The volume of ascetylene at `NTP` produced by reaction of `50 gm` of `CaC_(2)` with water is : `CaC_(2)+H_(2)O rarr Ca(OH)_(2)+C_(2)H_(2)`

Options

A. `10L`
B. `17.5L`
C. `26.25L`
D. `35L`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Write the balanced chemical equation
The reaction between calcium carbide (CaC₂) and water (H₂O) can be represented as:
\[ \text{CaC}_2 + 2 \text{H}_2\text{O} \rightarrow \text{Ca(OH)}_2 + \text{C}_2\text{H}_2 \]

### Step 2: Calculate the molar mass of CaC₂
The molar mass of calcium carbide (CaC₂) can be calculated as follows:
- Atomic mass of Calcium (Ca) = 40.08 g/mol
- Atomic mass of Carbon (C) = 12.01 g/mol

Thus, the molar mass of CaC₂:
\[ \text{Molar mass of CaC}_2 = 40.08 + (2 \times 12.01) = 40.08 + 24.02 = 64.10 \, \text{g/mol} \]

### Step 3: Calculate the number of moles of CaC₂
Using the formula for moles:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]

Substituting the values:
\[ \text{Number of moles of CaC}_2 = \frac{50 \, \text{g}}{64.10 \, \text{g/mol}} \approx 0.781 \, \text{mol} \]

### Step 4: Determine the number of moles of C₂H₂ produced
From the balanced equation, we can see that 1 mole of CaC₂ produces 1 mole of C₂H₂. Therefore, the number of moles of C₂H₂ produced will also be:
\[ \text{Number of moles of C}_2\text{H}_2 = 0.781 \, \text{mol} \]

### Step 5: Calculate the volume of C₂H₂ at NTP
At Normal Temperature and Pressure (NTP), 1 mole of gas occupies 22.4 liters. Therefore, the volume of C₂H₂ produced can be calculated as:
\[ \text{Volume of C}_2\text{H}_2 = \text{Number of moles} \times 22.4 \, \text{L/mol} \]
\[ \text{Volume of C}_2\text{H}_2 = 0.781 \, \text{mol} \times 22.4 \, \text{L/mol} \approx 17.5 \, \text{L} \]

### Final Answer
The volume of acetylene (C₂H₂) produced at NTP is approximately **17.5 liters**.

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