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.
![**Problem Statement:**
Calculate the molecular weight of a 3.39-liter sample of an unknown gas with a mass of 68.87 grams at STP (Standard Temperature and Pressure).
**Description:**
In this problem, you are given:
- Volume of the gas sample: 3.39 liters
- Mass of the gas sample: 68.87 grams
- Conditions: Standard Temperature and Pressure (STP), which means the temperature is 273.15 K (0°C) and the pressure is 1 atmosphere (atm).
To calculate the molecular weight (also known as molar mass) of the gas, you can use the Ideal Gas Law in conjunction with the definition of molecular weight.
**Relevant Formulas:**
1. **Ideal Gas Law:**
\[
PV = nRT
\]
Where:
- \( P \) is the pressure of the gas (in atm),
- \( V \) is the volume of the gas (in liters),
- \( n \) is the amount of substance (in moles),
- \( R \) is the gas constant (0.0821 L·atm/(K·mol)),
- \( T \) is the temperature (in Kelvin).
2. **Molecular Weight Formula:**
\[
\text{Molecular Weight} = \frac{\text{Mass}}{n}
\]
- Where the mass is given in grams, and \( n \) (number of moles) can be derived from the Ideal Gas Law.
3. At STP (Standard Temperature and Pressure):
\[
1 \text{ mole of an ideal gas occupies 22.414 liters}
\]
Based on this, the number of moles (\( n \)) can also be directly determined as:
\[
n = \frac{V}{22.414 \text{ L}}
\]
**Steps to Solve:**
1. Calculate the number of moles (\( n \)) of the gas using its volume at STP:
\[
n = \frac{3.39 \text{ L}}{22.414 \text{ L/mol}}
\]
2. Substitute \( n \) into the molecular weight formula to find the molecular weight.
**Solution Approach:**
1. Compute \( n \):
\[
n = \frac{3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4963a1b7-231e-4415-aa15-591e301cddd8%2F12f6abf9-22be-4c65-84a4-19f175beffd9%2Fnlvpq7.jpeg&w=3840&q=75)
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