Question

2.05 g of an unknown gas at 45 °C and 1.00 atm is stored in a 1.15-L flask.

What is the density of the gas?

Answer 1

I would use (V1/T1) = (V2/T2). You want to correct T = 45 C to (convert to kelvin of course) to T at zero and calculate the new V2 at those conditions. Then density = grams/V2 (in L) to give density in g/L.

Answer 2

T1 is 288K but what is T2?

Answer 3

T2 is T at standard conditions. Isn't that 273 K. So you're correct volume from 288 K to 273 K.
(Note: You know the density at 45 C; it's 2.05g/1.15 l)