We find the number of molecules in a sample by relating its mass to the number of moles, and then using Avogadro's number. Here's a breakdown of the process:
Calculating the Number of Molecules
The most common method to determine the number of molecules in a given sample involves understanding the relationship between mass, molar mass, and Avogadro's number. This calculation breaks down into several steps:
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Determine the Molar Mass: First, you need to identify the chemical formula of the substance and calculate its molar mass. The molar mass is the mass of one mole of the substance, and it is usually expressed in grams per mole (g/mol). To calculate it, sum the atomic masses of all the atoms in the molecule, using values found on the periodic table. For example, the molar mass of water (H₂O) is approximately (2 1.01 g/mol) + (1 16.00 g/mol) = 18.02 g/mol.
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Determine the Number of Moles: Divide the mass of your sample (in grams) by the molar mass of the substance. This gives you the number of moles present in the sample.
Formula: moles = mass (g) / molar mass (g/mol)
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Apply Avogadro's Number: Multiply the number of moles by Avogadro's number (approximately 6.022 x 10²³ molecules/mol). This will give you the number of molecules in the sample.
Formula: number of molecules = moles * Avogadro's number
Example Calculation
Let's say you have 36.04 grams of water (H₂O). How many water molecules do you have?
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Molar Mass of Water: As calculated above, the molar mass of water is approximately 18.02 g/mol.
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Number of Moles: moles = 36.04 g / 18.02 g/mol = 2 moles
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Number of Molecules: number of molecules = 2 moles * 6.022 x 10²³ molecules/mol = 1.2044 x 10²⁴ molecules
Therefore, 36.04 grams of water contain approximately 1.2044 x 10²⁴ water molecules.
Summary
To determine the number of molecules in a sample, calculate the molar mass of the substance, determine the number of moles by dividing the sample's mass by the molar mass, and then multiply the number of moles by Avogadro's number. This process allows us to bridge the gap between measurable macroscopic properties (mass) and the microscopic world of molecules.
