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To calculate the mass and number of moles of carbon dioxide (CO₂) collected, we will use the **ideal gas law** equation:

\[
PV = nRT
\]

Where:
- \( P \) = Pressure (in atm)
- \( V \) = Volume (in liters)
- \( n \) = Number of moles (mol)
- \( R \) = Ideal gas constant = 0.0821 L·atm/mol·K
- \( T \) = Temperature (in Kelvin)

### Step 1: Convert the temperature to Kelvin.
The temperature is given as 4.0°C. To convert it to Kelvin:
\[
T(K) = T(°C) + 273.15 = 4.0 + 273.15 = 277.15 \, \text{K}
\]

### Step 2: Plug the given values into the ideal gas law.
- \( P = 0.420 \, \text{atm} \)
- \( V = 15.0 \, \text{L} \)
- \( R = 0.0821 \, \text{L} \cdot \text{atm}/\text{mol} \cdot \text{K} \)
- \( T = 277.15 \, \text{K} \)

Using the formula \( PV = nRT \), solve for \( n \) (number of moles):
\[
n = \frac{PV}{RT} = \frac{(0.420 \, \text{atm})(15.0 \, \text{L})}{(0.0821 \, \text{L} \cdot \text{atm}/\text{mol} \cdot \text{K})(277.15 \, \text{K})}
\]

Now, let's calculate \( n \).

\[
n = \frac{6.30}{22.759215} \approx 0.2767 \, \text{mol}
\]

### Step 3: Calculate the mass of CO₂.
The molar mass of CO₂ is:
\[
\text{Molar mass of CO}_2 = 12.01 \, \text{g/mol} + 2 \times 16.00 \, \text{g/mol} = 44.01 \, \text{g/mol}
\]

Now, multiply the number of moles by the molar mass to find the mass of CO₂:
\[
\text{Mass of CO}_2 = n \times \text{Molar mass} = 0.2767 \, \text{mol} \times 44.01 \, \text{g/mol} \approx 12.17 \, \text{g}
\]

### Final Answer:
- Number of moles: \( 0.277 \, \text{mol} \) (rounded to 3 significant figures)
- Mass: \( 12.2 \, \text{g} \) (rounded to 3 significant figures)

Would you like more details or have any further questions?

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Here are 5 related questions to explore:
1. How does the ideal gas law change for real gases?
2. What are the conditions under which the ideal gas law is most accurate?
3. How would the mass change if the gas collected was oxygen instead of carbon dioxide?
4. What is the significance of using significant figures in gas law calculations?
5. How does temperature affect the number of moles in a gas?

**Tip:** Always check the units to ensure consistency, especially when using gas law equations.

Carbon dioxide gas is collected at 4.0 °C in an evacuated flask with a measured volume of 15.0 L. When all the gas has been collected, the pressure in the flask is measured to be 0.420 atm. Calculate the mass and number of moles of carbon dioxide gas that were collected.

Learn how to calculate the mass and moles of carbon dioxide using the ideal gas law (PV = nRT). Given pressure (0.420 atm), volume (15.0 L), and temperature (4.0 °C), this problem applies gas law principles for students in Grades 10-12.

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