A sample of krypton gas occupies a volume of 6.60 L at 52.0°C and 1.16 atm. If it is desired to increase the volume of the gas sample to 8.17 L, while decreasing its pressure to 0.785 atm, the temperature of the gas sample at the new volume and pressure must be °C.
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.
![**Gas Laws and Their Applications**
A sample of krypton gas occupies a volume of **6.60 L** at **52.0°C** and **1.16 atm**.
If it is desired to **increase** the volume of the gas sample to **8.17 L**, while **decreasing** its pressure to **0.785 atm**, the temperature of the gas sample at the new volume and pressure must be **_____**°C.
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To solve this, we'll use the combined gas law, which combines Boyle's Law, Charles's Law, and Gay-Lussac's Law:
\[
\frac{P_1 \times V_1}{T_1} = \frac{P_2 \times V_2}{T_2}
\]
Where:
- \( P_1 \) = Initial pressure (1.16 atm)
- \( V_1 \) = Initial volume (6.60 L)
- \( T_1 \) = Initial temperature (52.0°C + 273.15 = 325.15 K)
- \( P_2 \) = Final pressure (0.785 atm)
- \( V_2 \) = Final volume (8.17 L)
- \( T_2 \) = Final temperature (in Kelvin)
Rearranging to solve for \( T_2 \):
\[
T_2 = \frac{P_2 \times V_2 \times T_1}{P_1 \times V_1}
\]
Plugging in the values:
\[
T_2 = \frac{0.785 \times 8.17 \times 325.15}{1.16 \times 6.60}
\]
After calculating, convert \( T_2 \) from Kelvin back to Celsius:
\[
^oC = T_2 - 273.15
\]
Fill up the blank with the calculated temperature for educational purposes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa527ffdc-16df-4a1f-9953-96956a75d05e%2F910864d7-1c7b-4962-b2f4-d834f02cdb8f%2Flvva2i8.png&w=3840&q=75)
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