Question

How many electrons does \(1.00 \mathrm{~kg}\) of water contain?

Short answer

Answer: In 1 kg of water, there are approximately \(3.34\times10^{26}\) electrons.

Step-by-step solution

Determine the molar mass of water

The molar mass of water, H2O, can be calculated by adding up the molar masses of its constituent atoms: 2 hydrogen atoms and 1 oxygen atom. The molar mass of hydrogen is about 1 g/mol, and the molar mass of oxygen is about 16 g/mol. So the molar mass of water is: \(1 \mathrm{~g/mol} *2 + 16\mathrm{~g/mol} = 18\mathrm{~g/mol}\)

Convert mass of water to moles

To convert 1 kg (1000 g) of water to moles, divide the mass by the molar mass: \(\text{moles of water} = \frac{1000\mathrm{~g}}{18\mathrm{~g/mol}} = 55.56\mathrm{~mol}\)

Calculate the number of water molecules

Next, we will use Avogadro's number (\(6.022\times10^{23}\)) to convert moles of water into individual water molecules: \(\text{water molecules} = 55.56\mathrm{~mol} \times 6.022\times10^{23}\mathrm{~molecules/mol} \approx 3.34\times10^{25}\mathrm{~molecules}\)

Determine the number of electrons in 1 water molecule

A water molecule (H2O) contains 2 hydrogen atoms and 1 oxygen atom. Since hydrogen atoms have 1 electron each and oxygen atoms have 8 electrons each, the total number of electrons in a water molecule is: \(1\times2 + 8\times1 = 10\mathrm{~electrons}\)

Calculate the total number of electrons

Finally, multiply the number of water molecules in 1 kg of water by the number of electrons in each water molecule to find the total number of electrons: \(\text{total electrons} = 3.34\times10^{25}\mathrm{~molecules} \times 10\mathrm{~electrons/molecule} = 3.34\times10^{26}\mathrm{~electrons}\) In 1 kg of water, there are approximately \(3.34\times10^{26}\) electrons.

Key concepts

Molar Mass

Understanding molar mass is like understanding the mass of the building blocks of matter, called atoms. The molar mass of a compound tells us how much one mole of that compound weighs. For any substance, this is typically measured in grams per mole (g/mol).
For example, consider water (H₂O). To find its molar mass, you sum up the atomic masses of all the atoms in one molecule of water. Each hydrogen atom has a molar mass of approximately 1 g/mol, and since there are two hydrogen atoms in a water molecule, that's 2 g/mol. Oxygen contributes about 16 g/mol. So, the total molar mass of water is 18 g/mol.

• This means one mole of water molecules weighs 18 grams.
• Knowing molar mass helps in converting mass to moles, which is crucial for chemical calculations.

Avogadro's Number

Avogadro's number is a cornerstone concept in chemistry, providing a bridge between the microscopic worlds of atoms and molecules and the macroscopic world we observe.
It is defined as the number of atoms or molecules in one mole of a substance, and is approximately equal to: 6.022 x 10²³.
This means in 1 mole of any element or compound, like water, there are 6.022 x 10²³ molecules or atoms present. This large number helps in understanding the scale of atomic and molecular quantities in a palpable way.

• Avogadro's number allows chemists to convert moles into measurable numbers of atoms or molecules.
• For example, when calculating the number of water molecules in a given mass of water, Avogadro's number is essential.

Water Molecule

The water molecule, represented as H₂O, is composed of two hydrogen atoms and one oxygen atom. This simple yet vital compound exhibits properties that make it indispensable to life on Earth.
In the electronic structure, each hydrogen atom shares one electron with the oxygen atom, forming covalent bonds. The oxygen atom has two additional pairs of electrons, not shared in the bonding, that contribute to water's bent shape and polarity.

• The polarity of water molecules leads to hydrogen bonding, giving water its unique properties like high boiling point and surface tension.
• Understanding water at the molecular level gives insight into its behavior in various physical and chemical contexts.

Atomic Structure

The atomic structure of an element defines its properties. Atoms are made up of protons, neutrons, and electrons. While protons and neutrons reside in the nucleus, electrons orbit in electron shells around the nucleus.
The arrangement and number of these electrons determine the atom's chemical properties and its electronic configuration.
For instance, an oxygen atom has 8 protons and 8 electrons, with its electrons arranged in energy levels: 2 in the first shell and 6 in the second. Meanwhile, hydrogen atoms have 1 electron each.

• Each element’s unique atomic structure explains why different substances have different properties.
• These structural details are crucial for understanding not only elemental behavior but also compound formation, like water (H₂O).