Problem 134 - Chemistry

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) \(0.50 \mathrm{~mol} \mathrm{Cl}_{2}\).

Step-by-Step Solution

Answer

The substance with the greatest mass of chlorine is (e) \(0.50 \mathrm{~mol} \mathrm{Cl}_{2}\) with a mass of \(35.45 \mathrm{~g}\).

Step 1: Find atomic weights and formula weights

Look up the atomic weights of the elements. Chlorine's atomic weight is approximately \(35.45 \mathrm{~g/mol}\). Then, calculate the molar mass for the compounds \(\mathrm{NaClO}_{3}, \mathrm{KCl}, \) and \(\mathrm{MgCl}_{2}\) , which are approximately \(106.44 \mathrm{~g/mol}\), \(74.55 \mathrm{~g/mol}\) and \(95.21 \mathrm{~g/mol}\) respectively.

Step 2: Calculate the mass of Chlorine in each substance

Calculate the mass of chlorine in each substance. For (a), the mass is directly given as \(5.0 \mathrm{~g}\). For (b), the mass of chlorine is \(\frac{1}{3} \times 60.0 \mathrm{~g} = 20.0 \mathrm{~g}\), since \(\mathrm{NaClO}_{3}\) contains one chlorine atom per every three atomic units. For (c), the mass of chlorine is \(0.10 \mathrm{~mol} \times 35.45 \mathrm{~g/mol} = 3.545 \mathrm{~g}\). For (d), the mass of chlorine is \(\frac{2}{3} \times 30.0 \mathrm{~g} = 20.0 \mathrm{~g}\), since \(\mathrm{MgCl}_{2}\) contains two chlorine atoms per every three atomic units. For (e), the mass of chlorine is \(0.50 \mathrm{~mol} \times 70.90 \mathrm{~g/mol} = 35.45 \mathrm{~g}\), since molecular chlorine contains two chlorine atoms.

Step 3: Compare the masses

Compare the masses calculated in step 2. The substance with the greatest mass of chlorine is (e) \(0.50 \mathrm{~mol} \mathrm{Cl}_{2}\) with a mass of \(35.45 \mathrm{~g}\), followed by (a), (b) and (d) with masses of \(20.0 \mathrm{~g}\). The substance with the least mass of chlorine is (c) \(0.10 \mathrm{~mol} \mathrm{KCl}\) with a mass of \(3.545 \mathrm{~g}\).

Key Concepts

Atomic Weight

When trying to understand chemical compounds and their reactions, it's important to know about atomic weight. Atomic weight is like the average weight of an atom of an element, based on how it is naturally found with its isotopes. For chlorine (Cl), its atomic weight is about 35.45 g/mol. This value comes from the masses of its two main isotopes, chlorine-35 and chlorine-37.

Atomic weight helps us know more about how much of each element is in a compound. For students, it's key to grasp this concept as it lays the groundwork for calculating other properties, like molar mass.

Molar Mass

Molar mass is the mass of one mole of a given substance. To find it, we simply add up the atomic weights of all the atoms in a molecule of the compound. This is where atomic weights come into play, providing the numbers we need for this calculation.

Take the compound ext{NaClO}_3 as an example. By adding the atomic weights of sodium (Na), chlorine (Cl), and three oxygen (O) atoms, we get a molar mass of 106.44 g/mol.

• For ext{KCl} , it's calculated as 74.55 g/mol.
• For ext{MgCl}_2 , we calculate it as 95.21 g/mol.

Understanding molar mass allows you to convert between the mass of a substance and the amount in moles, a key step in chemical equations and reactions.

Chlorine-Containing Compounds

Chlorine plays a key role in a variety of chemical compounds. These are often referred to as "chlorine-containing compounds." In the context of the exercise, we deal with different such compounds like ext{NaClO}_3 , ext{KCl} , ext{MgCl}_2 , and ext{Cl}_2 . Each of these compounds contains chlorine atoms, but the number and arrangement differ.

ext{Cl}_2 is simply two chlorine atoms bonded together. Meanwhile, ext{NaClO}_3 contains one chlorine molecule in a more complex structure combined with sodium and oxygen. Understanding the composition of these compounds helps to analyze their chemical behavior and how much chlorine is in them.

Stoichiometry

Stoichiometry is the part of chemistry that helps us understand the relationship between reactants and products in a chemical reaction. It uses numbers and formulas to predict how much of each substance is needed or produced.

In the exercise, stoichiometry helps us calculate how much chlorine is present in a specified mass or moles of its compounds. For example, to find out how much chlorine is in 0.50 moles of ext{Cl}_2 , we multiply the moles by the molar mass (70.90 g/mol): (0.50 ext{ moles} imes 70.90 ext{ g/mol} = 35.45 ext{ g}) . This calculation method can help solve various real-world chemistry problems, from cooking to industrial manufacturing.

Thus, stoichiometry offers a structured way to think about quantities and how they interact in the world of chemistry.