## Quick Answer

1 liter of water has a mass of 1 kilogram. This is because water has a density of 1 kg/L at 4°C. So 1 L of water weighs exactly 1 kg.

## Explanation

Water has a density of 1 gram per milliliter. This means that 1 mL of water has a mass of 1 gram.

There are 1000 mL in 1 L. So if we multiply the mass of 1 mL (1 gram) by 1000, we get the mass of 1 L:

1 mL water = 1 gram

1000 mL = 1 L

So:

1000 grams = 1 kg

Therefore, 1 L of water has a mass of 1000 grams, which is equal to 1 kilogram.

This relationship between volume and mass holds true for water at 4°C. At this temperature, water reaches its maximum density of 1 g/mL.

### The Density of Water

In general, density is defined as mass per unit volume. It is calculated by dividing an object’s mass by its volume. The resulting value tells us how dense a substance is.

For water, the density at 4°C is:

Density of water = Mass / Volume

= 1 g / 1 mL

= 1 g/mL

So water has a density of 1 gram per milliliter at 4°C. This density varies slightly at other temperatures.

For example, at 20°C, the density of water is 0.998 g/mL. At 100°C, it drops to 0.958 g/mL. But at 4°C, water is at its densest and has a perfect 1 to 1 relationship between mass and volume.

### The Kilogram

The kilogram (kg) is the base unit of mass in the International System of Units (SI). It has the following definitions:

– 1 kg = 1000 grams

– 1 kg = 1 cubic decimeter (dm3) of water at 4°C

– 1 kg is the mass of the International Prototype Kilogram (a cylinder of platinum-iridium alloy)

So by definition, 1 dm3 of water at 4°C always has a mass of 1 kg.

And since 1 L = 1 dm3, 1 L of water at this temperature must have a mass of 1 kg as well.

### The Liter

The liter (L) is a unit of volume in the metric system. Some key facts about the liter:

– 1 L = 1 cubic decimeter (dm3)

– 1000 mL = 1 L

– 1 mL = 1 cm3

So 1 L represents a 10cm x 10cm x 10cm cube. This volume filled with water at 4°C will have a mass of 1 kg.

### Converting Between Mass and Volume

For water at 4°C, converting between mass and volume is straightforward:

– 1 L = 1 kg

– 1000 mL = 1 kg

– 1 mL = 1 g

So to convert between liquid volumes and mass, we simply move the decimal place 3 spots. Some examples:

– 0.5 L = 0.5 kg

– 350 mL = 350 g

– 0.25 mL = 0.25 g

This clean 1:1 conversion only holds for pure water at 4°C. For other liquids or temperatures, the density will differ slightly so the conversions will change.

## Why Does This Relationship Exist?

Water has this special 1:1 mass to volume ratio at 4°C because of its unique molecular structure. Here are a few key reasons:

### Water Molecules Are Polar

Water (H2O) is a polar molecule. This means it has a positively charged end and a negatively charged end. The oxygen atom has a slight negative charge, while the hydrogen atoms have a slight positive charge.

These opposing charges cause water molecules to attract to each other. This intermolecular attraction is called hydrogen bonding.

Hydrogen bonding allows water molecules to pack tightly together in liquid and solid states. This increases the density.

Other liquids lack hydrogen bonding and can’t pack together as tightly. So they are less dense than water.

### Water Expands When Heated

Unlike most materials, water expands and becomes less dense when heated. This is because the molecules move faster and break hydrogen bonds when heated.

So hot water takes up more volume than cold water. This causes the density to decrease as temperature increases.

At 4°C, the molecules have enough energy to break some weak bonds but still maintain a tightly packed structure. This maximizes density right before the expansive effect of heating takes hold.

### Water Crystals Have Open Structures

In solid form (ice), water crystalizes into hexagonal structures with lots of open space between molecules. This makes ice less dense than liquid water.

So when water freezes and becomes ice, it expands to fill up more volume. This is why frozen water pipes burst and ice floats in a glass of water.

Again, at 4°C water is just above freezing so it maintains a tightly packed liquid structure. This allows it to reach its densest state.

## Applications of the 1 kg/L Relationship

The fact that 1 L of water equals 1 kg at 4°C has many scientific and practical applications:

### Defining the Kilogram

As mentioned before, the kilogram was originally defined as the mass of 1 liter of water at 4°C. So this relationship allowed the kilogram to be physically realized and standardized.

### Checking Densities

The 1 kg/L density of water at 4°C provides a reference point for checking densities of other substances. Densities greater than 1 indicate the substance is heavier than water. Densities less than 1 indicate the substance is lighter than water.

### Oceanography

In oceanography, water density affects currents, waves, and tides. Scientists can calculate seawater density based on salinity and temperature relative to pure water at 4°C.

