Understanding Molar Volume at STP
In chemistry, Standard Temperature and Pressure (STP) is defined as a temperature of 273.15 K ($0^\circ\text{C}$) and a pressure of 1 atm. A fundamental concept in gas laws is that one mole of any ideal gas occupies 22.4 litres at STP.
This relationship allows us to easily convert between the volume of a gas and the number of moles, and subsequently, the mass (or weight) of the substance.
The Problem Statement
Question: Calculate the weight of 11.2 litres of $\text{CO}_2$ gas at STP (Molecular Weight of $\text{CO}_2 = 44$).
Step-by-Step Solution
1. Identify the Given Data
- Volume ($V$) of $\text{CO}_2 = 11.2\text{ L}$
- Molecular Weight ($M$) of $\text{CO}_2 = 44\text{ g/mol}$
- Molar Volume at STP = $22.4\text{ L/mol}$
2. Calculate the Number of Moles ($n$)
We use the formula: $$n = \frac{\text{Given Volume}}{\text{Molar Volume at STP}}$$
Substituting the values: $$n = \frac{11.2\text{ L}}{22.4\text{ L/mol}} = 0.5\text{ moles}$$
3. Calculate the Mass (Weight)
The relationship between mass ($m$), moles ($n$), and molar mass ($M$) is: $$m = n \times M$$
Substituting our values: $$m = 0.5\text{ moles} \times 44\text{ g/mol}$$ $$m = 22\text{ grams}$$
Conclusion
The weight of 11.2 litres of carbon dioxide gas at STP is 22 grams.
Intuition Check
Since 22.4 litres represents exactly one mole, 11.2 litres represents half of that amount. Since one mole of $\text{CO}_2$ weighs 44 grams, it makes logical sense that half a mole weighs exactly 22 grams.