Environmental Data Analysis EESC
BC
3017
Homework 2 - due Th 9/23
Unit Conversions/Back-of-the-envelope calculations
1.) ( 10p) Benjamin Franklin dropped oil on a lake's surface and
noticed that a given amount of oil could not be introduced to spread
out
beyond a certain area. If the number of drops of oil was doubled, then
so was the maximum area to which it would spread. His measurements
revealed
that 0.1 ml of oil spread to a maximum area of ~430ft2.
a) How thick is such an oil layer? Express the result in
'Angstrom'.
The Angstrom is a convenient unit because lighter atoms such as
hydrogen,
carbon, and oxygen are on the order of 1 Angstrom in diameter. The
answer
is about 25 A. For the oil that Franklin used this is approximately
equivalent
to the thickness of one molecule. Please show how you get the result.
b) Franklin actually showed that 1 teaspoon of oil would spread to
cover
about 0.5 acre. Determine how many cubic centimeters there are in a
teaspoon.
2.) (8p) Estimate he average spacing (distance between centers
of molecules) between H2O
molecules
in
liquid
water
by making use of two pieces of information: (a) liquid
water has a density of 1.00 g/cm3, and (b) every 18g of
water
contain
Avogadro's number (6.02x1023) of H2O molecules.
3.) (10p) Open the Aluminum.xlsx file (in the Statplus/data
folder), which contains measurements on eight aluminum chunks from a
high school chemistry lab. Both the mass in grams and the volume in
cubic centimeters were measured for each chunk.
a) Create a new column in the worksheet, computing the density of
each
chunk (the ratio of mass to volume).
b) Add a column on the left with a running sample number (1, 2,
3...).
Make a bar chart of the densities as a function of sample number.
c) Sort the data from the chunk with the highest density to that
with
the lowest (using the Excel SORT function).
d) Calculate the average density for all chunks.
e) Is there an outlier (an observation that stands out as being
different from the others)? Calculate the average density for all
chunks aside from the outlier. Print your results in a compact way (one
page only).
f) Which of the two averages gives the best approximation of the
density of aluminum? Why?