Understanding the Problem
To calculate the volume of a gas at Normal Temperature and Pressure (NTP), we need to bridge the gap between mass (grams) and volume (liters).
The Question: Calculate the volume of 11 g of CO₂ at NTP.
The Concept: Molar Volume
In chemistry, one of the most useful constants is the molar volume of an ideal gas at NTP.
- NTP (Normal Temperature and Pressure) is typically defined as 273.15 K (0°C) and 1 atm pressure.
- Under these conditions, 1 mole of any ideal gas occupies exactly 22.4 liters (L).
To solve this, we follow these two steps:
- Convert mass (grams) to moles.
- Convert moles to volume (liters) using the molar volume constant.
Step-by-Step Calculation
Step 1: Find the Molar Mass of CO₂
First, we look at the atomic masses of Carbon (C) and Oxygen (O):
- Atomic mass of C = 12 g/mol
- Atomic mass of O = 16 g/mol
The molar mass of CO₂ is calculated as: \[ \text{Molar mass} = 12 + (2 \times 16) = 12 + 32 = 44 \text{ g/mol} \]
Step 2: Calculate the Number of Moles
We use the formula: \[ n = \frac{\text{mass}}{\text{molar mass}} \]
Plugging in our values: \[ n = \frac{11 \text{ g}}{44 \text{ g/mol}} = 0.25 \text{ moles} \]
Step 3: Calculate the Volume at NTP
Since 1 mole occupies 22.4 L, we multiply the number of moles by 22.4 L/mol: \[ \text{Volume} = n \times 22.4 \text{ L/mol} \] \[ \text{Volume} = 0.25 \times 22.4 = 5.6 \text{ L} \]
Conclusion
The volume occupied by 11 g of CO₂ at NTP is 5.6 Liters.