# Which of the following is consistent with Avogadro’s law?

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A. #P/T# = constant (V, n constant)

B. #V/T# = constant (P, n constant)

C. #Vn# = constant (P, T constant)

D. #V/n# = constant (P, T constant)

So I tried rearranging the ideal gas law and moved everything that is constant onto one side and the variables to the other, but that tells me that both B and D are correct.

Example of what I mean:

Ideal gas law: #PV=nRT#

Move constants on one side and variables on another for answer B: #(nR)/P=V/T#

Answer D: #(RT)/P=V/n#

The correct answer is D, however, can someone please explain why what I'm doing is wrong and explain the correct answer?

A.

B.

C.

D.

So I tried rearranging the ideal gas law and moved everything that is constant onto one side and the variables to the other, but that tells me that both B and D are correct.

Example of what I mean:

Ideal gas law:

Move constants on one side and variables on another for answer B:

Answer D:

The correct answer is D, however, can someone please explain why what I'm doing is wrong and explain the correct answer?

##### 1 Answer

Option **D)** is indeed correct.

#### Explanation:

Keep in mind that **Avogadro's Law** is used to describe the behavior of an ideal gas under a very specific set of circumstances.

More specifically, in order for Avogadro's Law to apply, the *temperature* **and** the *pressure* of the gas must be kept **constant**.

Avogadro's Law states that when the temperature and the pressure of a gas are kept constant, the *volume* of the gas is **directly proportional** to the *number of moles* present in the sample.

#color(blue)(ul(color(black)("when T and P are constant" => V prop n)))#

In other words, when the number of moles of gas **increases**, the volume of the gas will *increase* as well. Similarly, when the number of moles of gas **decreases**, the volume of the gas will *decrease* as well.

So right from the start, options **A)** and **B)** are eliminated. Now, the direct relationship that exists between

#color(blue)(ul(color(black)(V/n = "constant")))#

*Why is that the case?*

Notice that when **increases**, the only way for the ratio **increases** by the **same factor** as

This is not what happens for

#V * n = "constant"#

In this case, when **increases**, the only way for the product **decreases** by the same fact as

Therefore, you can say that option **D)** is correct.

You can get the same result by rearranging the ideal gas law equation

#color(blue)(ul(color(black)(PV = nRT)))#

to isolate the *constants* on one side of the equation. In this case, you will have

#PV = nRT#

#V = (nRT)/P#

Divide both sides by

#V/n = (RT)/P implies color(blue)(ul(color(black)(V/n = "constant")))#

So remember, Avogadro's Law applies **only** to cases where the pressure and the temperature are **constant**.