Calculate the Kelvin temperature to which 15.0 L of a gas at 26°C would have to be heated to change the volume to 29.0 L. The pressure and number of particles remain constant.
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:**
Calculate the Kelvin temperature to which 15.0 L of a gas at 26°C would have to be heated to change the volume to 29.0 L. The pressure and number of particles remain constant.
**Answer Box:**
\[ \square \] K
**Instructions for Solving:**
1. This problem involves the application of Charles's Law, which states that the volume of a gas is directly proportional to its temperature in Kelvin, assuming constant pressure and amount of gas.
2. The formula for Charles's Law is:
\[
\frac{V_1}{T_1} = \frac{V_2}{T_2}
\]
Where:
- \( V_1 \) = initial volume = 15.0 L
- \( T_1 \) = initial temperature in Kelvin
- \( V_2 \) = final volume = 29.0 L
- \( T_2 \) = final temperature in Kelvin
3. Convert the initial temperature from Celsius to Kelvin:
\[
T_1 = 26°C + 273.15 = 299.15 \, K
\]
4. Rearrange Charles's Law to solve for \( T_2 \):
\[
T_2 = \frac{V_2 \cdot T_1}{V_1}
\]
5. Perform the calculation to find \( T_2 \):
\[
T_2 = \frac{29.0 \, \text{L} \cdot 299.15 \, \text{K}}{15.0 \, \text{L}}
\]
Calculate the value to get the final Kelvin temperature.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faed2933e-b67f-42a0-9fac-b6dce0e828b0%2Ff74026ba-2dfe-4ddd-8652-8304268ea7c8%2Fpxqrhej.jpeg&w=3840&q=75)
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