### Medical Applications

In medicine, saline solutions used for IVs contain 0.9% salt to match the density of blood (about 1.06 kg/L). This prevents damage to blood cells.

### Engineering

Civil engineers use the known density of water for calculations involving structures like dams, reservoirs, and plumbing systems.

### Cooking

Many cooking recipes involve conversions between volume and weight using water as the intermediate step. For example, converting ounces of flour to cups.

### Cleaning Products

Cleaning products often list dilution ratios by volume. Knowing the weight of water allows the right amount of cleaner concentrate to be added.

## Examples of Density Calculations

Here are some examples of using water’s density at 4°C to calculate the mass or volume of a given sample:

### Volume to Mass

If you have 0.5 L of water at 4°C, the mass is:

0.5 L x (1 kg/L) = 0.5 kg

### Mass to Volume

If you have a 2 kg sample of water at 4°C, the volume is:

2 kg x (1 L/1 kg) = 2 L

### Parts of a Whole

If you have a 5 L container that is 30% full of water at 4°C, the mass of the water is:

5 L x 0.30 = 1.5 L

1.5 L x (1 kg/L) = 1.5 kg

So the water has a mass of 1.5 kg.

### Known Density

If you have an object with a volume of 350 cm3 and a density of 5 g/cm3, its mass is:

350 cm3 x (5 g/cm3) = 1750 g

1750 g x (1 kg/1000 g) = 1.75 kg

So the object has a mass of 1.75 kg.

## Tables of Water Density at Different Temperatures

Here are some tables showing how the density of water changes at various temperatures:

Temperature (°C) | Density (g/mL) |
---|---|

0 | 0.99987 |

10 | 0.99970 |

20 | 0.99820 |

30 | 0.99565 |

40 | 0.99222 |

50 | 0.98805 |

60 | 0.98320 |

70 | 0.97760 |

80 | 0.97134 |

90 | 0.96450 |

100 | 0.95840 |

Temperature (°F) | Density (g/mL) |
---|---|

32 | 0.99987 |

50 | 0.99968 |

68 | 0.99897 |

86 | 0.99799 |

104 | 0.99691 |

122 | 0.99570 |

140 | 0.99435 |

158 | 0.99285 |

176 | 0.99120 |

194 | 0.98939 |

212 | 0.98740 |

These tables illustrate how density varies slightly above and below 1 g/mL as temperature changes. But at 4°C or 39°F, density equals 1 g/mL exactly.

## Converting Between Volume at Different Temperatures

Since density changes with temperature, the mass of 1 L of water changes as well.

To convert between volumes at different temperatures, you must account for the change in density.

For example, say you have 2 L of water at 20°C and want to know the volume at 4°C:

2 L x (0.998 g/mL at 20°C) = 1.996 kg

1.996 kg x (1 L/1 kg at 4°C) = 1.996 L

So 2 L at 20°C would occupy a volume of 1.996 L at 4°C due to the higher density at the lower temperature.

### Converting Between Any Two Temperatures

The full conversion formula between any two temperatures is:

V1 x ρ1 = m

m = V2 x ρ2

Where:

V1 = Initial volume

V2 = Final volume

ρ1 = Density at initial temperature

ρ2 = Density at final temperature

m = Mass (stays constant)

So first you calculate the mass at the initial volume and temperature. Then use the mass to calculate the new volume at the final temperature, accounting for the change in density.

## Effects of Pressure on Density

Increasing pressure also causes water density to increase slightly due to the compressibility of water.

However, this effect is minimal under standard temperature and pressure found at sea level on Earth.

For example, at 20°C the density increases from 0.998 g/mL at 1 atm to 1.002 g/mL at 100 atm.

So for most purposes, changing pressure has a negligible effect on water density. The main factor is temperature.

## Presence of Impurities or Particles

If water contains high levels of dissolved salts or other particles, the density will increase.

Seawater has a density of about 1.025 g/mL compared to pure water due to the extra mass of salt ions.

Similarly, adding a substance like sugar to water will increase the overall density relative to pure water.

However, in pure, distilled water the density depends only on temperature. Pressure and impurities have minimal effects.

## Conclusions

To summarize the key points:

- At 4°C, water has a density of exactly 1 g/mL or 1 kg/L.
- This means 1 L of pure water at this temperature will have a mass of 1 kg.
- As temperature increases, density decreases due to water expanding when heated.
- The 1:1 relationship at 4°C is useful for converting between mass and volume units.
- This relationship is applied in science fields like oceanography, medicine, and engineering.
- To convert volumes at different temperatures, you must adjust for density changes.
- Pressure and impurities have small effects on density relative to temperature.

So in any calculation involving the mass or volume of water, it’s crucial to specify the temperature. At 4°C, the math is nicely simplified with 1 L equaling 1 kg exactly. But at other temperatures, density changes must be taken into account.