Problem related to the Ideal Gas equation -- Nitrogen under pressure

[PhysicsDuki]

Homework Statement

A bottle filled with nitrogen under a pressure of 1.5x10^7 Pa at a temperature of 27 ° C has a mass of 97 kg. Part of the nitrogen is consumed, so the pressure in the bottle, at a temperature of -3 ° C, is 6x10^6 Pa, and the weight of the bottle is 93.5 kg. How much mass of nitrogen is left in the bottle?

Relevant Equations

pxV = m/M x R x T
(R = 8.314 J/K x Mol and M= Molar mass of N2 ( 28 g/mol) )

Solution from the textbook:

My work:

I constantly get 1.55kg. I also tried dividing the first and the second equation (pxV=m/M x R x T with different values). How did they come up with the equation in the solution? Also, I am sorry if I posted it in the wrong place and didn't follow the rules of the forum, but I am new member. Thanks in advance!

 

[mjc123]

You seem (as far as I can tell) to be calculating the volume of nitrogen that has been consumed, and equating it to the volume of nitrogen remaining, which makes no sense.

I haven't tried deriving the textbook equation, but did it like this:
The 6 MPa remaining at 270K corresponds to a pressure of 6.667 MPa at 300K.
This means that 8.333 MPa (at 300K) has been consumed, which has a mass of 3.5 kg.
6.667/8.333 = m2/3.5

 

[Chestermiller]

Let $n_1$ represent the number of moles of N2 in the tank initially and let $n_2=n_1-\frac{3500}{M}$ represent the number of moles of N2 in the tank finally. Let V represent the volume of the tank. In terms of $n_1$ and V, write down the ideal gas relationship for the initial and final states.