In a 6.00 L pressure cooker, water is brought to a boil. If the final temperature is 115 °C at 3.45 bar, how many moles of steam are in the cooker? (R = 0.08314 L-bar/mol-K)
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.
![### Educational Content
#### Question 12 of 12
**Problem Statement:**
In a 6.00 L pressure cooker, water is brought to a boil. If the final temperature is 115 °C at 3.45 bar, how many moles of steam are in the cooker? (Given: \( R = 0.08314 \, \text{L·bar/mol·K} \))
**Concepts Involved:**
- **Ideal Gas Law**: The problem requires understanding the Ideal Gas Law, expressed as \( PV = nRT \), where:
- \( P \) = pressure in bar.
- \( V \) = volume in liters.
- \( n \) = number of moles of the gas.
- \( R \) = ideal gas constant (\(0.08314 \, \text{L·bar/mol·K}\)).
- \( T \) = temperature in Kelvin (K).
**Approach:**
1. **Convert Temperature to Kelvin:**
- \( T_{\text{K}} = 115 + 273.15 = 388.15 \, \text{K} \)
2. **Apply the Ideal Gas Law:**
- Rearrange the formula to solve for \( n \) (moles of steam):
\[
n = \frac{PV}{RT}
\]
- Substitute the known values into the equation:
\[
n = \frac{(3.45 \, \text{bar})(6.00 \, \text{L})}{(0.08314 \, \text{L·bar/mol·K})(388.15 \, \text{K})}
\]
**Calculation:**
- Perform the calculation to find the value of \( n \), representing the number of moles of steam.
#### Note:
There are no graphs or diagrams associated with this question. The focus is on applying the Ideal Gas Law to solve for the number of moles of gas in a given system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa04b93a0-8cb6-4c4e-81fa-ab66edf67455%2Fca50262c-f380-4386-942b-afbabfb9ef5a%2F1rhndx_processed.jpeg&w=3840&q=75)
Step by step
Solved in 2 steps with 2 images
