THEORY AND GENERAL PRINCIPLES 3
n Factor Weights.—In Eq. (3) F is a constant for all determina-
g tions of the particular element or group of elements for which
}f it has been calculated. It is possible to choose the weight of the
}f sample taken so as to simplify the calculation of this equation.
For instance, by taking a sample weight equal in grams to the
F
rs | value of the factor, « = 1 and Eq. (3) becomes:
I- ' W=x. (4)
d In such a case the weight of precipitate, expressed in grams or f rac-
jr tions, becomes per cent, or fractions, of the constituent determined.
i: A weight of sample equal in grams to the value of the factor
is usually too large a quantity to be handled readily and a definite
' fraction of this weight (as 0.5, 0.2, 0.1, etc.) may be used instead.
j Any such weight is called a "factor weight/7 which may be
^ defined as a quantity equal in weight units to the value of the
s gravimetric factor, or to some simple fraction of this factor.
e Continuing the illustration given above, the factor weight of
g sample actually taken would be, for the sake of convenience,
e 0.6379 gm, in which case the per cent of phosphorus in the sample
would be one hundred times the weight, in grams, of magnesium
pyrophosphate found.
) When a Factor Weight Should be Used.—In considering the
actual practice of the operations with the balance it will be
« $ found that the manipulation of the sample to obtain any pre-
viously specified quantity requires considerable time, if the
, weighing is to be done accurately. One cannot judge quantities
[ accurately by means of the eye and it becomes necessary to
'j adjust the sample while it is on the balance pan, very carefully by
removing or replacing very minute quantities. On the other
\ hand, it is a comparatively simple matter to take approximately
) the required quantity and to weigh this accurately, using the
figure thus found in later calculations. It may then easily
be seen that all of the convenience and time-saving element
, that is involved in the calculations where factor weights (or,
in fact, any other definitely prescribed weights) have been used,
may be more than lost in the time and trouble required for
adjusting the sample weight to this exact value.
For the reason just mentioned it is inadvisable to use factor
weights except in cases where relatively large amounts of sample