Volume of } H_2O_2 = \frac{22.4 \text{ liters } O_2}{20} = 1.12 \text{ liters } H_2O_2 \]

### Step 5: Calculate the mass of \( H_2O_2 \)
The molar mass of \( H_2O_2 \) is 34 g/mol. Therefore, the mass of 1.12 liters of \( H_2O_2 \) can be calculated as follows:
- First, find the number of moles in 1.12 liters:
\[ \text{Number of moles} = \frac{1.12 \text{ liters}}{22.4 \text{ liters/mol}} = 0.05 \text{ moles} \]
- Now, calculate the mass:
\[ \text{Mass} = 0.05 \text{ moles} \times 34 \text{ g/mol} = 1.7 \text{ grams} \]

### Step 6: Calculate the strength in grams per liter
Since 1 liter of \( H_2O_2 \) gives us 20 liters of \( O_2 \), the strength of 20 volume \( H_2O_2 \) in grams per liter can be calculated as follows:
\[ \text{Strength} = \frac{68 \text{ grams}}{(22.4 \text{ liters}/20)} = \frac{68 \times 20}{22.4} \approx 60.71 \text{ grams per liter} \]

### Final Answer
The strength of 20 volume \( H_2O_2 \) is approximately **60.71 grams per liter**.

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