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

Explanation

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

### Step 1: Calculate the molar mass of \( CaCO_3 \)
The molar mass of \( CaCO_3 \) can be calculated by adding the atomic masses of its constituent elements:
- Calcium (Ca): 40.08 g/mol
- Carbon (C): 12.01 g/mol
- Oxygen (O): 16.00 g/mol (there are 3 oxygen atoms)

\[ \text{Molar mass of } CaCO_3 = 40.08 + 12.01 + (16.00 \times 3) = 100.09 \text{ g/mol} \]

### Step 2: Calculate the number of moles of \( CaCO_3 \) in 50 g
Using the formula for moles:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

Substituting the values:

\[ \text{Number of moles of } CaCO_3 = \frac{50 \text{ g}}{100.09 \text{ g/mol}} \approx 0.4995 \text{ moles} \]

### Step 3: Use the stoichiometry of the reaction
From the decomposition reaction:

\[ CaCO_3 (s) \leftrightarrow CaO (s) + CO_2 (g) \]

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 \( CaCO_3 \) decomposed.

### Step 4: Calculate the number of moles of \( CO_2 \)
Since we have approximately 0.4995 moles of \( CaCO_3 \):

\[ \text{Number of moles of } CO_2 = 0.4995 \text{ moles} \]

### Conclusion
Thus, the number of moles of \( CO_2 \) obtained from the decomposition of 50 g of \( CaCO_3 \) is approximately 0.5 moles.

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