A flexible container at an initial volume of 8.15 L contains 8.51 mol of gas. More gas is then added to the container until it reaches a final volume of 18.7 L. Assuming the pressure and temperature of the gas remain constant, calculate the number of moles of gas added to the container. number of moles of gas: mol
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 flexible container at an initial volume of 8.15 L contains 8.51 mol of gas. More gas is then added to the container until it reaches a final volume of 18.7 L. Assuming the pressure and temperature of the gas remain constant, calculate the number of moles of gas added to the container.
**Calculation Area:**
Number of moles of gas: [ _______ ] mol
---
**Explanation:**
This problem involves the application of the Ideal Gas Law in the context of the addition of gas to a system at constant pressure and temperature.
### Steps to Solve:
1. **Use the formula**:
\[
\text{PV} = \text{nRT}
\]
Since temperature (T) and pressure (P) are constant, the ratio \(\frac{V}{n}\) is also a constant.
2. **Initial state**:
- Volume (\(V_1\)) = 8.15 L
- Moles (\(n_1\)) = 8.51 mol
3. **Final state**:
- Volume (\(V_2\)) = 18.7 L
- Moles (\(n_2\)) = Unknown (we need to find this)
4. **Relate initial and final states** using: \(\frac{V_1}{n_1} = \frac{V_2}{n_2}\)
5. **Solve for \(n_2\)**:
\[
n_2 = \frac{V_2 \times n_1}{V_1}
\]
6. **Calculate the moles of gas added**:
\[
\text{Moles added} = n_2 - n_1
\]
Use these equations to find the number of moles added to the gas.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F533a1d18-b384-417a-b88f-3a32b213f48c%2Fe4c75319-8b38-48c6-b5be-e7ecd84aef71%2Fvgw85if_processed.jpeg&w=3840&q=75)
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