The volume of \(CO_2\) produced at 37.0 °C and 1.00 atm is approximately 105.15 liters.
To calculate the volume of carbon dioxide (\(CO_2\)) produced, we can follow these steps:
1. **Find the moles of \(CO_2\) produced:**
\[ \text{moles of } CO_2 = \frac{\text{moles of CaCO}_3}{1} \]
\[ \text{moles of } CO_2 = \frac{4.06 \, \text{mol}}{1} \]
2. **Use the Ideal Gas Law to find the volume of \(CO_2\):**
\[ PV = nRT \]
\[ V = \frac{nRT}{P} \]
\[ V = \frac{(4.06 \, \text{mol})(0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K})(310.15 \, \text{K})}{1.00 \, \text{atm}} \]
3. **Solve for \(V\):**
\[ V = \frac{(4.06 \times 0.0821 \times 310.15)}{1.00} \]
\[ V \approx \frac{105.151}{1.00} \]
\[ V \approx 105.15 \, \text{L} \]
Therefore, the volume of \(CO_2\) produced at 37.0 °C and 1.00 atm is approximately 105.15 liters.