In the electrolysis of aqueous `NaCl` ,what volume of `Cl_2`(g) is produced in the time that it takes to liberate 5.0 liter of `H_2`(g) ? Assume that both gases are measured at STP.

Options

A. 5
B. 2.5
C. 7.5
D. 10

Answer

To solve the problem of how much chlorine gas is produced during the electrolysis of aqueous NaCl when 5.0 liters of hydrogen gas is liberated, we can follow these steps:

### Step 1: Understand the Electrolysis Process
In the electrolysis of aqueous NaCl:
- At the anode (positive electrode), chlorine gas (Cl₂) is produced.
- At the cathode (negative electrode), hydrogen gas (H₂) is produced.

The overall reaction can be summarized as:
\[ \text{NaCl (aq)} + 2 \text{H}_2\text{O (l)} \rightarrow \text{NaOH (aq)} + \text{Cl}_2(g) + \text{H}_2(g) \]

### Step 2: Determine the Moles of Hydrogen Gas
Given that 5.0 liters of hydrogen gas is liberated, we need to convert this volume into moles using the molar volume of a gas at STP (Standard Temperature and Pressure), which is 22.4 liters per mole.

The number of moles of hydrogen gas (H₂) can be calculated as:
\[ \text{Moles of } H_2 = \frac{\text{Volume of } H_2}{\text{Molar Volume}} = \frac{5.0 \, \text{liters}}{22.4 \, \text{liters/mole}} \approx 0.223 \, \text{moles} \]

### Step 3: Relate Moles of Hydrogen to Moles of Chlorine
From the balanced electrolysis reaction, we see that the production of hydrogen gas and chlorine gas is in a 1:1 molar ratio. This means that for every mole of H₂ produced, one mole of Cl₂ is also produced.

Thus, the moles of chlorine gas produced will also be:
\[ \text{Moles of } Cl_2 = 0.223 \, \text{moles} \]

### Step 4: Convert Moles of Chlorine to Volume
Now, we can convert the moles of chlorine gas back into volume at STP using the molar volume:
\[ \text{Volume of } Cl_2 = \text{Moles of } Cl_2 \times \text{Molar Volume} = 0.223 \, \text{moles} \times 22.4 \, \text{liters/mole} \approx 5.0 \, \text{liters} \]

### Conclusion
Therefore, the volume of chlorine gas produced in the time it takes to liberate 5.0 liters of hydrogen gas is:
\[ \text{Volume of } Cl_2 = 5.0 \, \text{liters} \]

### Final Answer
The volume of chlorine gas produced is **5.0 liters**.

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