A mixture of 100 mL of oxygen and 500 mL of hydrogen is reacted to form water . What is maximum theoretical decrease in volume at `25^@C` ?

Options

A. 30 mL
B. 300 mL
C. 100 mL
D. 500 mL

Answer

To determine the maximum theoretical decrease in volume when a mixture of oxygen and hydrogen reacts to form water, we can follow these steps:

### Step 1: Identify the initial volumes of gases
We have:
- Volume of Oxygen (O₂) = 100 mL
- Volume of Hydrogen (H₂) = 500 mL

### Step 2: Write the balanced chemical equation
The balanced chemical equation for the reaction between hydrogen and oxygen to form water is:
\[ 2H_2 + O_2 \rightarrow 2H_2O \]

### Step 3: Determine the stoichiometric ratios
From the balanced equation, we see that:
- 2 moles of H₂ react with 1 mole of O₂ to produce 2 moles of H₂O.

### Step 4: Calculate the limiting reactant
To find out how much of each gas will be consumed, we need to determine the limiting reactant.

Using the stoichiometric ratios:
- For every 1 mole of O₂, we need 2 moles of H₂.
- Therefore, 100 mL of O₂ would require \( 100 \, \text{mL} \times 2 = 200 \, \text{mL} \) of H₂.

Since we have 500 mL of H₂ available, O₂ is the limiting reactant.

### Step 5: Calculate the volume of water produced
According to the balanced equation, 1 mole of O₂ produces 2 moles of H₂O. Thus:
- 100 mL of O₂ will produce \( 100 \, \text{mL} \times 2 = 200 \, \text{mL} \) of H₂O.

### Step 6: Determine the total initial volume of gases
The total initial volume of gases is:
\[ 100 \, \text{mL (O₂)} + 500 \, \text{mL (H₂)} = 600 \, \text{mL} \]

### Step 7: Calculate the volume decrease
The volume of gases consumed in the reaction is:
- Volume of O₂ consumed = 100 mL
- Volume of H₂ consumed = 200 mL (as calculated)

Total volume of gases consumed:
\[ 100 \, \text{mL} + 200 \, \text{mL} = 300 \, \text{mL} \]

### Step 8: Calculate the maximum theoretical decrease in volume
The maximum theoretical decrease in volume is equal to the total volume of gases consumed:
\[ \text{Decrease in volume} = 300 \, \text{mL} \]

### Conclusion
Thus, the maximum theoretical decrease in volume when 100 mL of oxygen reacts with 500 mL of hydrogen to form water is **300 mL**.