Chemistry Gas Laws: Combined Gas Law: Videos & Practice Problems

Understanding the relationships between pressure, volume, and temperature is crucial in the study of gases. The combined gas law integrates Boyle's Law, Charles's Law, and Gay-Lussac's Law to establish a direct relationship between these variables. Boyle's Law indicates that pressure and volume are inversely proportional, while Charles's Law shows that volume is directly proportional to temperature. Similarly, Gay-Lussac's Law states that pressure is directly proportional to temperature. The combined gas law formula,

$\frac{PV}{T}=\mathrm{constant}$

allows us to predict how changes in one variable affect the others under different conditions, using the equation

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

when comparing two different sets of conditions. This law is fundamental in predicting the behavior of gases under varying pressures, volumes, and temperatures, which is essential in fields such as chemistry and physics.

Combined Gas Law

The combined gas law is a fundamental principle in chemistry that illustrates the relationship between pressure, volume, and temperature of a gas. It is derived from three key gas laws: Boyle's law, Charles' law, and Gay-Lussac's law. Each of these laws describes how one variable affects another under specific conditions.

Boyle's law states that pressure (P) is inversely proportional to volume (V) when temperature is held constant, which can be expressed mathematically as:

\[ P \propto \frac{1}{V} \]

Charles' law indicates that volume is directly proportional to temperature (T) when pressure is constant, represented as:

\[ V \propto T \]

Gay-Lussac's law asserts that pressure is directly proportional to temperature when volume is constant, which can be written as:

\[ P \propto T \]

By combining these relationships, we arrive at the combined gas law, which can be expressed as:

\[ \frac{PV}{T} = k \]

Here, \( k \) is a constant that represents the specific conditions of the gas being studied.

Furthermore, when comparing two sets of conditions for a gas, the combined gas law can be rearranged to:

\[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \]

This equation allows for the calculation of one variable when the others are known, making it a powerful tool in thermodynamics and gas behavior analysis.

Combined Gas Law Example

In this scenario, we are analyzing the behavior of a gas sample as its volume and temperature change, while the number of moles remains constant. Initially, the gas has a volume of 900 milliliters (0.900 liters), a temperature of 520 Kelvin, and a pressure of 1.85 atmospheres. When the volume decreases to 330 milliliters (0.330 liters) and the temperature increases to 770 Kelvin, we need to determine the new pressure, denoted as \( P_2 \).

To solve this problem, we utilize the combined gas law, which is derived from the ideal gas law \( PV = nRT \). Since the number of moles (n) and the gas constant (R) remain unchanged, we can express the relationship between the initial and final states of the gas as:

\[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \]

Here, \( P_1 \) is the initial pressure, \( V_1 \) is the initial volume, \( T_1 \) is the initial temperature, \( P_2 \) is the final pressure, \( V_2 \) is the final volume, and \( T_2 \) is the final temperature. Plugging in the known values:

\[ P_1 = 1.85 \, \text{atm}, \quad V_1 = 0.900 \, \text{L}, \quad T_1 = 520 \, \text{K} \]

\[ V_2 = 0.330 \, \text{L}, \quad T_2 = 770 \, \text{K} \]

We can rearrange the equation to isolate \( P_2 \):

\[ P_2 = \frac{P_1 V_1 T_2}{V_2 T_1} \]

Substituting the values into the equation gives:

\[ P_2 = \frac{(1.85 \, \text{atm}) \times (0.900 \, \text{L}) \times (770 \, \text{K})}{(0.330 \, \text{L}) \times (520 \, \text{K})} \]

After performing the calculations, we find that:

\[ P_2 \approx 7.47 \, \text{atm} \]

This result indicates that the pressure of the gas increases significantly due to the decrease in volume and the increase in temperature, demonstrating the principles of gas behavior as described by the combined gas law.

A 4.30 L gas has a pressure of 7.0 atm when the temperature is 60.0 ºC. What will be the temperature of the gas mixture if the volume and pressure are decreased to 2.45 L and 403.0 kPa respectively?

• A. 110 K
• B. 181 K
• C. 206 K
• D. 310 K
• E. 381 K

Answer: (A)

A sealed container with a movable piston contains a gas with a pressure of 1380 torr, a volume of 820 mL and a temperature of 31°C. What would the volume be if the new pressure is now 2.83 atm, while the temperature decreased to 25°C?

• A. 0.0253 L
• B. 0.167 L
• C. 0.326 L
• D. 0.516 L
• E. 1.46 L

Answer: (D)

Here’s what students ask on this topic:

What is the combined gas law?

The combined gas law is a fundamental principle in chemistry that combines three gas laws: Boyle's Law, Charles's Law, and Gay-Lussac's Law. This law relates the pressure, volume, and temperature of a fixed amount of gas. The combined gas law is expressed mathematically as:

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

Here, P1 and P2 are the initial and final pressures of the gas, V1 and V2 are the initial and final volumes of the gas, and T1 and T2 are the initial and final temperatures of the gas in Kelvin. This law assumes that the amount of gas and the number of molecules (n) are constant.

When using the combined gas law, it's important to remember that temperature must always be in Kelvin for the law to be applied correctly. The combined gas law is useful for predicting the behavior of a gas when it undergoes changes in pressure, volume, and temperature.

How can the combined gas law be solved?

The combined gas law is a relation between the pressure, volume, and temperature of a fixed amount of gas. It combines the principles of Boyle's law, Charles's law, and Gay-Lussac's law. The combined gas law formula is:

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

Here's how to solve a problem using the combined gas law:

1. Make sure all your units are consistent. Pressure (P) should be in atmospheres, volume (V) in liters, and temperature (T) in Kelvin. If they're not, convert them before proceeding.
2. Identify the known values (P1, V1, T1) for the initial state of the gas and the known values (P2, V2, T2) for the final state of the gas. One of these six values will be your unknown that you're solving for.
3. Rearrange the formula to solve for the unknown variable. For example, if you're solving for P2, the formula becomes:

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

4. Plug in the known values and calculate the answer.

Remember to keep track of significant figures based on the precision of the given values, and always check your final units to ensure they make sense for the variable you're solving for.

What is the formula for the combined gas law?

The combined gas law is a formula that combines the three individual gas laws: Boyle's Law, Charles's Law, and Gay-Lussac's Law. It shows the relationship between the pressure, volume, and temperature of a fixed amount of gas. The formula for the combined gas law is:

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

In this formula:

• P1 and P2 are the initial and final pressures of the gas, respectively.
• V1 and V2 are the initial and final volumes of the gas, respectively.
• T1 and T2 are the initial and final temperatures of the gas, measured in Kelvin.

To use the combined gas law, you need to make sure that the temperatures are in Kelvin and that the pressure and volume units are consistent between the initial and final states. This law is useful when you need to predict the behavior of a gas when more than one property (pressure, volume, or temperature) is changing.