How many litres of `CO_(2)` at STP wil be formed when 100mL of `0.1 M H_(2)SO_(4)` reacts with excess of `Na_(2)CO_(3)`?

Options

A. 22.4
B. 2.24
C. 0.224
D. 5.6

Answer

To determine how many liters of \( \text{CO}_2 \) will be formed when 100 mL of 0.1 M \( \text{H}_2\text{SO}_4 \) reacts with excess \( \text{Na}_2\text{CO}_3 \), we can follow these steps:

### Step 1: Write the balanced chemical equation
The reaction between sulfuric acid and sodium carbonate can be represented as:
\[ \text{H}_2\text{SO}_4 + \text{Na}_2\text{CO}_3 \rightarrow \text{Na}_2\text{SO}_4 + \text{CO}_2 + \text{H}_2\text{O} \]
From the equation, we can see that 1 mole of \( \text{H}_2\text{SO}_4 \) reacts with 1 mole of \( \text{Na}_2\text{CO}_3 \) to produce 1 mole of \( \text{CO}_2 \).

### Step 2: Calculate the number of moles of \( \text{H}_2\text{SO}_4 \)
To find the number of moles of \( \text{H}_2\text{SO}_4 \) in 100 mL of a 0.1 M solution, we use the formula:
\[ \text{Number of moles} = \text{Molarity} \times \text{Volume (L)} \]
Converting 100 mL to liters:
\[ 100 \text{ mL} = 0.1 \text{ L} \]
Now, substituting the values:
\[ \text{Number of moles of } \text{H}_2\text{SO}_4 = 0.1 \, \text{mol/L} \times 0.1 \, \text{L} = 0.01 \, \text{mol} \]

### Step 3: Determine the moles of \( \text{CO}_2 \) produced
From the balanced equation, we see that 1 mole of \( \text{H}_2\text{SO}_4 \) produces 1 mole of \( \text{CO}_2 \). Therefore, the number of moles of \( \text{CO}_2 \) produced will also be:
\[ \text{Number of moles of } \text{CO}_2 = 0.01 \, \text{mol} \]

### Step 4: Calculate the volume of \( \text{CO}_2 \) at STP
At standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 liters. Thus, the volume of \( \text{CO}_2 \) produced can be calculated as:
\[ \text{Volume of } \text{CO}_2 = \text{Number of moles} \times \text{Molar volume} \]
Substituting the values:
\[ \text{Volume of } \text{CO}_2 = 0.01 \, \text{mol} \times 22.4 \, \text{L/mol} = 0.224 \, \text{L} \]

### Final Answer
The volume of \( \text{CO}_2 \) produced at STP is **0.224 liters**.

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