# Combined Gas Law vs. Ideal Gas Law

## What's the Difference?

The Combined Gas Law and Ideal Gas Law are both equations used to describe the behavior of gases. However, they differ in terms of the variables they consider. The Combined Gas Law combines Boyle's Law, Charles's Law, and Gay-Lussac's Law into a single equation, allowing for changes in pressure, volume, and temperature. It states that the product of pressure and volume is directly proportional to the product of temperature and the number of moles of gas. On the other hand, the Ideal Gas Law incorporates all the variables mentioned in the Combined Gas Law, but also includes the ideal gas constant. This law states that the product of pressure, volume, and temperature is directly proportional to the number of moles of gas and the ideal gas constant. In summary, while the Combined Gas Law focuses on the relationship between pressure, volume, and temperature, the Ideal Gas Law encompasses all these variables along with the ideal gas constant.

## Comparison

Attribute | Combined Gas Law | Ideal Gas Law |
---|---|---|

Formula | P1V1/T1 = P2V2/T2 | PV = nRT |

Variables | P1, V1, T1, P2, V2, T2 | P, V, n, R, T |

Pressure | Measured in Pascals (Pa) | Measured in Pascals (Pa) |

Volume | Measured in cubic meters (m³) | Measured in cubic meters (m³) |

Temperature | Measured in Kelvin (K) | Measured in Kelvin (K) |

Number of moles | Not explicitly included | Measured in moles (mol) |

Ideal gas constant | Not used | 8.314 J/(mol·K) |

Applicability | Applicable to any gas | Applicable to ideal gases |

Assumptions | Assumes constant amount of gas | Assumes ideal behavior of gas particles |

## Further Detail

### Introduction

Gas laws are fundamental principles in the field of thermodynamics that describe the behavior of gases under different conditions. Two important gas laws are the Combined Gas Law and the Ideal Gas Law. While both laws are used to analyze the properties of gases, they have distinct attributes that make them applicable in different scenarios. In this article, we will explore and compare the attributes of the Combined Gas Law and the Ideal Gas Law.

### Combined Gas Law

The Combined Gas Law is a mathematical relationship that combines Boyle's Law, Charles's Law, and Gay-Lussac's Law. It allows us to analyze the changes in pressure, volume, and temperature of a gas sample when all three variables are altered simultaneously. The formula for the Combined Gas Law is:

**P1V1/T1 = P2V2/T2**

Here, P1 and P2 represent the initial and final pressures, V1 and V2 represent the initial and final volumes, and T1 and T2 represent the initial and final temperatures.

The Combined Gas Law is particularly useful when studying situations where all three variables change simultaneously. For example, if we have a gas sample in a closed container and we increase the pressure while simultaneously decreasing the volume and increasing the temperature, we can use the Combined Gas Law to determine the final state of the gas.

### Ideal Gas Law

The Ideal Gas Law is a fundamental equation in thermodynamics that relates the pressure, volume, and temperature of an ideal gas. Unlike the Combined Gas Law, the Ideal Gas Law assumes that the gas behaves ideally, meaning it follows certain assumptions such as negligible molecular size and no intermolecular forces. The formula for the Ideal Gas Law is:

**PV = nRT**

Here, P represents the pressure, V represents the volume, n represents the number of moles of gas, R is the ideal gas constant, and T represents the temperature in Kelvin.

The Ideal Gas Law is widely applicable in various scenarios, especially when dealing with ideal gases. It allows us to calculate the unknown variables of pressure, volume, temperature, or number of moles of gas when the other variables are known. This law is particularly useful in the study of gases in open systems, where the number of moles of gas remains constant.

### Comparison of Attributes

While both the Combined Gas Law and the Ideal Gas Law are used to analyze the behavior of gases, they have distinct attributes that make them suitable for different situations. Let's compare their attributes:

#### Variables

The Combined Gas Law considers the simultaneous changes in pressure, volume, and temperature. It allows us to determine the final state of a gas sample when all three variables change. On the other hand, the Ideal Gas Law relates pressure, volume, and temperature assuming a constant number of moles of gas. It allows us to calculate the unknown variables when the others are known.

#### Assumptions

The Combined Gas Law does not make any specific assumptions about the behavior of gases. It combines the individual gas laws to provide a general relationship between the variables. In contrast, the Ideal Gas Law assumes that the gas behaves ideally, meaning it follows certain assumptions such as negligible molecular size and no intermolecular forces. These assumptions make the Ideal Gas Law applicable to ideal gases under specific conditions.

#### Applicability

The Combined Gas Law is particularly useful when studying situations where all three variables change simultaneously. It allows us to analyze the behavior of gases in closed systems where pressure, volume, and temperature are interrelated. On the other hand, the Ideal Gas Law is widely applicable in various scenarios, especially when dealing with ideal gases. It is commonly used in open systems where the number of moles of gas remains constant.

#### Calculations

The Combined Gas Law involves algebraic manipulations of the equation to solve for the unknown variables. It requires the initial and final values of pressure, volume, and temperature to determine the relationship between them. On the other hand, the Ideal Gas Law requires the known values of three variables to calculate the unknown variable. It involves simple rearrangement of the equation to solve for the desired variable.

#### Limitations

The Combined Gas Law is limited to situations where all three variables change simultaneously. It cannot be used to analyze the behavior of gases when only one or two variables change while the others remain constant. The Ideal Gas Law, although widely applicable, is limited to ideal gases that follow the assumptions of the law. Real gases may deviate from ideal behavior at high pressures or low temperatures, requiring the use of more complex equations.

### Conclusion

In conclusion, the Combined Gas Law and the Ideal Gas Law are both important tools in the study of gases. While the Combined Gas Law allows us to analyze the behavior of gases when pressure, volume, and temperature change simultaneously, the Ideal Gas Law relates these variables assuming ideal gas behavior. The Combined Gas Law is useful in closed systems, while the Ideal Gas Law is applicable in open systems. Understanding the attributes and limitations of these gas laws enables scientists and engineers to accurately analyze and predict the behavior of gases in various scenarios.

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