Calculating the Number of Molecules in 11.5 mol of Water

In chemistry, the mole is a unit that allows us to work with extremely large numbers of atoms and molecules. The mole represents 6.022×1023 particles, which is known as Avogadro’s number. This number is so large that counting individual molecules or atoms would be highly impractical. That’s where the mole comes in – it allows us to work with macroscopic amounts of substances while still relating them back to the microscopic level through Avogadro’s number.

Calculating the Number of Molecules in 11.5 mol of Water

The number of molecules in 11.5 mol of water is 1.247 x 1025 molecules.

To calculate:

  1. Molar mass of H2O is 18.015 g/mol
  2. 11.5 mol H2O has a mass of 11.5 x 18.015 = 207.1725 g
  3. Use Avogadro’s number: 207.1725 g x (6.022×1023 molecules/mol) = 1.247×1025 molecules

So 11.5 mol of water contains 1.247 x 1025 water molecules.

Defining the Mole

The mole is defined as the amount of a substance that contains 6.022×1023 constituent particles, which may be atoms, molecules, ions, or electrons. This number 6.022×1023 is known as Avogadro’s constant or Avogadro’s number, after the 19th century Italian scientist Amedeo Avogadro.

The mole provides chemists with a way to bridge the gap between the atomic/molecular world and the macroscopic properties we routinely measure in the laboratory. With the mole, we can convert back and forth between mass, which we can easily measure, and number of particles, which we cannot directly count. For example, one mole of carbon atoms has a mass of 12 grams, while one mole of water molecules has a mass of 18 grams. The mole allows us to flip between these mass and particle number representations with ease.

Molar Mass

The molar mass of a substance is the mass in grams of one mole of that substance. It is a conversion factor that allows us to switch between mass and amount in moles. For chemical compounds, the molar mass is simply the sum of the atomic masses of each element involved.

For water (H2O), the molar mass is calculated as:

  • 2 hydrogen atoms (1.008 amu each) = 2.016 amu
  • 1 oxygen atom (15.999 amu) = 15.999 amu
  • Total molar mass H2O = 18.015 grams/mole

So for water, each mole of molecules has a mass of 18.015 grams. This molar mass allows us to interconvert between mass in grams and amount in moles for any sample of water.

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Avogadro’s Number

As previously mentioned, Avogadro’s number gives the number of particles present in one mole of a substance. This number, 6.022×1023, is an enormous figure, reflecting the fact that we are working with molecular-scale amounts of matter. Some comparisons help put the sheer size of Avogadro’s number in perspective:

  • There are approximately 100 billion stars in the Milky Way galaxy. Avogadro’s number is 60 trillion times larger than this figure.
  • The Atlantic Ocean contains roughly 350 quintillion (350 billion billion) gallons of water. Avogadro’s number is about 20 billion times larger.
  • Counting at a rate of one number per second, it would take about one trillion years to count to Avogadro’s number. That’s over 70 times the current age of the universe.

Needless to say, trying to count individual atoms or molecules to Avogadro’s number would be futile. The mole gives us a way to work with such large numbers concisely as amounts of substance, without having to resort to impossible counting exercises.

Calculating Molecules from Moles

Now that we understand the basic foundations of the mole, let’s tackle our original question: how many water molecules are present in 11.5 mol of H2O?

We’ll follow a simple two-step process:

Step 1) Use the molar mass of water to convert from moles to grams: 11.5 mol H2O x (18.015 g/mol) = 207.1725 g H2O

Step 2) Use Avogadro’s number to convert from grams to molecules: 207.1725 g H2O x (6.022×1023 molecules/mol) = 1.247×1025 molecules

Therefore, 11.5 mol of water contains 1.247×1025 water molecules! That’s over 1 billion trillion individual water molecules, far more than we could ever hope to count individually. But using the mole concept, we can easily relate macroscale amounts of substances to the molecular level.

Conclusion

In this blog post, we’ve seen how chemists can use the mole to work with extraordinarily large numbers of atoms and molecules. By combining the molar mass with Avogadro’s number, we can easily interconvert between the mass of a substance and the number of constituent particles it contains. These fundamental concepts are essential for working quantitatively with chemical reactions and compounds. Understanding mole calculations unlocks the ability to connect real-world laboratory measurements to the atomic scale and to determine quantities of reactants and products in chemical reactions.

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