At 25.0° C, a 10.00 L vessel is filled with 5.25 moles of Gas A and 8.15 moles of Gas B. What is the total pressure in atm? atm 1 2 3 4 6. C 7 8 CO
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: Calculating Total Pressure in a Vessel**
**Problem Statement:**
At 25.0° C, a 10.00 L vessel is filled with 5.25 moles of Gas A and 8.15 moles of Gas B. What is the total pressure in atm?
**Instructions:**
1. Use the Ideal Gas Law to solve for the total pressure.
2. Remember that the total pressure is the sum of the partial pressures of the gases in the vessel.
**Equation:**
\[ PV = nRT \]
Where:
- \( P \) is the pressure in atm
- \( V \) is the volume in liters
- \( n \) is the number of moles
- \( R \) is the ideal gas constant (0.0821 L·atm/mol·K)
- \( T \) is the temperature in Kelvin
**Conversion:**
Convert the temperature from Celsius to Kelvin:
\[ T(K) = 25.0 + 273.15 = 298.15 \, K \]
**Total Moles:**
Total moles of gases = moles of Gas A + moles of Gas B
\[ n = 5.25 + 8.15 = 13.40 \, \text{moles} \]
**Calculations:**
Using the Ideal Gas Law, solve for \( P \):
\[ P = \frac{nRT}{V} \]
Substitute the values:
\[ P = \frac{(13.40 \, \text{moles})(0.0821 \, \text{L·atm/mol·K})(298.15 \, K)}{10.00 \, \text{L}} \]
Calculate to find the total pressure in atm.
**Note:**
Ensure your calculator is set to use the correct order of operations and unit conversions.
***Calculator Interface:***
A simple calculator interface is provided for manual calculation:
- Number buttons from 0 to 9
- Decimal point
- Plus/Minus sign
- "C" button to clear entries
- "x 10^" for scientific notation adjustments
This exercise helps students understand and apply gas laws in practical scenarios, strengthening problem-solving skills in chemistry.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7942b95-4b65-4fbc-b6c3-56b555608e9e%2F91800077-93c0-4490-ab25-cf2358264095%2F7lv41gi_processed.png&w=3840&q=75)
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