Understanding the Concept
In chemistry, STP (Standard Temperature and Pressure) is a standardized condition defined as a temperature of 273.15 K ($0^\circ\text{C}$) and a pressure of 1 atm. A fundamental law in chemistry states that one mole of any ideal gas occupies a volume of 22.4 liters at STP.
To find the molecular mass (molar mass) of a gas, we need to relate the mass of the gas to the number of moles present.
The Relationship
- Avogadro's Law: 1 mole of any gas at STP = 22.4 L.
- Mole Concept: Number of moles ($n$) = $\frac{\text{Given Mass}}{\text{Molar Mass}}$
- Volume Relation: Number of moles ($n$) = $\frac{\text{Volume at STP (L)}}{22.4 \text{ L/mol}}$
Step-by-Step Solution
Given:
- Mass of the gas ($m$) = $16 \text{ g}$
- Volume of the gas ($V$) = $5.6 \text{ L}$
- Molar volume of gas at STP = $22.4 \text{ L/mol}$
Step 1: Calculate the number of moles ($n$) of the gas. Using the volume relation: $$n = \frac{V}{22.4} = \frac{5.6}{22.4}$$ $$n = 0.25 \text{ moles}$$
Step 2: Calculate the molecular mass ($M$). Using the mole formula: $$n = \frac{m}{M}$$ Rearranging to solve for $M$: $$M = \frac{m}{n}$$ $$M = \frac{16 \text{ g}}{0.25 \text{ mol}}$$ $$M = 64 \text{ g/mol}$$
Conclusion
The molecular mass of the gas is 64 g/mol.
Quick Summary
By identifying how many 'molar volumes' the gas occupies (in this case, 5.6/22.4 = 1/4 of a mole), we can easily determine that if 0.25 moles weighs 16 grams, then 1 full mole must weigh $16 \times 4 = 64$ grams.