Understanding Molar Volume at NTP
In chemistry, the concept of the mole is central to understanding the quantity of a substance. When dealing with gases, we often use the property of Molar Volume.
At NTP (Normal Temperature and Pressure), which is defined as $0^\circ\text{C}$ (273.15 K) and 1 atmosphere of pressure, one mole of any ideal gas occupies a standard volume of 22.4 Liters (or 22,400 mL).
This relationship gives us a simple formula to find the number of moles ($n$):
$$n = \frac{\text{Volume of gas at NTP}}{\text{Molar volume at NTP}}$$
Solving the Problem
Question: How many moles of oxygen molecules are present in 112 mL of $O_2$ gas at NTP?
Step 1: Identify the given values
- Given Volume ($V$) = 112 mL
- Molar Volume ($V_m$) at NTP = 22,400 mL/mol
Step 2: Set up the calculation
Using our formula:
$$n = \frac{112 \text{ mL}}{22400 \text{ mL/mol}}$$
Step 3: Perform the division
$$n = \frac{112}{22400}$$
To simplify: $$n = \frac{1}{200}$$ $$n = 0.005 \text{ moles}$$
Answer: There are 0.005 moles of oxygen molecules in 112 mL of $O_2$ gas at NTP.
Key Takeaways
- Molar Volume Concept: Always remember that 1 mole of gas at NTP = 22.4 L = 22,400 mL.
- Unit Consistency: Ensure that the volume provided in the question matches the units of the molar volume constant (both in mL or both in L).
- Application: This method works for any ideal gas, regardless of its molecular identity (like $O_2$, $H_2$, or $CO_2$), because the volume depends on the number of particles, not the type of gas molecule.