Answer 1:
A most interesting question! (I am going to assume
that you mean a fresh egg. It turns out that bad
eggs will also float in (relatively) fresh water
due to the build up of gas inside the egg. This is
because the shell is porous, and over time liquid
evaporates from the shell and gas goes in.)
Whether or not an egg floats in a solution of
salt water can be estimated using the concept of
density. For something to float, it must
have a smaller density than whatever it is
floating in.
So let's estimate how much (table) salt it takes
using density. The mass of an egg is about 50 g.
To measure the volume, you can submerge (put just
under the water surface) to see how much water is
displaced; the volume of water it displaces is the
volume of the egg! This is based on a concept
behind the story of
'Eureka!' and Archimedes
The definition of density is mass per unit volume
(density = mass/volume). For example, you could
have a pound of steel and pound of feathers. While
both would weigh the same, the amount of space the
pound of feathers would take would be much larger!
Thus, the density of feathers is smaller.
Luckily others were also curious to the density
of an egg, so we will use their )
value of 1.031 g/cm^{3} (averaged
across 23 bird species) for this estimate. The
density of fresh water is taken to be 1.00
g/cm^{3}. Likewise, the density of (table)
salt is 2.16 g/cm^{3}. For the egg to
float, the density of the water needs to be just
barely higher than the density of the egg. To
make the math easier, let's say I have 1 g of
water (i.e., 1 cm^{3}). I'll assume that
the masses and volumes of the water and salt just
add together (this is not always the case; look to
the mixing of water and ethanol where the mixing
the two leads to a volume smaller than adding the
two separate volumes together!). Although you
probably have not learned the math behind this,
I'll write down the equation used for this
estimate for future reference:
total density
The total density we will take to be that of the
egg, since this is the minimum density the salt
water needs for the egg to float. The mass of the
water is set to 1 g, and volume may be found from
the original equation for density. What we solve
for is the mass of the salt using algebra. In this
estimate, we find that you need at least about
0.06 g of salt for every 1 g of water for an egg
to float.
For reference,
click here the ocean has on average 35 g of
salt for every 1000 g of water. Our estimate is
equal to 60 g of salt per 1000 g of water. So
about twice as salty. If you were at the Dead
Sea, you wouldn't need to add any more salt. It's
salty enough that a human could float!
As with any estimation or experiment in
science, there are errors, and it is good practice
to understand where they come from. Nevertheless,
our estimate gives us a ball park number of what
to expect.
But don't take my word for it, try it yourself!
There are several home style experiments you can
try for yourself, like this
click here please methodical one that tries
different concentrations of salt.
Hope this helps!
Best,
