Question

A 1.5-L container of liquid nitrogen is kept in a closet measuring 1.2 m by 1.0 m by 2.0 m. Assuming that the container is completely full, that the temperature is 21.3 °C, and that the atmospheric pressure is 1.1 atm, calculate the percent (by volume) of air that would be displaced if all of the liquid nitrogen evaporated. (Liquid nitrogen has a density of 0.807 g/mL.)

A) 6.5%
B) 13.0%
C) 19.5%
D) 26.0%

Answer 1

The percent (by volume) of air that would be displaced if all the liquid nitrogen evaporated is approximately 13.0% (Option B).

Step-by-step explanation:

To calculate the volume of the liquid nitrogen, we use the formula V = m/ρ, where V is volume, m is mass, and ρ is density. The mass of the liquid nitrogen can be found using the formula m = ρV, where ρ is the density of liquid nitrogen. Knowing the volume of the container and the density of liquid nitrogen, we can find the mass.

Next, we use the ideal gas law, PV = nRT, to find the volume of the air displaced when the liquid nitrogen evaporates. Rearranging the formula to solve for V, we get V = nRT/P, where n is the number of moles, R is the ideal gas constant, T is the temperature in Kelvin, and P is the pressure.

Finally, to find the percent (by volume) of air displaced, we use the formula (V_air_displaced / V_container) * 100%. Substituting the values calculated earlier, we find that the percent is approximately 13.0%.

In summary, by applying the principles of physics and gas laws, we can calculate the percent (by volume) of air displaced when all the liquid nitrogen evaporates, yielding the final answer of approximately 13.0%.(Option B)