The molarity of 20 ml of 20 volumes `H_(2)O_(2)` is

Options

A. 0.9
B. 1.8
C. 2.7
D. 1.9

Answer

To find the molarity of 20 ml of 20 volumes of H₂O₂, we can follow these steps:

### Step 1: Understand the meaning of "20 volumes" of H₂O₂
"20 volumes" of H₂O₂ means that 1 liter (1000 ml) of H₂O₂ can produce 20 liters of oxygen gas (O₂) at standard temperature and pressure (STP).

### Step 2: Calculate the amount of oxygen produced
At STP, 1 mole of any gas occupies 22.4 liters. Therefore, to find the number of moles of O₂ produced from 20 volumes:

\[ \text{Moles of O}_2 = \frac{20 \text{ L}}{22.4 \text{ L/mol}} \approx 0.892 \text{ mol} \]

### Step 3: Relate moles of O₂ to moles of H₂O₂
From the decomposition reaction of hydrogen peroxide:

\[ 2 \text{ H}_2\text{O}_2 \rightarrow 2 \text{ H}_2\text{O} + \text{ O}_2 \]

This shows that 2 moles of H₂O₂ produce 1 mole of O₂. Therefore, to find the moles of H₂O₂ needed to produce 0.892 moles of O₂:

\[ \text{Moles of H}_2\text{O}_2 = 2 \times 0.892 \approx 1.784 \text{ mol} \]

### Step 4: Calculate the molarity of H₂O₂
Since we have calculated that 1.784 moles of H₂O₂ are present in 1 liter of solution, the molarity (M) is given by the formula:

\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume in liters}} \]

Here, the volume is 1 liter, so:

\[ \text{Molarity} = \frac{1.784 \text{ mol}}{1 \text{ L}} = 1.784 \text{ M} \]

### Step 5: Find the molarity in 20 ml
To find the molarity in 20 ml, we can convert 20 ml to liters:

\[ 20 \text{ ml} = 0.020 \text{ L} \]

The molarity remains the same, but if we want to find out how many moles are in 20 ml:

\[ \text{Moles in 20 ml} = \text{Molarity} \times \text{Volume in liters} = 1.784 \text{ mol/L} \times 0.020 \text{ L} = 0.03568 \text{ mol} \]

### Conclusion
The molarity of 20 ml of 20 volumes H₂O₂ is approximately 1.784 M, which can be rounded to 1.8 M.