Using The Combined Gas Law Below, Identify The Variables That Would Be In The Numerator (A) And The Denominator (B) If You Were To Rearrange The Gas Law To Solve For Final Pressure.$\[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \\]$\[ P_2

Introduction

The combined gas law is a fundamental concept in chemistry that describes the relationship between the pressure, volume, and temperature of a gas. It is a combination of Boyle's Law, Charles' Law, and Gay-Lussac's Law, and is expressed mathematically as:

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

This equation is a powerful tool for solving problems involving gases, and is widely used in a variety of fields, including chemistry, physics, and engineering.

Rearranging the Gas Law to Solve for Final Pressure

In this article, we will explore how to rearrange the combined gas law to solve for final pressure. To do this, we need to isolate the variable $P_2$ on one side of the equation.

Step 1: Multiply Both Sides by $T_2$

The first step in rearranging the equation is to multiply both sides by $T_2$. This will allow us to eliminate the $T_2$ term from the denominator.

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

This simplifies to:

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

Step 2: Multiply Both Sides by $T_1$

Next, we need to multiply both sides by $T_1$ to eliminate the $T_1$ term from the denominator.

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

This simplifies to:

$P_1 V_1 T_2 = P_2 V_2 T_1$

Step 3: Divide Both Sides by $V_2 T_1$

Finally, we need to divide both sides by $V_2 T_1$ to isolate the variable $P_2$.

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

This simplifies to:

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

Conclusion

In conclusion, to rearrange the combined gas law to solve for final pressure, we need to multiply both sides by $T_2$, then multiply both sides by $T_1$, and finally divide both sides by $V_2 T_1$. This will give us the equation:

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

This equation can be used to solve for final pressure in a variety of problems involving gases.

Variables in the Numerator (A) and Denominator (B)

Based on the rearranged equation, we can identify the variables that would be in the numerator (A) and the denominator (B) as follows:

• Numerator (A): $P_1 V_1 T_2$
• Denominator (B): $V_2 T_1$

Key Takeaways

• The combined gas law is a fundamental concept in chemistry that describes the relationship between the pressure, volume, and temperature of a gas.
• To rearrange the gas law to solve for final pressure, we need to multiply both sides by $T_2$, then multiply both sides by $T_1$, and finally divide both sides by $V_2 T_1$.
• The variables in the numerator (A) and the denominator (B) are $P_1 V_1 T_2$ and $V_2 T_1$, respectively.

Applications of the Combined Gas Law

The combined gas law has a wide range of applications in various fields, including:

• Chemical Engineering: The combined gas law is used to design and optimize chemical processes, such as distillation and absorption.
• Physics: The combined gas law is used to describe the behavior of gases in various physical systems, such as thermodynamic systems.
• Biology: The combined gas law is used to describe the behavior of gases in living organisms, such as the respiratory system.

Conclusion

Introduction

The combined gas law is a fundamental concept in chemistry that describes the relationship between the pressure, volume, and temperature of a gas. In our previous article, we explored how to rearrange the combined gas law to solve for final pressure. In this article, we will answer some of the most frequently asked questions about the combined gas law.

Q: What is the combined gas law?

A: The combined gas law is a mathematical equation that describes the relationship between the pressure, volume, and temperature of a gas. It is a combination of Boyle's Law, Charles' Law, and Gay-Lussac's Law.

Q: What is the equation for the combined gas law?

A: The equation for the combined gas law is:

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

Q: How do I rearrange the combined gas law to solve for final pressure?

A: To rearrange the combined gas law to solve for final pressure, you need to multiply both sides by $T_2$, then multiply both sides by $T_1$, and finally divide both sides by $V_2 T_1$. This will give you the equation:

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

Q: What are the variables in the numerator (A) and the denominator (B) of the rearranged equation?

A: The variables in the numerator (A) and the denominator (B) of the rearranged equation are:

• Numerator (A): $P_1 V_1 T_2$
• Denominator (B): $V_2 T_1$

Q: What are some of the applications of the combined gas law?

A: The combined gas law has a wide range of applications in various fields, including:

• Chemical Engineering: The combined gas law is used to design and optimize chemical processes, such as distillation and absorption.
• Physics: The combined gas law is used to describe the behavior of gases in various physical systems, such as thermodynamic systems.
• Biology: The combined gas law is used to describe the behavior of gases in living organisms, such as the respiratory system.

Q: What are some of the limitations of the combined gas law?

A: The combined gas law assumes that the gas is ideal and that the volume of the gas is constant. In reality, gases are not ideal and their behavior can be affected by various factors, such as the presence of impurities and the shape of the container.

Q: How do I use the combined gas law to solve problems involving gases?

A: To use the combined gas law to solve problems involving gases, you need to:

1. Identify the given variables and the variable you need to solve for.
2. Rearrange the equation to solve for the desired variable.
3. Plug in the values of the given variables and solve for the desired variable.

Conclusion

In conclusion, the combined gas law is a powerful tool for solving problems involving gases. By understanding the equation and how to rearrange it to solve for final pressure, you can apply the combined gas law to a wide range of problems in chemistry, physics, and biology.

Common Mistakes to Avoid

• Not identifying the given variables and the variable you need to solve for.
• Not rearranging the equation correctly to solve for the desired variable.
• Not plugging in the values of the given variables correctly.

Tips and Tricks

• Use the combined gas law to solve problems involving gases in a variety of fields, including chemistry, physics, and biology.
• Rearrange the equation to solve for final pressure by multiplying both sides by $T_2$, then multiplying both sides by $T_1$, and finally dividing both sides by $V_2 T_1$.
• Use the variables in the numerator (A) and the denominator (B) to solve for the desired variable.