If a sample of gas at constant pressure has a volume of 441 mL at 36.5 °C, what will its volume be if the temperature is increased to 77.6 °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 Behavior Under Temperature Change**
**Problem Statement:**
If a sample of gas at constant pressure has a volume of 441 mL at 36.5 °C, what will its volume be if the temperature is increased to 77.6 °C?
This question relates to the principles of gas behavior under constant pressure, typically described by Charles's Law. Charles's Law states that the volume of a gas is directly proportional to its temperature when measured in Kelvin. To solve this problem, we'll use the following formula derived from Charles's Law:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
Where:
- \( V_1 \) is the initial volume (441 mL),
- \( T_1 \) is the initial temperature in Kelvin (36.5 °C converted to Kelvin),
- \( V_2 \) is the final volume (unknown),
- \( T_2 \) is the final temperature in Kelvin (77.6 °C converted to Kelvin).
**Step-by-Step Solution:**
1. Convert the temperatures from Celsius to Kelvin:
\[ T_1 = 36.5 + 273.15 = 309.65 \text{ K} \]
\[ T_2 = 77.6 + 273.15 = 350.75 \text{ K} \]
2. Apply Charles's Law:
\[ \frac{441 \text{ mL}}{309.65 \text{ K}} = \frac{V_2}{350.75 \text{ K}} \]
3. Solve for \( V_2 \):
\[ V_2 = \frac{441 \text{ mL} \times 350.75 \text{ K}}{309.65 \text{ K}} \]
\[ V_2 \approx 499.15 \text{ mL} \]
Thus, if the temperature of the gas is increased to 77.6 °C, the volume of the gas will increase to approximately 499.15 mL.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F878f7b50-6050-483a-af47-6a6f18eb659f%2F15100a0a-7860-43fa-91cb-2d65e5049b6c%2Ff6n5yb_processed.jpeg&w=3840&q=75)
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