# How been agreed upon as the average

How do you convert 1 liter of water to grams? The answer is relatively simple, but the science behind it is both complex and fascinating. Keep reading to find out more!

## Setting Up the Problem

Marvin is puzzled when he looks at his high school physics homework.

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The question, ‘What is the weight, in grams, of 1 liter of water?’ is simple, and Marvin finds an answer online very quickly. What’s puzzling Marvin is that he knows his teacher doesn’t give out easy assignments. What is he missing with this simple question?Marvin eventually figures out that the question is so simple that it’s ambiguous. His teacher has stressed throughout the year that ambiguity in science leads to poor answers. The answer Marvin finds so quickly (given below) has a lot of assumptions built into it.

But what are those assumptions, and why do they have to be made to make the standard answer correct? It turns out that the mass of 1 liter of water changes based on a number of factors: temperature, pressure, and most importantly, the amount of dissolved solids present. Let’s take a closer look at each so we can have a better understanding of the standard answer.The more solids that are dissolved in a liquid, the denser the water will be. Seawater is typically 3% to 4% denser than distilled water, which is water with all impurities removed. Even tap water has some dissolved minerals that make it slightly heavier than distilled water.

As strange as it may seem, there is a naturally occurring body of water on Earth, Don Juan Pond, which has a water density 40% higher than distilled water. So, one of the assumptions we have to make to get this answer correct is that we are talking about distilled water.Temperature can have as large an effect on water density as the seawater example we saw above, although in the opposite direction.

Water is at its most dense at 4 degrees Celsius. Water that is warmer or cooler than that will have a lower density. Distilled water at just below 100 degrees Celsius (just before boiling) is more than 4% less dense than the same water at a temperature of 4 degrees Celsius.

The second assumption Marvin will have to make about the water is that it is exactly 4 degrees Celsius.Pressure has a small, but measurable effect on density. For standard pressures on the Earth’s surface, the effects on water density are much less than 1%. But, since the standard answer is accurate to 4 digits, we’ll have to make a third assumption: Our water is exposed to a standard atmospheric pressure of exactly 101,325 Pascals or 101.325 kilopascals (kPa). This amount of pressure has been agreed upon as the average atmospheric pressure at sea level.The answer that Marvin found on his quick search is that 1 liter of water weighs exactly 1 kilogram.

## Solution

Since there are 1000 grams in a kilogram, our answer is that 1 liter of water weighs 1000 grams.However, there are three important assumptions built into this answer that need to be noted. For our answer to be accurate, the water must be:

1. Distilled (pure water)
2. At a temperature of exactly 4 degrees Celsius
3. Exposed to standard atmospheric pressure of 101.

325 kPa

If we vary those things, it is possible to find densities of 1 liter of naturally-occurring surface water ranging between 958g and 1400g. 