A 250 mL container of CO2 exerting a pressure of 1.00 atm is connected through a valve to a 500 mL container of O2 exerting a pressure of 2.00 atm. When the valve is opened, the gases mix, forming a 750 mL mixture of CO2 and O2. What is the total pressure of this mixture? 3.00 atm 1.33 atm 2.50 atm 1.50 atm 1.67 atm
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 250 mL container of CO₂ exerting a pressure of 1.00 atm is connected through a valve to a 500 mL container of O₂ exerting a pressure of 2.00 atm. When the valve is opened, the gases mix, forming a 750 mL mixture of CO₂ and O₂. What is the total pressure of this mixture?
**Options:**
- 3.00 atm
- 1.33 atm
- 2.50 atm
- 1.50 atm
- 1.67 atm
**Explanation:**
To find the total pressure of the gas mixture, we can use the ideal gas law and the concept of partial pressures. Here's a step-by-step breakdown:
1. Calculate the moles of CO₂ using the relation P₁V₁ = nRT:
- Volume of CO₂ = 250 mL = 0.25 L
- Pressure of CO₂ = 1.00 atm
- Since temperature and R (ideal gas constant) are constant, find the initial number of moles.
2. Calculate the moles of O₂:
- Volume of O₂ = 500 mL = 0.5 L
- Pressure of O₂ = 2.00 atm
- Use the ideal gas relation similarly to find the initial number of moles.
3. Calculate the partial pressures in the new volume (750 mL = 0.75 L):
- Find the partial pressure contributed by CO₂ in 750 mL.
- Find the partial pressure contributed by O₂ in 750 mL.
4. Add the partial pressures to find the total pressure of the mixture.
This problem is essential for understanding gas laws, particularly Dalton's Law of Partial Pressures, and is crucial for students learning about chemical reactions and gas behavior.
**Answer:**
To solve the problem and select the correct option, apply the described calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F941d3a8f-f99f-475d-9938-4bf36f3c2918%2Fd8485180-3336-4d41-9ed5-53bfedad713a%2F63qrzz9_processed.png&w=3840&q=75)
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