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Let's go over the gas laws associated with each equation:

a. \( P_1V_1 = P_2V_2 \): This is **Boyle's Law**, which describes the inverse relationship between pressure and volume when temperature and the amount of gas are held constant.

b. \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \): This is **Charles's Law**, which states that the volume of a gas is directly proportional to its temperature (in Kelvin) when pressure and the amount of gas are constant.

c. \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \): This is **Gay-Lussac's Law**, which explains that the pressure of a gas is directly proportional to its temperature when volume and the amount of gas are constant.

d. \( PV = nRT \): This is the **Ideal Gas Law**, which combines several gas laws into one formula, where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.

If you have any more questions or need further details, feel free to ask!

### Related questions:
1. How can you derive the Ideal Gas Law from Boyle's, Charles's, and Gay-Lussac's laws?
2. What are the units typically used for the gas constant \( R \) in the Ideal Gas Law?
3. How does temperature affect gas pressure according to Gay-Lussac's Law?
4. What real-world applications use Boyle's Law?
5. How do assumptions in the Ideal Gas Law break down under real conditions?

### Tip:
Always make sure to convert temperatures to Kelvin when using gas law equations to avoid errors due to temperature units.

Identify which gas law goes with the following equations:
a. P1V1 = P2V2
b. V1/T1 = V2/T2
c. P1/T1 = P2/T2
d. PV = nRT

Learn how to identify gas laws such as Boyle's Law, Charles's Law, Gay-Lussac's Law, and the Ideal Gas Law from their corresponding equations. Suitable for students in Grades 9-12 and those studying thermodynamics.

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