Question

How many molecules of water are there in a \(10.0-\mathrm{g}\) sample of water? How many hydrogen atoms are there in this sample?

Short answer

In a 10.0-g sample of water, there are approximately \(3.34 \times 10^{23}\) water molecules and \(6.68 \times 10^{23}\) hydrogen atoms.

Step-by-step solution

Convert the mass to moles

Before we can find the number of water molecules in the sample, we must first determine how many moles of water there are in 10.0 g of water. We do this using the molar mass of water, which is approximately 18.015 g/mol. The conversion is given by: moles of water = (mass of sample) / (molar mass of water)

Calculate the number of moles in the sample

Now, plug the values into the formula from Step 1: moles of water = (10.0 g) / (18.015 g/mol) moles of water ≈ 0.555 moles

Use Avogadro's number to find the number of molecules

Now that we have the number of moles in the sample, we can use Avogadro's number to find the number of molecules. Avogadro's number is approximately \(6.022 \times 10^{23}\) molecules/mol. The formula is: number of water molecules = (moles of water) * (Avogadro's number)

Calculate the number of water molecules in the sample

Plug the values into the formula from Step 3: number of water molecules = (0.555 moles) * \(6.022 \times 10^{23}\) molecules/mol number of water molecules ≈ \(3.34 \times 10^{23}\) molecules

Find the number of hydrogen atoms in the sample

Now, remember that each water molecule (H₂O) has two hydrogen atoms. To find the total number of hydrogen atoms in the sample, multiply the number of water molecules by 2: number of hydrogen atoms = (number of water molecules) * 2

Calculate the number of hydrogen atoms

Using the value from Step 4: number of hydrogen atoms = \(3.34 \times 10^{23}\) molecules * 2 number of hydrogen atoms ≈ \(6.68 \times 10^{23}\) atoms In conclusion, there are approximately \(3.34 \times 10^{23}\) water molecules and \(6.68 \times 10^{23}\) hydrogen atoms in a 10.0-g sample of water.

Key concepts

Avogadro's Number

Avogadro's Number is an essential constant in chemistry that makes it possible to calculate the number of individual entities, like atoms or molecules, in a substance when given the amount in moles. This constant, named after the scientist Amedeo Avogadro, is approximately \(6.022 \times 10^{23}\) entities per mole. This massive number is crucial because substances at the molecular level are incredibly small, and counting them directly is impractical.
To put it into perspective, imagine counting each grain of rice in a pile of \(6.022 \times 10^{23}\) grains. This would be an enormous task, demonstrating how much easier it is to use Avogadro's Number to simplify the concept of counting molecules in chemical reactions or ordinary objects like a glass of water.

Moles Conversion

Moles are the bridge between the atomic world and the macroscopic world we observe daily. When converting between grams and moles, we use the molar mass as a conversion factor. Molar mass, detailed in another section, tells us the mass of one mole of a substance.
For example, if we have a 10.0 g sample of water, we aim to convert this measurement to moles using the molar mass of water. The formula used is:

• Moles of water = \(\frac{\text{mass of sample}}{\text{molar mass of water}}\)

In our case, the molar mass of water is approximately 18.015 g/mol. So, by dividing 10.0 g by 18.015 g/mol, we obtain roughly 0.555 moles of water.
Understanding how to convert between grams and moles is crucial for solving many chemistry problems because it allows us to quantitively describe the amount of a substance present.

Molar Mass

Molar Mass is the weight of one mole of a substance and is expressed in grams per mole (g/mol). For any compound, the molar mass can be determined by adding up the atomic masses of all atoms present in the molecular formula.
In the case of water (H₂O), the molar mass is calculated by adding the atomic masses of two hydrogen atoms (approximately 1.008 g/mol each) and one oxygen atom (approximately 16.00 g/mol). Hence, the molar mass of water turns out to be approximately 18.015 g/mol.

• Atomic mass of H: ~1.008 g/mol
• Atomic mass of O: ~16.00 g/mol
• Thus, molar mass of H₂O = \(2 \times 1.008 + 16.00 \approx 18.015\) g/mol

This value is crucial for converting between mass and moles. Knowing the molar mass allows us to understand how much a specific mole weighs, which can then be utilized in various calculations, such as determining the number of molecules or atoms in a given sample.