Chemistry
Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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### Chemical Reaction and Carbon Dioxide Volume Calculation

#### Problem Statement
What volume of carbon dioxide is produced when 16.1 g of calcium carbonate reacts completely according to the following reaction at 25°C and 1 atm?

#### Chemical Reaction
\[ \text{calcium carbonate (s)} \rightarrow \text{calcium oxide (s)} + \text{carbon dioxide(g)} \]

#### Data Input
* Mass of calcium carbonate: 16.1 g
* Temperature: 25°C
* Pressure: 1 atm

#### Data Required
* Volume of carbon dioxide produced (in liters)

#### Procedure
1. **Identify the molar mass of calcium carbonate (CaCO₃)**:
   - Calcium (Ca): 40.08 g/mol
   - Carbon (C): 12.01 g/mol
   - Oxygen (O): 16.00 g/mol (x 3)
   - Molar mass of CaCO₃ = 40.08 + 12.01 + (16.00 x 3) = 100.09 g/mol

2. **Calculate the moles of calcium carbonate**:
   \[
   \text{Moles of CaCO₃} = \frac{\text{mass of CaCO₃}}{\text{molar mass of CaCO₃}} = \frac{16.1\ g}{100.09\ g/mol}
   \]

3. **Use the stoichiometry of the reaction**:
   - The reaction shows a 1:1 molar ratio between CaCO₃ and CO₂.
   - Therefore, moles of CaCO₃ will equal moles of CO₂ produced.

4. **Calculate the volume of CO₂ produced**:
   - Use the Ideal Gas Law: PV = nRT
   - Where:
     - P is the pressure (1 atm),
     - V is the volume,
     - n is the number of moles,
     - R is the gas constant (0.0821 L atm / K mol),
     - T is the temperature in Kelvin (25°C + 273.15 = 298.15 K).
   \[
   V = \frac{nRT}{P} = \frac{(\text{moles of CO₂}) \cdot (0.0821\ L\ atm / K\ mol) \cdot (298.
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Transcribed Image Text:### Chemical Reaction and Carbon Dioxide Volume Calculation #### Problem Statement What volume of carbon dioxide is produced when 16.1 g of calcium carbonate reacts completely according to the following reaction at 25°C and 1 atm? #### Chemical Reaction \[ \text{calcium carbonate (s)} \rightarrow \text{calcium oxide (s)} + \text{carbon dioxide(g)} \] #### Data Input * Mass of calcium carbonate: 16.1 g * Temperature: 25°C * Pressure: 1 atm #### Data Required * Volume of carbon dioxide produced (in liters) #### Procedure 1. **Identify the molar mass of calcium carbonate (CaCO₃)**: - Calcium (Ca): 40.08 g/mol - Carbon (C): 12.01 g/mol - Oxygen (O): 16.00 g/mol (x 3) - Molar mass of CaCO₃ = 40.08 + 12.01 + (16.00 x 3) = 100.09 g/mol 2. **Calculate the moles of calcium carbonate**: \[ \text{Moles of CaCO₃} = \frac{\text{mass of CaCO₃}}{\text{molar mass of CaCO₃}} = \frac{16.1\ g}{100.09\ g/mol} \] 3. **Use the stoichiometry of the reaction**: - The reaction shows a 1:1 molar ratio between CaCO₃ and CO₂. - Therefore, moles of CaCO₃ will equal moles of CO₂ produced. 4. **Calculate the volume of CO₂ produced**: - Use the Ideal Gas Law: PV = nRT - Where: - P is the pressure (1 atm), - V is the volume, - n is the number of moles, - R is the gas constant (0.0821 L atm / K mol), - T is the temperature in Kelvin (25°C + 273.15 = 298.15 K). \[ V = \frac{nRT}{P} = \frac{(\text{moles of CO₂}) \cdot (0.0821\ L\ atm / K\ mol) \cdot (298.
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