A sample of nitrogen gas collected at a pressure of 1.24 atm and a temperature of 27.0 °C is found to occupy a volume of 22.7 liters. How many moles of N₂ gas are in the sample? mol
Ideal and Real Gases
Ideal gases obey conditions of the general gas laws under all states of pressure and temperature. Ideal gases are also named perfect gases. The attributes of ideal gases are as follows,
Gas Laws
Gas laws describe the ways in which volume, temperature, pressure, and other conditions correlate when matter is in a gaseous state. The very first observations about the physical properties of gases was made by Robert Boyle in 1662. Later discoveries were made by Charles, Gay-Lussac, Avogadro, and others. Eventually, these observations were combined to produce the ideal gas law.
Gaseous State
It is well known that matter exists in different forms in our surroundings. There are five known states of matter, such as solids, gases, liquids, plasma and Bose-Einstein condensate. The last two are known newly in the recent days. Thus, the detailed forms of matter studied are solids, gases and liquids. The best example of a substance that is present in different states is water. It is solid ice, gaseous vapor or steam and liquid water depending on the temperature and pressure conditions. This is due to the difference in the intermolecular forces and distances. The occurrence of three different phases is due to the difference in the two major forces, the force which tends to tightly hold molecules i.e., forces of attraction and the disruptive forces obtained from the thermal energy of molecules.
6a
![**Problem Statement:**
A sample of **nitrogen** gas collected at a pressure of **1.24 atm** and a temperature of **27.0 °C** is found to occupy a volume of **22.7 liters**. How many moles of \( \text{N}_2 \) gas are in the sample?
[Input Box: ______] mol
**Explanation:**
You are given a scenario involving a gas sample where you need to calculate the amount of substance in moles. The parameters provided are:
- **Pressure (P):** 1.24 atm
- **Temperature (T):** 27.0 °C
- **Volume (V):** 22.7 liters
To find the number of moles, you can use the Ideal Gas Law equation:
\[ PV = nRT \]
Where:
- \( P \) is the pressure,
- \( V \) is the volume,
- \( n \) is the number of moles,
- \( R \) is the ideal gas constant \((0.0821 \, \text{L} \cdot \text{atm/mol} \cdot \text{K})\),
- \( T \) is the temperature in Kelvin.
**Steps to Solve:**
1. Convert the temperature from Celsius to Kelvin: \( T(K) = 27.0 + 273.15 = 300.15 \, \text{K} \)
2. Rearrange the Ideal Gas Law to solve for \( n \): \[ n = \frac{PV}{RT} \]
3. Substitute the known values into the equation to find \( n \).
This exercise helps in understanding the application of the Ideal Gas Law in real-world scenarios.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe0f1975b-ad07-4857-b626-1368fa1e7067%2F83935cd1-dbe8-4e7e-9316-2a66dfa8434a%2Fe6ogd4_processed.png&w=3840&q=75)
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