A sample of Cl₂ gas has a volume of 17.0 L at a pressure of 1.50 atm and a temperature of 23 °C. What volume, in liters, will the gas occupy at 3.50 atm and 281 °C? Assume ideal behavior. V- 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:**
*A sample of Cl₂ gas has a volume of 17.0 L at a pressure of 1.50 atm and a temperature of 23 °C.*
*What volume, in liters, will the gas occupy at 3.50 atm and 281 °C? Assume ideal behavior.*
**Answer:**
*V =* [Enter the calculated volume in liters] *L*
**Explanation:**
To solve this problem, apply the Ideal Gas Law and the combined gas law. You'd need to convert temperatures to Kelvin and use the formula:
\[
\frac{{P_1 \cdot V_1}}{{T_1}} = \frac{{P_2 \cdot V_2}}{{T_2}}
\]
Where:
- \(P_1\), \(V_1\), and \(T_1\) are the initial conditions.
- \(P_2\), \(V_2\), and \(T_2\) are the conditions under which you want to find the new volume \(V_2\).
Convert temperatures from Celsius to Kelvin by adding 273.15.
Given:
- \(P_1 = 1.50 \, \text{atm}\)
- \(V_1 = 17.0 \, \text{L}\)
- \(T_1 = 23\, ^{\circ}\text{C} = 296.15 \, \text{K}\)
- \(P_2 = 3.50 \, \text{atm}\)
- \(T_2 = 281 \, ^{\circ}\text{C} = 554.15 \, \text{K}\)
Substitute these values into the equation to solve for \(V_2\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb0d79c4c-40ce-427b-b4a0-26ffd9f423cd%2F043e4103-6103-4481-956a-e84219c285a2%2Fju1tp0g_processed.png&w=3840&q=75)
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