Question

Which of the following substances contains the greatest mass of chlorine: (a) \(5.0 \mathrm{~g} \mathrm{Cl}_{2},\) (b) \(60.0 \mathrm{~g} \mathrm{NaClO}_{3}\), (c) \(0.10 \mathrm{~mol} \mathrm{KCl}\), (d) \(30.0 \mathrm{~g} \mathrm{MgCl}_{2}\) (e) \(0.50 \mathrm{~mol} \mathrm{Cl}_{2}\) ?

Short answer

Option (e) 0.50 mol Cl2 has the greatest mass of chlorine, 35.450 g.

Step-by-step solution

Calculate the moles of chlorine in each compound

For each compound, calculate the moles of chlorine present. 1. For \( \mathrm{Cl}_2, \) with 5.0 g of \( \mathrm{Cl}_2: \) - Molar mass of \( \mathrm{Cl}_2 = 70.9 \text{ g/mol} \) - Moles of \( \mathrm{Cl}_2 = \frac{5.0}{70.9} \approx 0.0706 \text{ mol} \) - Since each \( \mathrm{Cl}_2 \) molecule contains 2 atoms of Cl, moles of Cl = \(2 \times 0.0706 = 0.1412 \text{ mol} \)2. For \( \mathrm{NaClO}_3, \) with 60.0 g of \( \mathrm{NaClO}_3: \) - Molar mass of \( \mathrm{NaClO}_3 = 106.44 \text{ g/mol} \) - Moles of \( \mathrm{NaClO}_3 = \frac{60.0}{106.44} \approx 0.5638 \text{ mol} \) - Each molecule contains 1 atom of Cl, moles of Cl = \(0.5638 \text{ mol} \)3. For \( \mathrm{KCl} \) with 0.10 mol: - Moles of Cl = 0.10 mol4. For \( \mathrm{MgCl}_2, \) with 30.0 g of \( \mathrm{MgCl}_2: \) - Molar mass of \( \mathrm{MgCl}_2 = 95.21 \text{ g/mol} \) - Moles of \( \mathrm{MgCl}_2 = \frac{30.0}{95.21} \approx 0.315 \text{ mol} \) - Each molecule contains 2 atoms of Cl, moles of Cl = \(2 \times 0.315 = 0.630 \text{ mol} \)5. For \( \mathrm{Cl}_2 \) with 0.50 mol: - Moles of Cl = 1.0 mol (as each \( \mathrm{Cl}_2 \) contains 2 atoms of Cl, \( 2 \times 0.50 = 1.00 \text{ mol} \) )

Calculate the mass of chlorine in each compound

Use the moles of Cl calculated in Step 1 to find the mass of Cl. The atomic mass of Cl is approximately 35.45 g/mol.1. For \( 5.0 \text{ g } \mathrm{Cl}_2 \): - Mass of Cl = \(0.1412 \text{ mol} \times 35.45 \text{ g/mol} = 5.007 \text{ g} \)2. For \( 60.0 \text{ g } \mathrm{NaClO}_3 \): - Mass of Cl = \(0.5638 \text{ mol} \times 35.45 \text{ g/mol} = 19.988 \text{ g} \)3. For \( 0.10 \text{ mol } \mathrm{KCl} \): - Mass of Cl = \(0.10 \text{ mol} \times 35.45 \text{ g/mol} = 3.545 \text{ g} \)4. For \( 30.0 \text{ g } \mathrm{MgCl}_2 \): - Mass of Cl = \(0.630 \text{ mol} \times 35.45 \text{ g/mol} = 22.324 \text{ g} \)5. For \( 0.50 \text{ mol } \mathrm{Cl}_2 \): - Mass of Cl = \(1.0 \text{ mol} \times 35.45 \text{ g/mol} = 35.450 \text{ g} \)

Determine the substance with the greatest mass of chlorine

Compare the calculated mass of chlorine for each option:- (a) 5.007 g from \( 5.0 \text{ g } \mathrm{Cl}_2 \)- (b) 19.988 g from \( 60.0 \text{ g } \mathrm{NaClO}_3 \)- (c) 3.545 g from \( 0.10 \text{ mol } \mathrm{KCl} \)- (d) 22.324 g from \( 30.0 \text{ g } \mathrm{MgCl}_2 \)- (e) 35.450 g from \( 0.50 \text{ mol } \mathrm{Cl}_2 \)The greatest mass of chlorine comes from option (e), 0.50 mol \( \mathrm{Cl}_2 \).

Key concepts

Molar Mass

Understanding molar mass is crucial in chemistry. It is the mass of one mole of a substance. Molar mass is expressed in grams per mole (g/mol). You can think of it as the weight of 6.022 x 10^23 (Avogadro's number) of molecules or atoms of a substance.
Molar mass is calculated by adding up the atomic masses of all the atoms in a molecule. For example, the molar mass of Cl2 is the sum of the atomic masses of two chlorine atoms. Since the atomic mass of chlorine is about 35.45 g/mol, the molar mass of Cl2 is approximately 70.9 g/mol.
When solving problems involving chemical reactions, molar mass allows us to convert grams of a molecule to moles, which is often more useful in stoichiometry.

Calculate Moles

Calculating moles is an essential skill in chemistry, as it connects the mass of a substance to its quantity in terms of molecules or atoms. Moles provide a bridge between the atomic world and the macroscopic world.
To find the number of moles, you use the formula: \[ \text{Moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
In a problem, when you're asked to calculate moles from a given mass, determine the molar mass first and then apply the formula. For instance, finding moles of Cl2 with a mass of 5.0 g and a molar mass of 70.9 g/mol involves dividing 5.0 by 70.9, giving approximately 0.0706 mol. This approach is fundamental in chemistry for understanding reactions and quantities.

Atomic Mass

Atomic mass might seem similar to molar mass, but it is a distinctive and foundational concept. It represents the average mass of an atom, usually expressed in atomic mass units (amu). One amu is defined as one twelfth the mass of a carbon-12 atom.
Each element's atomic mass can be found on the periodic table. For chlorine, it is about 35.45 amu. This atomic mass is an average, considering the natural isotopic distribution of the element.
In the context of calculations like determining the mass of chlorine in various compounds, knowing the atomic mass helps in converting moles to grams and vice versa, as it's a component of the molar mass.

Chemical Compounds

Chemical compounds are substances formed by two or more elements chemically bonded together. These compounds have unique properties distinct from the elements that constitute them.
Understanding the composition of chemical compounds aids in determining how elements like chlorine behave when part of multiple compounds. For example, in compounds such as NaClO3 and MgCl2, chlorine shows up differently, influencing the compound’s properties and interactions.
When working with such compounds, knowing the chemical formula and the type of bonds between elements helps you calculate how much of each element is involved, particularly how much chlorine is present in these instances.

Comparison

Comparison in chemistry often involves assessing different substances to understand which yields the greatest mass or reaction outcome. Such comparisons require careful analysis of moles, masses, and chemical composition.
In the exercise concerning mass of chlorine, comparison involves calculating how much chlorine is present in each of the given substances. You calculate the mass of chlorine in each compound, then directly compare their amounts to find which has the greatest mass of chlorine.
This skill is vital in laboratory settings and chemical industry as it determines how best to use resources and predict chemical change outcomes based on known quantities.