Understanding Molar Volume at STP
In chemistry, STP stands for Standard Temperature and Pressure. It is defined as a temperature of 0°C (273.15 K) and a pressure of 1 atm. A fundamental rule in chemistry is that one mole of any ideal gas occupies a volume of 22.4 liters at STP.
To find the volume of a specific mass of gas, we follow a simple two-step process:
- Convert the mass of the gas into moles.
- Convert the number of moles into volume using the molar volume constant.
Step-by-Step Solution
Step 1: Calculate the Molar Mass of $CO_2$
To find the moles, we first need the molar mass of carbon dioxide ($CO_2$).
- Atomic mass of Carbon (C) ≈ 12 g/mol
- Atomic mass of Oxygen (O) ≈ 16 g/mol
The molar mass of $CO_2$ is: $$M = 12 + (2 \times 16) = 12 + 32 = 44 \text{ g/mol}$$
Step 2: Convert Mass to Moles
We use the formula: $n = \frac{m}{M}$ Where $m = 5.5 \text{ g}$ and $M = 44 \text{ g/mol}$.
$$n = \frac{5.5 \text{ g}}{44 \text{ g/mol}} = 0.125 \text{ moles}$$
Step 3: Calculate Volume at STP
Since 1 mole of gas occupies 22.4 L at STP, we multiply the number of moles by 22.4 L/mol:
$$V = n \times 22.4 \text{ L/mol}$$ $$V = 0.125 \text{ mol} \times 22.4 \text{ L/mol} = 2.8 \text{ Liters}$$
Final Answer
The volume occupied by 5.5 g of $CO_2$ at STP is 2.8 Liters.