Answer
The maximum fraction of the air in the room that could be displaced by the gaseous nitrogen is equal to $0.492$
Work Step by Step
1. When the liquid nitrogen vaporizes, its volume changes, but the mass still constant. Calculate the total mass in 175 L of $liquid$ nitrogen.
$$175 \space L \times \frac{0.808 \space g}{1 \space mL} \times \frac{1000 \space mL}{1 \space L} = 141400 \space g$$
2. The fraction of the air in the room that could be displaced by the gaseous nitrogen is:
$$\frac{Volume \space of \space gaseous \space nitrogen }{Total \space volume \space of \space the \space room}$$
Volume ($N_2$):
$$141400 \space g \times \frac{1 \space L}{1.15 \space g} = 122956.5$$
Volume (room):
$$V_{room} = 10.00 \space m \times 10.00 \space m \times 2.50 \space m = 250 \space m^3 \times \frac{1000 \space L}{1 \space m^3}$$ $$V_{room} = 250000 \space L$$
Thus, the fraction is equal to:
$$\frac{122956.5}{250000} = 0.492$$ (3 significant figures)
