Please see the attached file.

.25 moles of oxygen are place in a cylinder with a moveable piston, at a pressure of 1.5 atm and a temp. of 50.C The diameter of the piston face is 20cm.

what mass, in kg, would have to be placed on top of the piston to develop a pressure of 10 atm inside the cylinder if the temp. were held constant. Prof. said to take into account the initial 1.5atm

The temperature remains the same, so we have an isothermal process here.

Where 1 is the initial stage of 1.5atm, and 2 is the final stage of 10atm.
According to the ideal gas law,

Now. We consider the gas inside the cylinder, the work done by the gas to the outside during the change from stage 1 to stage 2 is
(1)
And since it is a isothermal process, then (2)
Plug (2) into (1)
(3)
Now

The gas constant
The temperature is
N=0.25 mol
Plug the above values into the equation (3)

So the system actually needs to get the work from the outside.
Then the work done by the mass is equal to the above value.
The work done by the mass is
(4)
Where is the change of the height of the piston.

The initial volume of the gas is , and the height is
At the final stage 2, and the height is
So
(5)
Plug (5) into (4)
(6)
The diameter of the piston is
Plug P1, P2 and r into (6)

So the mass is 0.106 kg.