Question

How many molecules of water are there in 18 grams of water?

Short answer

18 grams of water contains approximately \( 6.016 \times 10^{23} \) molecules.

Step-by-step solution

Calculate Moles of Water

First, we need to find out how many moles of water 18 grams correspond to. The molar mass of water (H2O) is calculated as follows: hydrogens (2 × 1.01 g/mol) + oxygen (16.00 g/mol), which sums up to 18.02 g/mol. Therefore, 18 grams of water is approximately equal to \( \frac{18\, \text{grams}}{18.02\, \text{g/mol}} \approx 0.999 \text{ moles} \).

Use Avogadro's Number to Find Molecules

Now, use Avogadro's number to convert moles into molecules. Avogadro's number states that there are \( 6.022 \times 10^{23} \) molecules in one mole of a substance. Therefore, the number of molecules in 0.999 moles of water is \( 0.999 \times 6.022 \times 10^{23} \approx 6.016 \times 10^{23} \) molecules.

Key concepts

Molar Mass of Water

The molar mass of water is fundamental to understanding how mass, moles, and molecules relate. Water, with the chemical formula \(H_2O\), consists of two hydrogen atoms and one oxygen atom. To find its molar mass, add the atomic masses of these elements:

• Each hydrogen atom has a molar mass of about 1.01 g/mol.
• There are two hydrogen atoms, so that's \(2 \times 1.01 \text{ g/mol} = 2.02\text{ g/mol}\).
• Oxygen has a molar mass of 16.00 g/mol.

Combine these values for a total molar mass: \[2.02 \text{ g/mol} + 16.00 \text{ g/mol} = 18.02 \text{ g/mol}\].This means that 1 mole of water weighs 18.02 grams. When you have a precise mass of water, such as 18 grams, dividing by 18.02 g/mol gives the number of moles, providing a bridge to further calculations.

Avogadro's Number

Avogadro's number is like a counting tool for chemists, used to link the macroscopic and microscopic worlds. It tells us how many particles, such as atoms or molecules, are in a mole of a substance. This number is an incredibly large constant, approximately \(6.022 \times 10^{23}\), and is vital for transforming moles into tangible particle counts.For instance, when you have 1 mole of water, you're effectively holding \(6.022 \times 10^{23}\) molecules in your hand. If you calculated that you have 0.999 moles of water from 18 grams, multiplying these moles by Avogadro's number gives you the total number of water molecules, turning abstract moles into countable entities.

Molecule Calculation

Calculating the molecules in a given mass of substance is straightforward once the molar mass and Avogadro's number are understood. The first step is always to determine how many moles you're dealing with. For instance, with 18 grams of water and knowing its molar mass is 18.02 g/mol, this results in approximately 0.999 moles.The equation used here is: \[ \text{Number of Moles} = \frac{\text{Mass of Substance}}{\text{Molar Mass}} \]Once the number of moles is known, multiply by Avogadro's number to find the number of molecules: \[ \text{Number of Molecules} = \text{Number of Moles} \times 6.022 \times 10^{23} \]Using the values from the example, you multiply 0.999 moles by \(6.022 \times 10^{23}\) to find that there are approximately \(6.016 \times 10^{23}\) molecules of water.Understanding and employing these steps allows you to bridge the mass of a substance with the actual count of its molecules, thus revealing the true scale of chemical reactions.