Question

Which of the following correctly represents \(180 \mathrm{~g}\) of water? (i) 5 moles of water (ii) 10 moles of water (iii) \(6.023 \times 10^{23}\) molecules of water (iv) \(6.023 \times 10^{24}\) molecules of water (a) (i) and (ii) (b) (i) and (iv) (c) (ii) ând (iv) (d) (ii) and (iii)

Short answer

(ii) and (iv)

Step-by-step solution

Determine the molar mass of water

Find the molar mass of water (H2O) by adding up the atomic masses of hydrogen and oxygen. Each hydrogen atom has an approximate atomic mass of 1 g/mol and oxygen has an atomic mass of approximately 16 g/mol. Therefore, the molar mass of water is approximately 2(1) + 16 = 18 g/mol.

Calculate the number of moles in 180 g of water

Use the molar mass of water to find out the number of moles in 180 g of water. Number of moles = mass (in grams) / molar mass (in g/mol), which is 180 g / 18 g/mol = 10 moles.

Convert moles to molecules

Use Avogadro's number to convert moles to molecules. 1 mole of any substance contains exactly 6.023 x 10^23 molecules. So, 10 moles will contain 10 x 6.023 x 10^23 = 6.023 x 10^24 molecules of water.

Compare the options with calculations

Compare the calculated values with the given options. The value 10 moles matches option (ii), and the number of molecules 6.023 x 10^24 matches option (iv).

Key concepts

Molar Mass of Water

Understanding the molar mass of water is crucial for a variety of chemistry calculations. The molar mass is the weight of one mole of a substance and is expressed in grams per mole (g/mol). To calculate the molar mass of water, which has the chemical formula H₂O, we simply add the molar masses of its constituent atoms.

Each hydrogen atom contributes approximately 1 g/mol, and there are two hydrogen atoms in each water molecule. Oxygen, on the other hand, has a molar mass of approximately 16 g/mol. Thus, by summing these values, we calculate the molar mass of water to be 2(1) + 16 = 18 g/mol.

This computation allows us to perform tasks such as converting the mass of a water sample to the number of moles it contains, which is a foundational concept in chemistry. For example, a 180 g sample of water divided by its molar mass (18 g/mol) yields 10 moles of water, bridging the gap between physical mass and the mole concept.

Avogadro's Number

At the heart of the mole concept in chemistry lies Avogadro's number. It is defined as the exact number of entities, be they atoms, ions, or molecules, in one mole of a substance. Avogadro's number is a constant at approximately 6.022 x 10²³.

The significance of this number is profound because it establishes a direct link between the macroscopic world we perceive and the microscopic world of atoms and molecules. Whenever we have one mole of any substance, we can confidently say that we possess 6.022 x 10²³ of its fundamental units.

For instance, in the context of our 10 moles of water, we multiply 10 by Avogadro's number to determine the total number of water molecules, which gives us 6.022 x 10²⁴ water molecules. This conversion is essential for problems that transition between the number of moles and the exact count of molecules.

Moles to Molecules Conversion

Translating moles to molecules is a common and pivotal operation in chemistry, allowing us to quantify the exact number of molecules in a given amount of substance. This conversion utilizes Avogadro's number as the conversion factor.

For this conversion, the formula used is: Number of molecules = Number of moles x Avogadro's number. Applying this formula to our problem: if we have 10 moles of water, we multiply those 10 moles by Avogadro's number (6.022 x 10²³ molecules/mole), which equals 6.022 x 10²⁴ molecules.

Understanding this conversion helps to interpret chemical reactions on a molecular level, ensuring students can transition between macroscopic measurements and microscopic implications. This is fundamental for stoichiometry and for comprehending the composition of compounds and the reactions they undergo.