Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
Nitrogen has a critical temperature of and a critical pressure of . (a) Find the van der Waals constants and from these two numbers. (b) The constant is four times the volume of the molecules in one mole. Treat a molecule as a sphere, and find its radius in nm, with . (c) Find the Boyle temperature. Is nitrogen above or below its Boyle temperature at ?
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. , , .
Step 1. The constant . .
Step 2. The constant . .
Step 3. The radius. We want from . So , and .
Step 4. The Boyle temperature. . It also equals .
Step 5. At . is below , so at low pressure for nitrogen. Attraction wins at low pressure.
Check. A radius of has the right order of size. A diatomic molecule is a few tenths of a nanometre across, and the model treats it as one sphere.
Answer: , , and . Nitrogen at is below its Boyle temperature.
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. The van der Waals equation is . Its critical constants are , and . From and , and . The Boyle temperature is .