Which of the following is not a valid equation for describing the behavior of
gases?
A. (P1/V1) = (P2/V2)
B. PV = nRT
C. P1V1 = P2V2
D. (V2/T1) = (V2/T2)

A. (P1/V1) = (P2/V2) is not a valid equation

D. (V2/T1) =V2/T2) is not a valid equation.  ( V1/T1) = (V2/T2) is a valid equation

Explanation:

Step 1: Data given

The gas law is p*V = nRT (this means option B is a valid equation)

If we compare 2 gases we can write this as:

p1*V1 / ( n1*R*T1 ) = p2*V2 / ( n2*R*T2 )

Step 2: When temperature and number of moles are constant

This means volume and pressure will change.

p1*V1 / ( n1*R*T1 ) = p2*V2 / ( n2*R*T2 )  OR p1¨V1 = p2*V2

The relationship for Boyle’s Law can be expressed as follows: p1V1 = p2V2, where p1 and V1 are the initial pressure and volume values, and p2 and V2 are the changed values of the pressure and volume of the gas.

When the initial pressure rises, the initial volume will decrease (and vice versa). For a fixed mass of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional.

For the formula (P1/V1) = (P2/V2) it would mean pressure and volume are directly proportional, this is not true. So option A is not a valid equation.

Step 3: When pressure and number of moles are constant

This means volume and temperature will change.

p1*V1 / ( n1*R*T1 ) = p2*V2 / ( n2*R*T2 )  OR V1/T1 = V2/T2

For the formula (V1/T1) =V2/T2) it would mean volume  and temperature are directly proportional. This is a valid equation

Option D would only be a valid equation if its (V1/T1) =V2/T2)

(V2/T1) =V2/T2) is not a valid equation. ( I don't know if this was a thypo or not).