A cylinder is filled with 10.0 L of gas and a piston is put into it. The initial pressure of the gas is measured to be 128. kPa. The piston is now pushed down, compressing the gas, until the gas has a final volume of 5.20 L. Calculate the final pressure of the gas. Round your answer to 3 significant digits. gas kPa piston cylinder X
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.
![**Educational Content: Boyle's Law Application**
**Scenario: Compression of Gas in a Cylinder**
A cylinder is initially filled with 10.0 L of gas, and a piston is inserted into it. The initial pressure of the gas inside the cylinder is 128 kPa.
As the piston is pushed down, it compresses the gas, reducing its volume. The final volume of the gas inside the cylinder is 5.20 L. The task is to calculate the final pressure of the gas after compression, using the principles of Boyle's Law.
**Boyle's Law** states that the pressure of a given mass of gas is inversely proportional to its volume, provided the temperature remains constant. This can be mathematically expressed as:
\[ P_1 \times V_1 = P_2 \times V_2 \]
where:
- \( P_1 \) = Initial pressure
- \( V_1 \) = Initial volume
- \( P_2 \) = Final pressure
- \( V_2 \) = Final volume
**Calculate** the final pressure \( P_2 \) of the gas and round your answer to three significant digits.
**Diagram Explanation:**
The provided diagram illustrates a cylindrical container with gas inside it. There is a piston at the top, which can move up and down to compress or expand the gas. Labels in the diagram identify the "piston" and the "cylinder."
**Solution Steps:**
1. Identify the given values:
- \( V_1 = 10.0 \, \text{L} \)
- \( P_1 = 128 \, \text{kPa} \)
- \( V_2 = 5.20 \, \text{L} \)
2. Use Boyle's Law to find \( P_2 \):
\[ P_2 = \frac{P_1 \times V_1}{V_2} \]
\[ P_2 = \frac{128 \, \text{kPa} \times 10.0 \, \text{L}}{5.20 \, \text{L}} \]
3. Calculate and round the answer to three significant digits.
Click on "Check" to verify your calculated answer, or "Explanation" for detailed steps and solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe29df97a-ca2b-4b68-9729-7d6f03ce33cb%2F7be679cb-2172-435b-a3f2-464d8534d7fe%2F2nljda_processed.jpeg&w=3840&q=75)
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