Rectangular cube 3.2 m length 1.2 m in height and 5 m in length is split into two parts. The container has a movable airtight divider that divides its length as necessary. Part A has 58 moles of gas and part B has 165 moles of a gas. Required:
At what length will the divider to equilibrium?

The length the divider is to  equilibrium from Part A = 1.30 m and from Part B = 3.70 m

Explanation:

Given that:

A rectangular cube with 3.2 m breadth, 1.2 m height and 5 m in length is splitted into two parts.

The diagrammatic expression for the above statement can be found in the attached diagram below.

The container has a movable airtight divider that divides its length as necessary.

Part A has 58 moles of gas

Part B has 165 moles of a gas.

Thus, the movable airtight divider will stop at a length where the pressure on it is equal on both sides.

i.e

Using the ideal gas equation,

PV = nRT

where, P,R,and  T are constant.

Then :

--- (1)

since Volume of a cube = L × B × H

From the question; the L = 5m

i,e

= 5

From equation (1) , we divide both sides by (B × H)

Then :

By cross multiplying; we have:

165 ( 5 - )  = 58 (

825 - 165  = 58

825 = 165 +58

825 = 223

= 825/223

 = 3.70 m

= 1.30 m

The length the divider is to  equilibrium from Part A = 1.30 m and from Part B = 3.70 m