PhET Simulation for Density
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## Group Activity: Density

### Introduction

PhET Simulation for Density

It is sometimes the job of a chemist to identify an unknown substance. One tool used by chemists in this work is the measurement of density. The identity of many simple substances can be narrowed down by comparing the density of a sample with the density of the known substances.

Density (symbol, d; or the Greek letter rho, ρ) is defined as mass per unit volume. Density is calculated by dividing the mass of an object by its volume. This is shown in equation form, as follows:

```           Mass          m
Density = ——————— or d = —
Volume        V
```

To find the density of a sample, two measurements are required. First, you must measure the mass. Second, you must measure the volume. People often say that lead is heavy. What they really mean is that lead is dense. For example, which is heavier: a pound of lead or a pound of aluminum? This is a trick question, if you are wondering. What if you have the same volume of each metal? If you have exactly one mL (one cm3) of lead it will have a mass of 11.3 g. If you have the same volume of aluminum it will have a mass of 2.7 g. So which one is more dense?

We can calculate the density of a solid, liquid, or gas. The density of a gas will be dealt with elsewhere, because its density is very sensitive to temperature and pressure. Although the density of liquids and solids do change with temperature and pressure changes, the amount is fairly small. We will assume that temperature and pressure make little difference in our calculations. The density of a solid is often reported in units of grams per cubic centimeter (g/cm3). The density of a liquid is usually reported in units of grams per milliliter (g/mL). These units are perfectly equivalent because 1 mL = 1 cm3 exactly.

Density is an intensive property, which means that the density of a substance is the same no matter how large or small a sample of it is. Water has a density of 1 g/mL whether you have 1 mL or 1,000,000 mL. Other intensive properties include melting point, boiling point, temperature, and concentration. By contrast with intensive properties, things like duration, volume, mass, and length are extensive properties. This means that they measure things that change when the size of a sample changes.

Density determines what will float and what will sink in a given liquid. If a substance is more dense than a given liquid, then it will sink. If it is less dense, then it will float. For instance, aluminum (Al) has a density of 2.70 g/cm3 and mercury (Hg, a liquid at room temperature) has a density of 13.6 g/mL. Aluminum floats in mercury but not in water. Water has a density of 1 g/mL.

 Densities as Conversion Factors Aluminum (Al) 2.70 g = 1 cm3 Lead (Pb) 11.3 g = 1 cm3 Water (H2O) 1.00 g = 1 mL Mercury (Hg) 13.6 g = 1 cm3

Buoyancy (the tendency to float) really depends on the amount of water or other fluid displaced by an object placed in it. For this reason, objects made of substances which have a density higher than that of the liquid can be made to float. This is possible by shaping them to displace more water; that is, by increasing their volume.

The useful thing about density is that if you know the mass of a sample you can simply calculate the volume. Similarly, if you know the volume of a sample you can caculate its mass. Just use density as a conversion factor between the mass and volume of a sample of a specific material.

```You have 47 g of Pb:
what is the volume of the sample?
1 cm3
47 g x -------- = 4.2 cm3
11.3 g
```
```You have 1300 mL of Pb:
what is the mass of the sample?
11.3 g
1300 mL x -------- = 1.5×104 g (or 15 kg)
1 mL
```

A milliliter (mL) and a cubic centimeter (cm3) are the same size and so they are mathematically interchangeable. The mL is used for liquid densities and the cm3 unit is used for solid densities but really, either one is fine.

#### Exercises

Show your work for all calculations as dimensional analysis calculations.

1. A block of aluminum occupies a volume of 15.56 mL and weighs 42.0 g. What is its density?
1. Mercury metal (Hg) in a graduated cylinder has a volume of 22.5 mL. The Hg used to fill the cylinder has a mass of 306.0 g. From this information, calculate the density of Hg.

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1. A flask that weighs 345.8 g is filled with 225 mL of carbon tetrachloride (CCl4). The weight of the flask and CCl4 is found to be 703.6 g. From this information, calculate the density of CCl4.
2. A sample of zinc pellets is weighed on a balance and the mass is found to be 19.54 g. The pellets are placed into a graduated cylinder containing 32.1 mL of water. After the zinc is placed in the water the volume in the cylinder reads as 34.8 mL. What is the density of zinc?
3. Find the mass of 2500 mL of benzene (C6H6). The density of C6H6 is 0.90 g/mL.
4. A strong-smelling liquid is given to you to identify. You find the mass of a 100 mL graduated cylinder is 373.92 g. When you have added some of the substance to the cylinder you measure the volume to be 51.2 mL and the new mass to be 420.0 g. What is the density of the substance? Can you identify it?
5. What is the volume of 64.0 g of benzene?
6. What volume of silver metal (Ag) will weigh exactly 2500 g? The density of Ag is 10.5 g/cm3.
7. What mass of silver has a volume of 21.0 mL? Use the density given in the previous problem.
1. What volume of lead (the density is in the introduction text) has a mass of 150. g?
2. What mass of lead has a volume of 1,000 cm3?
3. A rectangular block of copper metal weighs 1896 g. The dimensions of the block are 8.4 cm by 5.5 cm by 4.6 cm. From these data, what is the density of copper? Will it float in the liquid metal mercury?
4. A student counts 15 pieces of copper shot, weighs them and measures their volume by displacement. She then calculates the density: 9.0 g/cm3. Would the calculation have resulted in a different value if she had only counted out 12 pieces? Explain your answer with 1 or 2 complete sentences.
5. A piece of balsa wood of mass 0.128 kg will float on water. Will a piece of balsa wood with a mass of 170 kg float? Justify your answer with one or two complete sentences.
6. Define the following terms in your own words. Give two examples for each word:
intensive property:

extensive property:
Density Homework
Last updated: Oct 14, 2022       Home