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Chapter 7: Problem 30

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

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

Step by step solution

01

- 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
02

- 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%
03

- 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%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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 BaCl鈧�: Molar mass of Ba = 137.3 g/mol, Molar mass of Cl = 35.5 g/mol, Total = 137.3 + (2 脳 35.5) = 208.3 g/mol
- For SiCl鈧�: Molar mass of Si = 28.1 g/mol, Molar mass of Cl = 35.5 g/mol, Total = 28.1 + (4 脳 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 BaCl鈧�: \[ \text{Percentage of Cl} = \left( \frac{2 \times 35.5}{208.3} \right) \times 100 = 34.05\% \]
- For SiCl鈧�: \[ \text{Percentage of Cl} = \left( \frac{4 \times 35.5}{169.1} \right) \times 100 = 83.85\% \]
- 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).
- BaCl鈧� indicates 1 atom of Barium (Ba) and 2 atoms of Chlorine (Cl).
- SiCl鈧� 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:
- SiCl鈧� has the highest chlorine percentage with 83.85%.
- BaCl鈧� 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.

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Most popular questions from this chapter

Determine the molar masses of these compounds: (a) \(\mathrm{NaOH}\) (f) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\) (b) \(\mathrm{Ag}_{2} \mathrm{CO}_{3}\) (g) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (c) \(\mathrm{Cr}_{2} \mathrm{O}_{3}\) (h) \(\mathrm{K}_{4} \mathrm{Fe}(\mathrm{CN})_{6}\) (d) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}\) (i) \(\mathrm{BaCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) (e) \(\mathrm{Mg}\left(\mathrm{HCO}_{3}\right)_{2}\)

125 grams of disulfur decafluoride contain (a) how many moles? (d) how many atoms of sulfur? (b) how many molecules? (e) how many atoms of fluorine? (c) how many total atoms?

Researchers at Anna Gudmundsdottir's laboratory at the University of Cincinnati have been studying extremely reactive chemicals known as radicals. One of the interesting phenomena they have discovered is that these radicals can be chemically attached to fragrance molecules, effectively tethering them to a solution. When light strikes these tethered molecules, the fragrance is released. This property would allow us to produce perfumes, cleansers, and other consumer products that release fragrance only when exposed to light. If limonene, \(\mathrm{C}_{10} \mathrm{H}_{16}\), the molecule that gives fruits their citrus scent, were able to be tethered to one of these radicals and every photon of light would release one molecule of limonene, calculate the time in seconds required to release \(1.00\) picogram of limonene if ambient light releases \(2.64 \times 10^{18} \mathrm{photons} / \mathrm{sec}\).

\- Vomitoxin is produced by some fungi that grow on wheat and barley. It derives its name from the fact that it causes pigs that eat contaminated wheat to vomit. The chemical formula for vomitoxin is \(\mathrm{C}_{15} \mathrm{H}_{20} \mathrm{O}_{6}\). What is the percent composition of this compound?

Given 1.00-g samples of each of the compounds \(\mathrm{CO}_{2}, \mathrm{O}_{2}\), \(\mathrm{H}_{2} \mathrm{O}\), and \(\mathrm{CH}_{3} \mathrm{OH}\), (a) which sample will contain the largest number of molecules? (b) which sample will contain the largest number of atoms? Show proof for your answers.
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