Question

Calculate the number of water molecules \(\left(\mathrm{H}_{2} \mathrm{O}\right)\) in \(50.0 \mathrm{~g}\) of water.

Short answer

The number of water molecules in 50.0 g of water is approximately \(1.67 \times 10^{25}\) water molecules.

Step-by-step solution

Find the molar mass of one water molecule

To find the number of water molecules, we need to know the molar mass of water. Calculate this by adding the atomic masses of two hydrogen atoms (2 * 1.008 g/mol) and one oxygen atom (16.00 g/mol).

Calculate the number of moles of water

Use the molar mass from step one to convert grams of water to moles. The formula is moles = mass (grams) / molar mass (grams/mol).

Calculate the number of water molecules

Use Avogadro's number (\(6.022 \times 10^{23}\) molecules/mol) to convert the number of moles from step two to the number of molecules. The formula is number of molecules = moles \times Avogadro's number.

Key concepts

Molar Mass Calculation

Understanding the molar mass of a substance is a fundamental concept in chemistry. Molar mass represents the mass of one mole of a given substance and is expressed in grams per mole (g/mol). To calculate the molar mass of a molecule like water (H_2O) , we sum up the atomic masses of all the atoms in the molecule.

For water, each hydrogen atom contributes approximately 1.008 g/mol, and since there are two hydrogen atoms in each molecule of water, we have 2 \times 1.008 g/mol. Oxygen's contribution is 16.00 g/mol. Thus, the molar mass of water is calculated as follows:\[ (\text{2 Hydrogens} \times 1.008 \text{ g/mol}) + (\text{1 Oxygen} \times 16.00 \text{ g/mol}) = 18.016 \text{ g/mol}.\]
Having the accurate molar mass is essential as it acts as a conversion factor between the weight of a substance and the amount in moles, a concept we'll explore in the next section.

Moles and Molecular Conversion

Once the molar mass is determined, the next step is to convert mass into moles, as moles provide a way to quantify particles on a macro scale, applicable in laboratory measurements. The relationship is straightforward: the number of moles of a substance is equal to its mass (in grams) divided by its molar mass (in grams per mole).

For example, if we have 50.0 g of water, we use the molar mass of water (18.016 g/mol) to find the number of moles:\[\frac{50.0 \text{ g}}{18.016 \text{ g/mol}}\]
By performing this division, we can find how many 'units' of water we have, in terms of moles. This conversion is vital because while weight is an easy measurement, chemical reactions and the properties of substances are often described in terms of the number of molecules or atoms rather than their mass.

Avogadro's Number Application

Avogadro's number (6.022 \times 10^{23}) is a constant that assists in the conversion between moles and the actual number of particles, be they molecules, atoms, or ions. This large number signifies how many particles are contained in one mole of a substance.

When a question asks for the number of water molecules in a given mass of water, Avogadro's number is used as a conversion factor. After calculating the number of moles from the previous step, we then multiply by Avogadro's number to get the total number of molecules:\[\text{number of molecules} = \text{moles} \times 6.022 \times 10^{23} \text{molecules/mol}\].
By applying Avogadro's number, we can bridge the gap between the abstract concept of moles and tangible count of water molecules, providing an insight into the scale of atoms and molecules in chemical processes.