# How does density of alkali metals increase down the group?

Size of alkali metals increases down the group, so volume also shows increment, and since volume is inversely proportional to density, how does density also increase down the group?

• Because mass is also increasing, presumably faster than volume. – ringo Feb 20 '17 at 15:49
• Do you mean "why"? "How" suggests you may want to know whether the increase is linear or some other mathematical function. – bpedit Feb 20 '17 at 16:10
• The molar volume increases from 13.10 cm$^{3}$/mol for Li to 71.07 cm$^{3}$/mol for Cs. Mass increases from 6.9 gm/mol for Li to 132.9 gm/mol for Cs. So, the mass per atom increases faster than the atomic density decreases. – Jon Custer Feb 20 '17 at 17:05

$Density=mass/volume$

1) If mass is increasing and volume is decreasing, then density (mass/volume) will increase.

2)If mass is decreasing and volume is increasing simultaneously, then the density (mass/volume) will decrease.

*3)If both mass and volume are increasing, then we need to check which one of them is increasing at a faster rate(since both are contradictory factors)

a) If mass is increasing at a faster rate than volume, then density will increase.

b) If volume is increasing at a faster rate than mass (i.e denominator in mass/volume is increasing making the overall fraction smaller), then density decreases.

You can apply same logic when both volume and mass are decreasing simultaneously.

Generally, we see that in alkali metals the rate of increase of mass is greater than rate of increase of volume, therefore the density increases down the group.

Also, note that there is no definite reason for why mass is increasing at a faster rate than volume. So asking "why" does it happen isn't a great question.

Its just because density is directly proportional to mass. And the mass increases faster than that of volume expect for the case of potassium which is lighter than sodium.