3. An ideal gas is in a sealed container with a movable piston to keep the pressure constant. The gas has an initial volume of 10.0 L at a temperature of 10.0 °C. If the gas is heated to a temperature of 150 °C, what would you expect for the final volume? A. 6.69 L B. 14.9 L C. 22.4 L D. 88.0 L E. 150 L
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:**
An ideal gas is in a sealed container with a movable piston to keep the pressure constant. The gas has an initial volume of 10.0 L at a temperature of 10.0 °C. If the gas is heated to a temperature of 150 °C, what would you expect for the final volume?
**Options:**
A. 6.69 L
B. 14.9 L
C. 22.4 L
D. 88.0 L
E. 150 L (correct answer)
**Explanation:**
The problem requires the application of Charles's Law, which states that the volume of an ideal gas is directly proportional to its temperature when pressure is held constant. As the temperature increases, the volume increases proportionally, provided the temperature is measured in Kelvin.
**Key Points for Educational Understanding:**
1. **Convert Temperatures to Kelvin:**
- Initial Temperature (T1) = 10.0 °C = 283.15 K
- Final Temperature (T2) = 150 °C = 423.15 K
2. **Charles's Law Formula:**
\[
\frac{V1}{T1} = \frac{V2}{T2}
\]
Rearrange to find V2:
\[
V2 = V1 \times \frac{T2}{T1}
\]
3. **Calculation:**
- Initial Volume (V1) = 10.0 L
- V2 = 10.0 L × (423.15 K / 283.15 K) ≈ 14.9 L
4. **Conclusion:**
- The final volume expected for the gas when heated to 150 °C is approximately 14.9 L, making option B the correct choice. However, it seems the correct answer is highlighted as E (150 L), indicating possible typo in option marking.
This demonstrates understanding of gas laws and the importance of precise conversions and calculations in thermodynamics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ea102a8-ea29-42c9-bc12-ff472d16c24f%2F1e4b08e1-52a4-4a7a-acfa-061f997a3b90%2F89x8zm2_processed.png&w=3840&q=75)
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