Problem 29 - Chemistry The Central Science

Question

(a) Write "true" or "false" for each statement. (a) A mole of horses contain a mole of horse legs. (b) A mole of water has a mass of 18.0 \(\mathrm{g} .\) (c) The mass of 1 molecule of water is 18.0 \(\mathrm{g}\) (d) A mole of NaCl (s) contains 2 moles of ions.

Step-by-Step Solution

Answer

The short version of the answer is: (a) False (b) True (c) False (d) True

Step 1: Statement (a)

First, let's analyze statement (a): "A mole of horses contains a mole of horse legs." A mole is a unit of measurement used to represent a very large number of particles or entities, typically 6.022 x 10^23. In this case, the statement is suggesting that when there is a mole of horses, there would also be a mole of horse legs. Since a horse typically has 4 legs, a mole of horses would have 4 moles of horse legs. Therefore, the given statement is false.

Step 2: Statement (b)

Now, let's analyze statement (b): "A mole of water has a mass of 18.0 g." To find the mass of a mole of a substance, we need to multiply its molar mass (the mass of one mole of a substance, in grams) by the number of moles. The molar mass of water \((H_2O)\) is 18.0 g/mol as it consists of two hydrogen atoms and one oxygen atom (1.0 g/mol + 1.0 g/mol + 16.0 g/mol). So, one mole of water would indeed have a mass of 18.0 g. Therefore, the given statement is true.

Step 3: Statement (c)

Let's now examine statement (c): "The mass of 1 molecule of water is 18.0 g." As discussed earlier, the molar mass of water is 18.0 g/mol. The statement is asking about the mass of a single molecule of water, not a mole of water. To find the mass of a single molecule of water, we can divide the molar mass by Avogadro's number \((6.022 \times 10^23)\), so the mass of a single molecule of water is about 2.99 x 10^(-23) g. Therefore, the given statement is false.

Step 4: Statement (d)

Finally, let's analyze statement (d): "A mole of NaCl (s) contains 2 moles of ions." Sodium chloride \((NaCl)\) is an ionic compound formed by sodium atoms \((Na^+)\) and chloride atoms \((Cl^-)\), which are bonded together as ions. When one mole of sodium chloride dissociates in solution, it produces one mole of sodium ions \((Na^+)\) and one mole of chloride ions \((Cl^-)\), resulting in a total of 2 moles of ions. Therefore, the given statement is true.

Key Concepts

Molar Mass

The concept of molar mass is a fundamental part of chemistry. It is the mass of one mole of a substance, which is expressed in grams per mole (g/mol). To find the molar mass of a compound, you add up the mass of each element within the compound, multiplied by its respective number of atoms. For example, in water (H₂O),

• Each hydrogen atom has a molar mass of about 1.0 g/mol.
• Oxygen has a molar mass of 16.0 g/mol.

Summing these up, the molar mass of water becomes:

• 2 x 1.0 (for the two hydrogens) + 16.0 (for oxygen), which equals 18.0 g/mol.

This means that one mole of water weighs 18 grams. Understanding molar mass is crucial for converting between moles and grams in chemical calculations.
When dealing with any chemical reaction or process, we often calculate how much of a substance is needed or produced by using its molar mass.

Avogadro's Number

Avogadro's number is key to understanding the mole concept in chemistry. It represents the amount of particles, be they atoms, molecules, or ions, in one mole of substance. Specifically, Avogadro's number is approximately 6.022 x 10²³.
This large number simplifies calculations when dealing with particles at the atomic scale. For example, if we consider one mole of water:

• It wouldn't only weigh 18 grams, but also contain 6.022 x 10²³ molecules of water.

To find the mass of an individual molecule, we divide the molar mass by Avogadro's number. This calculation can help us translate between the macroscopic world that we observe and the microscopic world where atoms and molecules reside.
Understanding Avogadro's number allows chemists to determine amounts of reactants and products in chemical equations accurately.

Ionic Compounds

Ionic compounds are formed when atoms transfer electrons to achieve a stable electron configuration, usually creating ions. These compounds typically consist of metal cations and non-metal anions.

• For example, in sodium chloride (NaCl), sodium (Na) loses one electron to become a cation (Na⁺), and chlorine (Cl) gains that electron to become an anion (Cl⁻). This ionic bond results from the electrostatic attraction between these oppositely charged ions.

When an ionic compound like NaCl dissolves in water, it dissociates into its ions:

• One mole of NaCl yields one mole of Na⁺ and one mole of Cl⁻, totaling 2 moles of ions.

Ionic compounds are important because they have unique physical and chemical properties such as high melting points and the ability to conduct electricity when melted or dissolved in water.
Understanding how ionic compounds form and behave is key in fields ranging from materials science to biochemistry.