# A sample of ammonia has a mass of 82.9 g. How many molecules are in this sample?

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How many molecules are in a sample of ammonia?

This question is not as easy to answer as you might think. There are three different ways to calculate the number of molecules, and they will all give you very different answers! The mass of 82.9 g divided by the molecular weight (28) gives us an estimate that there are about 3 x 10^7 molecules in this sample. This is the number of molecules based on mass.

Another way to calculate this answer would be by volume, which has a different molecular weight and density than grams per millilitre (g/mL). So if we do that calculation instead, it becomes about 0.09 mL x 28 g/mol = 22 moles in the sample! This method tells us how many molecules there are according to volume.

The third way to measure this problem is by surface area: 82.99 cm^(squared). If we divide by Avogadro’s constant (0.0625*molecules-cm), then our answer is 46 million square meters squared or 17 billion trillion molecules!

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