Page 33 - Theory and Problems of BEGINNING CHEMISTRY

22 MATHEMATICAL METHODS IN CHEMISTRY [CHAP. 2

Density is a ratio—the number of grams per milliliter, for example. In this regard, it is similar to speed.
The word per means divided by. To get a speed in miles per hour, divide the number of miles by the number
of hours.
Say the following speed aloud: 50 miles/hour.
“Fifty miles per hour.” (The division symbol is read as the word per.)
Distinguish carefully between density and mass, which are often confused in everyday conversation.

EXAMPLE 2.29. Which weighs more, a pound of bricks or a pound of feathers?
Ans. Since a pound of each is specified, neither weighs more. But everyone knows that bricks are heavier than feathers.
The confusion stems from the fact that heavy is defined in the dictionary as either “having great mass” or “having
high density.” Per unit volume, bricks weigh more than feathers; that is, bricks are denser.

It is relative densities that determine whether an object will float in a liquid. If the object is less dense, it
will float (unless it dissolves, of course).

EXAMPLE 2.30. Which has a greater mass, a large wooden desk or a metal sewing needle? Which one will float in water?
Ans. The desk has a greater mass. (You can pick up the needle with one finger, but not the desk.) Since the desk is so
much larger (greater volume), it displaces more than its own mass of water. Its density is less than that of water, and
it will float despite its greater mass. The needle is so small that it does not displace its own mass of water, and thus
it sinks.

In doing numerical density problems, you may always use the equation d = m/V or the same equation
rearranged into the form V = m/d or m = dV . You are often given two of these quantities and asked to find
the third. You will use the equation d = m/V if you are given mass and volume; but if you are given density
and either of the others, you probably should use the factor-label method. That way, you need not manipulate
the equation and then substitute; you can solve immediately. You need not memorize any density value except
that of water— approximately 1.00 g/mL throughout its liquid range.

EXAMPLE 2.31. Calculate the density of a 4.00-L body which has a mass of 7.50 kg.
m (7.50 kg)
Ans. d = = = 1.88 kg/L
V (4.00 L)

EXAMPLE 2.32. What is the mass of 10.00 mL of gold, which has a density of 19.3 g/mL?
Ans. Using the factor-label method, we find

19.3g
10.00 mL = 193 g (The density is given to three significant digits.)
1mL
With the equation:
m
d =
V

19.3g
m = Vd = (10.00 mL) = 193 g
1mL
EXAMPLE 2.33. What is the volume of 72.4 g of lead? (Density = 11.3 g/mL.)
m 72.4g
Ans. V = = = 6.41 mL
d 11.3g/mL

1mL

or 72.4g = 6.41 mL
11.3g