Which Equation Represents the Combined Gas Law?
The combined gas law elegantly combines Boyle's, Charles's, and Gay-Lussac's laws to describe the relationship between pressure, volume, and temperature of a fixed amount of gas. Understanding this law is crucial in various scientific fields, from chemistry and physics to engineering. This article will explore the equation itself, its derivation, and answer frequently asked questions.
The equation representing the combined gas law is:
P₁V₁/T₁ = P₂V₂/T₂
Where:
- P₁ represents the initial pressure of the gas.
- V₁ represents the initial volume of the gas.
- T₁ represents the initial temperature of the gas (in Kelvin!).
- P₂ represents the final pressure of the gas.
- V₂ represents the final volume of the gas.
- T₂ represents the final temperature of the gas (in Kelvin!).
Why is the Temperature in Kelvin?
H2: Why must temperature be expressed in Kelvin when using the combined gas law?
The combined gas law, and indeed most gas laws, require the use of the Kelvin scale (absolute temperature). This is because the Kelvin scale starts at absolute zero, the theoretical point where all molecular motion ceases. Using Celsius or Fahrenheit would introduce a non-linear relationship, leading to inaccurate calculations. Kelvin avoids this issue by providing a direct proportionality between temperature and the kinetic energy of the gas particles. Therefore, always convert Celsius or Fahrenheit to Kelvin before applying the combined gas law. The conversion is straightforward: K = °C + 273.15.
What Happens if One Variable Remains Constant?
H2: What happens to the combined gas law if one of the variables (pressure, volume, or temperature) is held constant?
When one variable remains constant, the combined gas law simplifies to a different gas law:
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Constant Temperature (Isothermal Process): If the temperature (T₁ = T₂) remains constant, the equation simplifies to Boyle's Law: P₁V₁ = P₂V₂ (pressure and volume are inversely proportional).
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Constant Pressure (Isobaric Process): If the pressure (P₁ = P₂) remains constant, the equation simplifies to Charles's Law: V₁/T₁ = V₂/T₂ (volume and temperature are directly proportional).
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Constant Volume (Isochoric Process): If the volume (V₁ = V₂) remains constant, the equation simplifies to Gay-Lussac's Law: P₁/T₁ = P₂/T₂ (pressure and temperature are directly proportional).
How to Use the Combined Gas Law in Problem Solving?
H2: Can you provide an example of how to use the combined gas law to solve a problem?
Let's say a gas has an initial pressure of 1 atm, a volume of 2 L, and a temperature of 27°C (300 K). If the pressure is increased to 2 atm and the volume is decreased to 1 L, what will the final temperature be?
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Identify known variables: P₁ = 1 atm, V₁ = 2 L, T₁ = 300 K, P₂ = 2 atm, V₂ = 1 L.
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Apply the combined gas law: (1 atm)(2 L) / 300 K = (2 atm)(1 L) / T₂
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Solve for the unknown variable (T₂): T₂ = (2 atm)(1 L)(300 K) / (1 atm)(2 L) = 300 K
Therefore, the final temperature will be 300 K (27°C).
Limitations of the Combined Gas Law
H2: Does the combined gas law have any limitations?
The combined gas law is an idealization. It assumes that the gas behaves ideally, meaning that the gas particles have negligible volume and that there are no intermolecular forces between them. Real gases deviate from ideal behavior at high pressures and low temperatures. For accurate calculations under extreme conditions, more complex equations of state, such as the van der Waals equation, are necessary.
By understanding the combined gas law and its underlying principles, scientists and engineers can effectively predict and control the behavior of gases in a wide variety of applications. Remember to always convert temperatures to Kelvin for accurate results.
