Calcium carbonate decomposes on heating according to the following equations:
`CaCO_(3)(s) Leftrightarrow CaO(s)+CO_(2)(g)`
How many moles of `CO_(2)` will be obtained by decomposition of 50g of `CaCO_(3)`?

Options

A. `3/2`
B. `5/2`
C. `1/2`
D. 1

Answer

To solve the problem of how many moles of \( CO_2 \) will be obtained by the decomposition of 50 g of \( CaCO_3 \), we can follow these steps:

### Step 1: Write the decomposition reaction
The decomposition of calcium carbonate is given by the equation:
\[ CaCO_3(s) \leftrightarrow CaO(s) + CO_2(g) \]

### Step 2: Determine the molar mass of \( CaCO_3 \)
To find the number of moles, we first need to calculate the molar mass of \( CaCO_3 \):
- Calcium (Ca) = 40.08 g/mol
- Carbon (C) = 12.01 g/mol
- Oxygen (O) = 16.00 g/mol (and there are 3 oxygen atoms)

Calculating the molar mass:
\[ Molar \, mass \, of \, CaCO_3 = 40.08 + 12.01 + (3 \times 16.00) = 100.09 \, g/mol \]

### Step 3: Calculate the number of moles of \( CaCO_3 \)
Using the formula for moles:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]
Substituting the values:
\[ \text{Number of moles of } CaCO_3 = \frac{50 \, g}{100.09 \, g/mol} \approx 0.4995 \, moles \]

### Step 4: Relate moles of \( CaCO_3 \) to moles of \( CO_2 \)
From the balanced equation, we see that 1 mole of \( CaCO_3 \) produces 1 mole of \( CO_2 \). Therefore, the number of moles of \( CO_2 \) produced will be equal to the number of moles of \( CaCO_3 \):
\[ \text{Number of moles of } CO_2 = \text{Number of moles of } CaCO_3 \approx 0.4995 \, moles \]

### Step 5: Round the answer
For practical purposes, we can round the number of moles of \( CO_2 \) to:
\[ \text{Number of moles of } CO_2 \approx 0.5 \, moles \]

### Final Answer
The number of moles of \( CO_2 \) obtained by the decomposition of 50 g of \( CaCO_3 \) is approximately **0.5 moles**.

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