Question

Consider the flask apparatus below, which contains 2.00 L H₂ at a pressure of 360. torr and 1.00 L of N₂ at an unknown pressure. If the total pressure in the flasks is 300. torr after the stopcock is opened, determine the initial pressure of N₂ in the 1.00 L flask.

Answer 1

To find the initial pressure of N₂, use Boyle's Law to calculate the final pressure of H₂ after mixing. Subtract this from the total final pressure to obtain the pressure that N₂ contributes, which reveals the initial pressure of N₂.

Step-by-step explanation:

The student is asking to calculate the initial pressure of N₂ (nitrogen gas) in a flask using Dalton's Law of Partial Pressures and the Ideal Gas Law. The setup includes a 2.00 L flask containing H₂ (hydrogen gas) at 360 torr and a 1.00 L flask of N₂ at an unknown pressure. When mixed, the total pressure is 300 torr. To solve this, we use the formula for partial pressures P₁V₁ = P₂V₂ (Boyle's Law) for the hydrogen gas, and then apply Dalton's Law to find the pressure contributed by the nitrogen gas. We assume that temperature remains constant.

First, calculate the final pressure of H₂ using Boyle's Law:

PₓH₂Vₓ = PₔH₂Vₔ

PₓH₂ = 360 torr (initial pressure of H₂), Vₓ = 2.00 L (initial volume of H₂), Vₔ = 3.00 L (total volume after combining both flasks).

The final pressure of H₂, PₔH₂, can be calculated as:

(360 torr) (2.00 L) = PₔH₂ (3.00 L)

PₔH₂ = 240 torr

Since the total final pressure is 300 torr, the pressure of N₂ by itself, PₔN₂, is:

300 torr - 240 torr = 60 torr

This is the initial pressure of N₂ since the volume did not change for N₂.