How Do Nitrogen Molecules Separate When Changing From Liquid to Gas?

[JasonRox]

This is a question in my book.

Density of Liquid Nitrogen 804 grams per litre.

Density of Nitrogen Gas 4.4 grams per litre.

Calculate the increase in the separation of nitrogen molecules from the liquid to vapour states.

Note: Can someone tell me how many cubic metres there is in a litre.

 

[Chi Meson]

A liter is one cubic decimeter, so there are 10 x 10 x 10 liters (that's 1000, just in case you don't have a calculator!) in a cubic meter.

 

[Leong]

$$1 litre = 1000 cm^3$$
$$1 cm = 10^{-2} m$$
$$(1 cm)^3 = (10^{-2} m)^3$$
$$1 cm^3 = 10^{-6} m^3$$

$$1000 cm^3 = 10^{-3} m^3$$

$$1 litre = 10^{-3} m^3$$

Use the density formula,

$$\rho = \frac {m}{v}$$
Consider m mass of some liquid nitrogen and get the volume increase in percentage since no definite mass of liquid nitrogen is given. The mass of the liquid nitrogen doesn't change when it vapours to the gas form.

Doing other's homework is strictly not encouraged here. so, try it yourself first. when you are stuck, post what you have done here and help will come. good luck.

 

[JasonRox]

It's not my homework for gods sake. It's in an old physics book I bought at a second hand store.

I did try it, and I got 182x more distant, but the book says 5.7x, so I wanted to see where my mistake was. Knowing what a litre is(in metres), which the book did not explain would certainly help a little.

I understand that you don't like doing peoples homework, but it isn't even school season. Sheesh!

 

[Leong]

i guess you don't like what i have said here. anyway, i got the same answer as your.

 

[wisky40]

look, when you have 1Liter of nitrogen gas, this contains 4.4 grams ; now imagine how many Liters do you need for 804 grams => (V/804)=(1L/4.4) => V=804/4.4 Liters = 182.7272... Liters and also V=l^3 => l=(V)^(1/3) => l=(182.7...)^(1/3) = 5.6745...~5.7.
wisky40

 

[JasonRox]

Thanks! That helps me out.

 

[Leong]

Let
$$x_{g}= N_{2}$$ molecules' separation in gas form
$$x_{l}= N_{2}$$ molecules' separation in liquid form

$$\frac{x_{g}^3-x_{l}^3}{x_{l}^3} = 182$$
$$\frac{x_{g}}{x_{l}}= 5.7$$