Question

chemistry in context 2008-9
perhaps someone has tried to trick you with this question: \which is heavier, a pound of lead or a pound of feathers?\ many people would instinctively answer \lead.\ when they give this incorrect answer, these people are really thinking of density. if a piece of lead and a feather of the same volume are weighed, the lead would have a greater mass than the feather. it would take a much larger volume of feathers to equal the mass of a given volume of lead.

density is the relationship of the mass of an object to its volume. density is usually reported in units of grams per cubic centimeter (g/cm³). for example, water has a density of 1.00 g/cm³. since a cubic centimeter contains the same volume as a milliliter, in some cases you may see density expressed as g/ml.
density = \\(\frac{\text{mass}}{\text{volume}}\\) or \\(d = \frac{m}{v}\\)

to solve density problems, list the known and unknown values, then use one of the following.

• when a problem requires you to calculate density, use the density equation, \\(d = \frac{m}{v}\\)
• you can solve for mass by multiplying both sides of the density equation by volume.

\\(d \\, v = \frac{m \\, v}{v}\\) or \\(m = d \\, v\\)

• you can solve for volume by dividing both sides of the equation above by density.

\\(\frac{m}{d} = \frac{d \\, v}{d}\\) or \\(v = \frac{m}{d}\\)

example: what is the mass of an object that has a density of 8 g/cm³ and a volume of 64 cm³?
known:
\\(d = 8 \\, \text{g/cm³}\\)
\\(v = 64 \\, \text{cm³}\\)

unknown:
\\(m = ?\\)

equation to use:
\\(m = d \\, v\\)

\plug and chug\:
\\(m = (8 \\, \text{g/cm³})(64 \\, \text{cm³}) = 512 \\, \text{g}\\)

problems list the known and unknown values; try to derive the equation without looking above.

1. a piece of tin has a mass of 16.52 g and a volume of 2.26 cm³. what is the density of tin?

known:

unknown:

1. a man has a 50.0 cm³ bottle completely filled with 163 g of a slimy green liquid. what is the density of the liquid?

known:

unknown:

Explanation:

Problem 1

Step1: Identify known and unknown

Known: \( M = 16.52\ g \), \( V = 2.26\ cm^3 \)
Unknown: \( D =? \)

Step2: Use density formula

Density formula: \( D=\frac{M}{V} \)
Substitute values: \( D = \frac{16.52\ g}{2.26\ cm^3} \)

Step3: Calculate density

\( D=\frac{16.52}{2.26}\approx7.31\ g/cm^3 \)

Step1: Identify known and unknown

Known: \( M = 163\ g \), \( V = 50.0\ cm^3 \)
Unknown: \( D =? \)

Step2: Use density formula

Density formula: \( D=\frac{M}{V} \)
Substitute values: \( D = \frac{163\ g}{50.0\ cm^3} \)

Step3: Calculate density

\( D=\frac{163}{50.0}=3.26\ g/cm^3 \)

Answer:

The density of tin is approximately \( 7.31\ g/cm^3 \)

Problem 2