Question

Which of the following chlorides has the highest and which ha the lowest percentage of chlorine, by mass, in its formula? (a) \(\mathrm{KCl}\) (c) \(\mathrm{SiCl}_{4}\) (b) \(\mathrm{BaCl}_{2}\) (d) \(\mathrm{LiCl}\)Which of the following chlorides has the highest and which ha the lowest percentage of chlorine, by mass, in its formula? (a) \(\mathrm{KCl}\) (c) \(\mathrm{SiCl}_{4}\) (b) \(\mathrm{BaCl}_{2}\) (d) \(\mathrm{LiCl}\)

Short answer

Highest: \(\text{SiCl}_{4}\) with 83.85%. Lowest: \(\text{BaCl}_{2}\) with 34.05%.

Step-by-step solution

- Calculate Molar Mass of Each Compound

Find the molar masses of each element in the given compounds and sum them to get the total molar mass.a) For \(\text{KCl}\):- Molar mass of K = 39.1 g/mol- Molar mass of Cl = 35.5 g/mol- Total molar mass = 39.1 + 35.5 = 74.6 g/molb) For \(\text{BaCl}_{2}\):- Molar mass of Ba = 137.3 g/mol- Molar mass of Cl = 35.5 g/mol- Total molar mass = 137.3 + (2 \times 35.5) = 208.3 g/molc) For \(\text{SiCl}_{4}\):- Molar mass of Si = 28.1 g/mol- Molar mass of Cl = 35.5 g/mol- Total molar mass = 28.1 + (4 \times 35.5) = 169.1 g/mold) For \(\text{LiCl}\):- Molar mass of Li = 6.9 g/mol- Molar mass of Cl = 35.5 g/mol- Total molar mass = 6.9 + 35.5 = 42.4 g/mol

- Calculate the Mass Percentage of Chlorine

Use the formula for percentage mass of an element in a compound: (mass of the element / total molar mass of the compound) \(\times 100\)a) For \(\text{KCl}\):- Percentage of Cl = (35.5 / 74.6) \(\times 100\) = 47.59%b) For \(\text{BaCl}_{2}\):- Percentage of Cl = (2 \times 35.5) / (208.3) \(\times 100\) = 34.05%c) For \(\text{SiCl}_{4}\):- Percentage of Cl = (4 \times 35.5) / (169.1) \(\times 100\) = 83.85%d) For \(\text{LiCl}\):- Percentage of Cl = (35.5 / 42.4) \(\times 100\) = 83.73%

- Compare the Percentages

Compare the calculated mass percentages of chlorine.Highest percentage of chlorine: \(\text{SiCl}_{4}\) with 83.85%.Lowest percentage of chlorine: \(\text{BaCl}_{2}\) with 34.05%.

Key concepts

Molar Mass Calculation

The first step in determining the chlorine percentage in a compound is to calculate the molar mass of each compound. This is vital as it influences the final mass percentage. To find the molar mass, sum up the atomic masses of all the atoms in the compound.
For example:
- For KCl: Molar mass of K = 39.1 g/mol, Molar mass of Cl = 35.5 g/mol, Total = 39.1 + 35.5 = 74.6 g/mol
- For BaCl₂: Molar mass of Ba = 137.3 g/mol, Molar mass of Cl = 35.5 g/mol, Total = 137.3 + (2 × 35.5) = 208.3 g/mol
- For SiCl₄: Molar mass of Si = 28.1 g/mol, Molar mass of Cl = 35.5 g/mol, Total = 28.1 + (4 × 35.5) = 169.1 g/mol
- For LiCl: Molar mass of Li = 6.9 g/mol, Molar mass of Cl = 35.5 g/mol, Total = 6.9 + 35.5 = 42.4 g/mol
This calculation sets the foundation for further steps in determining the mass percentage of chlorine.

Mass Percentage

Once you know the molar mass of the compound, you can calculate the mass percentage of any element within the compound. The formula is: \[ \text{Percentage of Element} = \left( \frac{\text{Mass of the Element}}{\text{Total Molar Mass of the Compound}} \right) \times 100 \] For example:
- For KCl: \[ \text{Percentage of Cl} = \left( \frac{35.5}{74.6} \right) \times 100 = 47.59\% \]
- For BaCl₂: \[ \text{Percentage of Cl} = \left( \frac{2 \times 35.5}{208.3} \right) \times 100 = 34.05\% \]
- For SiCl₄: \[ \text{Percentage of Cl} = \left( \frac{4 \times 35.5}{169.1} \right) \times 100 = 83.85\% \]
- For LiCl: \[ \text{Percentage of Cl} = \left( \frac{35.5}{42.4} \right) \times 100 = 83.73\% \] This step helps to determine how much of the compound's mass is due to chlorine.

Chemical Formulas

Understanding chemical formulas is essential in accurately performing molar mass calculations. A chemical formula lists the elements and the number of atoms for each element in the compound.
For instance:
- KCl indicates 1 atom of Potassium (K) and 1 atom of Chlorine (Cl).
- BaCl₂ indicates 1 atom of Barium (Ba) and 2 atoms of Chlorine (Cl).
- SiCl₄ indicates 1 atom of Silicon (Si) and 4 atoms of Chlorine (Cl).
- LiCl indicates 1 atom of Lithium (Li) and 1 atom of Chlorine (Cl).
Each formula provides the information needed to calculate the molar mass, which is crucial for determining the mass percentage of elements in the compound.

Stoichiometry

Stoichiometry refers to the calculations of relative quantities of reactants and products in chemical reactions. It also applies to understanding the composition of compounds. In this context, it helps determine the mass percentage of chlorine in various compounds. By knowing stoichiometry, you can:
- Balance chemical equations.
- Calculate reactant and product quantities.
- Determine the composition of substances.
It's essential to grasp this concept as it ensures accuracy in calculating the molar masses and mass percentages, essential parts of chemistry.

Chemical Compound Comparison

The final step involves comparing the mass percentages of chlorine in different compounds to determine which one has the highest and lowest. This comparison enables you to understand the distribution of chlorine across various compounds. For instance, in our example:
- SiCl₄ has the highest chlorine percentage with 83.85%.
- BaCl₂ has the lowest chlorine percentage with 34.05%.
This comparison aids in understanding how different elements in a compound influence the overall composition and characteristics of the compound.
By mastering these comparisons, you can analyze various compounds effectively in terms of their elemental composition.