MATH 261, Spring 2001 Due Date: Name(s):
Honors Project 4: Propagation of Error in Chemistry
If f = f(x1, x2, . . . , xn) is a quantity whose value depends on the measurable quantities x1, x2, . . . , xn, then
the error df in the measurement of f, in terms of the errors dxi in the measurements of xi, i = 1, 2, . . . , n, is
given by
df =
i
f
xi
dxi.
In practice, df is often computed using the fact that
|df| =


i
f
xi
dxi
2


1/2
=


i
f
xi
2
dx2
i +
i=j
f
xi
f
xj
dxidxj


1/2
.
Since the "cross terms"
f
xi
f
xj
dxidxj
may be positive or negative, their sum is generally significantly smaller than the sum of the squared terms,
and their effect on |df| can be ignored. Hence,
|df| 
i
f
xi
2
dx2
i
1/2
.
A 20.00 mL sample of a 0.1250 molarity CuSO4 solution is diluted to 500.0 mL. If the error in measurement
of the molarity is 0.0002, of the 20.00 mL pipet is 0.03 mL, and of the volume of the 500 mL flask is 0.15
mL, use the above analysis to determine how the molarity of the resulting solution should be reported. That
is, what is the molarity of the resulting solution, and what error is there in this measurement? (Recall that the
molarity M of a solution is given by M = n/V where n is the number of moles of solute, and V is the volume of
the solution in liters. Thus, in our case, MbeforeVbefore = MafterVafter, or Mafter = MbeforeVbefore/Vafter.)
Contributor: Dr. Gordon Fricke
Department of Chemistry, IUPUI