# Measuring the Volume of Liquids: Tools and Calculation

## The Volume of a Liquid

The volume is one of many ways to scientifically describe an object or substance. It measures the occupancy of the object in a three-dimensional space; therefore, it takes into consideration the object's length, width, and height.

The approach for volume measurement can change according to the physical state of the matter. For solids, the volume is usually measured by finding the length of the object's sides and inserting the values into an equation. On the other hand, measuring the volume of a gas can be more complicated since the substance occupies the entire space of its recipient. In this case, pressure and temperature values should always be measured to give meaning to the volume.

Liquids fall between the characteristics related to gases and solids, since they do adapt their shape according to their recipient. However, liquids do maintain their volume even when their containers change. The following table compares the shape and volume of substances in three different physical states.

Physical state of substance | Shape | Volume |
---|---|---|

Solid | Does not change | Dos not change |

Liquid | Adapts to the shape of recipient | Does not change |

Gas | Adapts to the shape of recipient | Expands to occupy recipient |

## Measuring Liquid Volume

The shape of liquids change according to their recipients. If one pours one liter of water in a jar or in a bowl, the shape of that amount of water will vary. Its volume, however, will remain the same: one liter. The most basic method of liquid volume measuring is to pour the substance into a graduated recipient. The observer must check where the liquid level matches the recipient's marks, which will indicate the volume. A more complex way to calculate volume is by using the density formula. This method requires measurement of the values of density and mass.

### How to Find the Volume of a Liquid Using Liquid Measurement Tools

Pouring a liquid into a graduated recipient is the simplest form of measuring the volume of a liquid. In science laboratories it is common to see a variety of these recipients that can be used for different tasks. In all cases, the volume marks imprinted on the vessels are the reference for measurement.

**Graduated cylinders**

These are long and thin recipients that are used only to measure volume of liquids. They are known for presenting a low error percentage due to the high number of graduation marks on them.

**Beakers and Erlenmeyer flasks**

These are graduated vessels that can serve to mix liquids and measure their volumes. Some differences between them can make one more appropriate than another for different tasks. For example, beakers cannot be covered due to its spout, and Erlenmeyer flasks usually need a funnel to receive fluids from another recipient.

**Burettes**

Burettes are laboratory glassware used to dispense specific volumes of liquid. The outflow is controlled through a stopcock placed in one of their ends.

**Pipettes**

These are accurate tools mainly used to transport a volume of liquid between vessels. Pipettes suck and release liquids by permitting a vacuum regulation, usually through a bulb, in one of their ends.

**Example 1:** Find the approximate volume of liquid measured shown in items 'a' and 'b.'

A)

The green liquid fills the burette up to, approximately, midway between the 30 ml and 40 ml marks. Therefore, the volume of the liquid is around 35 ml.

B)

The blue liquid fills the entire capacity of the flask, marked as 100 ml by the graduation line at the top of the vessel. Therefore, the volume of the liquid is 100 ml.

### How to Calculate Liquid Volume Using the Density Formula

The volume of a liquid can also be calculated indirectly through its values of mass and density. Scientifically, mass is defined as the quantity of inertia of an object. However, for the purposes of this lesson, a more basic definition for mass will be used: the amount of matter contained in a body. Density (d), in its turn, measures the consistency of a body by displaying its mass per unit of volume. Therefore, density is the division between mass and volume:

{eq}d = \frac mV {/eq}

The unit used to measure density ({eq}Kg/L, g/cm^3, etc. {/eq}) results from a combination between the units chosen to represent mass ({eq}Kg, g, lb, etc. {/eq}) and volume ({eq}L, ml, cm^3, etc. {/eq}).

**Example 2:** Find the density of a substance 'X' of mass 40 g concentrated in a volume of 16 ml.

Solution:

{eq}d = \frac mV = \frac {40 g}{16 ml} = 2.5 g/mL. {/eq}

The equation can be modified allowing one to find volume from the values of mass and density. One only needs to multiply both sides of the equation by ''V' and divide them by 'd.'

{eq}d = \frac mV {/eq}

{eq}V * d = \frac {m*V}{V} {/eq}

{eq}V * d = m {/eq}

{eq}\frac {V * d}{d} = \frac md {/eq}

{eq}V = \frac md {/eq}

**Example 3:** Find the volume that contains 100 g of water, given that the density of water is 997 {eq}Kg/m^3 {/eq}.

Solution:

The unit for mass of water needs to match the unit used for density.

100 g = 0.1 Kg

Thus,

{eq}V = \frac md = \frac {0.1 Kg}{997 Kg/m^3} = 0.0001003009 m^3 {/eq}

Which is equivalent to approximately 0.1 liters.

## Lesson Summary

The objective of this lesson was to present different ways of measuring the volume of liquids. First, the lesson discussed volume and shape of substances in three different physical states: solids, gases, and liquids. Solids are known to maintain their volume and shape regardless of the recipient they are in. Gases expand, changing their volumes and shapes according to the recipient. Liquids do adapt their shapes following the shape of the recipient, but the volume does not vary. These features facilitate volume measurements for liquids using graduated recipients, such as beakers, flasks, and burets. Indirectly, the volume of a liquid can be calculated by dividing its mass by its density.

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#### Does liquid have volume?

Yes, liquids do occupy space, therefore, they have volume. Even though the dimensions of a liquid, at first, cannot be measured as in solids, the recipient that contains the liquid can be measured.

#### What is an example of liquid volume?

Liquid volumes can be measured through the use of graduated recipients (flasks, pipettes, burettes, etc.). Also, an indirect measure of volume through the values of mass and density can be made.

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