Zirconium has a density of 6.51 g/cm³, a molar mass of 91.2 g/mol and an atomic radius of 160 pm…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Zirconium has a density of , a molar mass of and an atomic radius of . Hafnium has the same crystal structure, a molar mass of and an atomic radius of . Estimate the density of hafnium. The measured value is . Find the percentage error of your estimate.
Need a reminder? The key ideaShow
Going down a group adds a shell, and the radius rises. Between La and Hf, 14 electrons enter the 4f subshell, which shields badly. The effective charge on the outer electrons rises by about at each step, and the ions shrink: . The ionic potential is charge divided by radius. A larger value means a stronger pull on and a weaker base.
The worked solution
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.
Step 1. The mass ratio. .
Step 2. The volume ratio. The hafnium atom is smaller, so the same mole takes less space. .
Step 3. The density. .
Step 4. The error. .
Answer: , which is below the measured value.
Check. A simple count of mass and radius gets within a few per cent. The near-equal radii of Zr and Hf explain the doubled density: the mass of the atom nearly doubles and its size does not change.
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