# Density

Which is heavier – the wood in the trunk of a tree or the metal in a coin? Your first answer might be to say the trunk of the tree, but it can float on water while a coin would quickly sink to the bottom,

To be a fair comparison we need to find the masses of equal volumes, if we found the mass of a piece of wood the size of a coin we would see it was lighter.

In the school laboratory, when small amounts of materials are used, the density of a substance is often calculated using masses measured in grams and volumes in centimeters cubed, giving a density value in g/cm^{3}, The density value in units of g/cm^{3} can be converted to a value in kg/m^{3} by multiplying it by 1000. For example, ice was found to have a density of 0.920 g/cm^{3}. This can also be expressed as 0.920 x 1000 = 920 kg/m^{3}

*Density is the mass of unit volume*

In SI density measured in kg/m^{3}

But can be measured also in g/cm^{3}

**Density (d ) = mass (m) / volume (V)**

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**At constant mass**

The density is ** inversely proportional **with volume of the substance.

*d inversely proportional to*** V**

**At constant volume**

The density is ** directly proportional** with mass of the substance

** d is directly proportional to m**

Material |
Density / kg/m^{3} |

Ice | 920 |

Cork | 250 |

Wood | 650 |

Pure water (at 4^{0}C) |
1000 |

Steel | 7900 |

Aluminum | 2700 |

Copper | 8940 |

Lead | 11350 |

Gold | 19320 |

Polythene | 920 |

Perspex | 1200 |

Expanded polystyrene | 15 |

If equal volumes are compared, the one of the greatest mass will have the greatest density.

If equal masses are compared, the one with smallest volume will have the greatest density.

** **

**Question**

**1. **Arrange the materials in this table in order of density, starting with the least dense material.

**2. **Which is heavier, 1 m^{3} of steel or 1 m^{3} of aluminum?

**3. **Which is heavier, 1 kg of steel or 1 kg of cork?

**Notes:**

** i. **Density of water at 4 ^{0}C is 1000 kg/m^{3} = 1 g/cm^{3}.

** ii. **Density doesn’t depend on the volume (how big) of the body only; it depends on both its volume and its mass.

** iii. **Density changes with temperature but the density of water is a very exceptional with heat change.

** iv. **Densities of gases depend on their pressure too.

** v. **The less dense float over the surface of the denser.

** vi. **The denser will sink or goes down.

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**Density Experiments**

**A- To determine the density of a liquid**

**Apparatus**

Measuring cylinder, electronic balance

**Procedures**

**1. **Find the mass of the dry measuring cylinder using an electronic balance m_{1}.

**2. **Add a specific volume of the liquid into the measuring cylinder, record the volume V.

**3. **Measure the mass of the cylinder with the liquid m_{2}.

**Calculation**

The mass of the liquid m = m_{2} – m_{1}

The density of the liquid can be calculated from the formula *ρ* = m/v** **

**Precaution**

When reading from the burette, make sure that the eye is placed at the same level as the meniscus of the liquid. (To avoid ……… error)

**B- To determine the density of a regular object**

**Apparatus**

Ruler, Vernier calipers or micrometer screw gauge

Electronic or digital balance

**Procedures**

**1. **Measure the mass of the regular object using an electronic balance m.

**2. **Find the volume (v) of the regular object by measuring its dimensions then the volume can be calculated using the respective formulae.

**Calculation**

Density can be calculate using the formula *ρ *= m/v

**Note:**

Density can be used to indicate the degree of purity.