A Gas At 300 K And 4.0 Atm Is Moved To A New Location With A Temperature Of 250 K. The Volume Changes From 5.5 L To 2.0 L. What Is The Pressure Of The Gas At The New Location?Use The Formula: P 1 V 1 T 1 = P 2 V 2 T 2 \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} T 1 ​ P 1 ​ V 1 ​ ​ = T 2 ​ P 2 ​ V 2 ​ ​

Understanding the Ideal Gas Law

The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It is expressed by the equation PV = nRT, where P is the pressure of the gas, V is the volume of the gas, n is the number of moles of the gas, R is the gas constant, and T is the temperature of the gas in Kelvin. In this article, we will use the ideal gas law to solve a problem involving a gas at different temperatures and pressures.

The Problem

A gas at 300 K and 4.0 atm is moved to a new location with a temperature of 250 K. The volume changes from 5.5 L to 2.0 L. What is the pressure of the gas at the new location?

Using the Ideal Gas Law to Solve the Problem

To solve this problem, we can use the formula:

$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$

where $P_1$ and $P_2$ are the initial and final pressures, $V_1$ and $V_2$ are the initial and final volumes, and $T_1$ and $T_2$ are the initial and final temperatures.

Step 1: Identify the Given Values

• $P_1$ = 4.0 atm
• $V_1$ = 5.5 L
• $T_1$ = 300 K
• $V_2$ = 2.0 L
• $T_2$ = 250 K

Step 2: Plug in the Values into the Formula

$\frac{4.0 \text{ atm} \times 5.5 \text{ L}}{300 \text{ K}} = \frac{P_2 \times 2.0 \text{ L}}{250 \text{ K}}$

Step 3: Simplify the Equation

$\frac{22 \text{ atm L}}{300 \text{ K}} = \frac{P_2 \times 2.0 \text{ L}}{250 \text{ K}}$

Step 4: Solve for $P_2$

$P_2 = \frac{22 \text{ atm L} \times 250 \text{ K}}{300 \text{ K} \times 2.0 \text{ L}}$

Step 5: Calculate the Value of $P_2$

$P_2 = \frac{5500}{600}$

$P_2 = 9.17 \text{ atm}$

Conclusion

In this article, we used the ideal gas law to solve a problem involving a gas at different temperatures and pressures. We applied the formula $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$ to find the pressure of the gas at the new location. The final answer is $P_2 = 9.17 \text{ atm}$.

Real-World Applications

The ideal gas law has numerous real-world applications in various fields, including:

• Chemical Engineering: The ideal gas law is used to design and optimize chemical processes, such as distillation and reaction systems.
• Materials Science: The ideal gas law is used to study the behavior of materials at high temperatures and pressures.
• Aerospace Engineering: The ideal gas law is used to design and optimize aircraft and spacecraft systems.

Limitations of the Ideal Gas Law

The ideal gas law is a simplified model that assumes ideal behavior of gases. However, real gases do not behave ideally, and the ideal gas law has several limitations, including:

• Non-ideal behavior: Real gases do not obey the ideal gas law at high pressures and low temperatures.
• Intermolecular forces: Real gases have intermolecular forces that affect their behavior.
• Quantum effects: Real gases have quantum effects that affect their behavior.

Conclusion

Understanding the Ideal Gas Law

The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It is expressed by the equation PV = nRT, where P is the pressure of the gas, V is the volume of the gas, n is the number of moles of the gas, R is the gas constant, and T is the temperature of the gas in Kelvin. In this article, we will use the ideal gas law to solve a problem involving a gas at different temperatures and pressures.

The Problem

A gas at 300 K and 4.0 atm is moved to a new location with a temperature of 250 K. The volume changes from 5.5 L to 2.0 L. What is the pressure of the gas at the new location?

Using the Ideal Gas Law to Solve the Problem

To solve this problem, we can use the formula:

$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$

where $P_1$ and $P_2$ are the initial and final pressures, $V_1$ and $V_2$ are the initial and final volumes, and $T_1$ and $T_2$ are the initial and final temperatures.

Step 1: Identify the Given Values

• $P_1$ = 4.0 atm
• $V_1$ = 5.5 L
• $T_1$ = 300 K
• $V_2$ = 2.0 L
• $T_2$ = 250 K

Step 2: Plug in the Values into the Formula

$\frac{4.0 \text{ atm} \times 5.5 \text{ L}}{300 \text{ K}} = \frac{P_2 \times 2.0 \text{ L}}{250 \text{ K}}$

Step 3: Simplify the Equation

$\frac{22 \text{ atm L}}{300 \text{ K}} = \frac{P_2 \times 2.0 \text{ L}}{250 \text{ K}}$

Step 4: Solve for $P_2$

$P_2 = \frac{22 \text{ atm L} \times 250 \text{ K}}{300 \text{ K} \times 2.0 \text{ L}}$

Step 5: Calculate the Value of $P_2$

$P_2 = \frac{5500}{600}$

$P_2 = 9.17 \text{ atm}$

Conclusion

In this article, we used the ideal gas law to solve a problem involving a gas at different temperatures and pressures. We applied the formula $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$ to find the pressure of the gas at the new location. The final answer is $P_2 = 9.17 \text{ atm}$.

Real-World Applications

The ideal gas law has numerous real-world applications in various fields, including:

• Chemical Engineering: The ideal gas law is used to design and optimize chemical processes, such as distillation and reaction systems.
• Materials Science: The ideal gas law is used to study the behavior of materials at high temperatures and pressures.
• Aerospace Engineering: The ideal gas law is used to design and optimize aircraft and spacecraft systems.

Limitations of the Ideal Gas Law

The ideal gas law is a simplified model that assumes ideal behavior of gases. However, real gases do not behave ideally, and the ideal gas law has several limitations, including:

• Non-ideal behavior: Real gases do not obey the ideal gas law at high pressures and low temperatures.
• Intermolecular forces: Real gases have intermolecular forces that affect their behavior.
• Quantum effects: Real gases have quantum effects that affect their behavior.

Q&A

Q: What is the ideal gas law? A: The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions.

Q: What is the formula for the ideal gas law? A: The formula for the ideal gas law is PV = nRT, where P is the pressure of the gas, V is the volume of the gas, n is the number of moles of the gas, R is the gas constant, and T is the temperature of the gas in Kelvin.

Q: How is the ideal gas law used to solve problems involving gases? A: The ideal gas law is used to solve problems involving gases by applying the formula $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$, where $P_1$ and $P_2$ are the initial and final pressures, $V_1$ and $V_2$ are the initial and final volumes, and $T_1$ and $T_2$ are the initial and final temperatures.

Q: What are some real-world applications of the ideal gas law? A: The ideal gas law has numerous real-world applications in various fields, including chemical engineering, materials science, and aerospace engineering.

Q: What are some limitations of the ideal gas law? A: The ideal gas law is a simplified model that assumes ideal behavior of gases. However, real gases do not behave ideally, and the ideal gas law has several limitations, including non-ideal behavior, intermolecular forces, and quantum effects.

Conclusion

In conclusion, the ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It has numerous real-world applications in various fields, including chemical engineering, materials science, and aerospace engineering. However, the ideal gas law has several limitations, including non-ideal behavior, intermolecular forces, and quantum effects.