Problem 107 - Chemistry and Chemical Reactivity

Question

The mass of 2.50 mol of a compound with the formula \(\mathrm{ECl}_{4},\) in which \(\mathrm{E}\) is a nonmetallic element, is \(385 \mathrm{g} .\) What is the molar mass of ECl \(_{4} ?\) What is the identity of E?

Step-by-Step Solution

Answer

The molar mass of \( \mathrm{ECl}_{4} \) is \( 154 \, \mathrm{g/mol} \). The element \( \mathrm{E} \) is carbon (\( \mathrm{C} \)).

Step 1: Identify Given Information

First, let's note the information provided. The mass of 2.50 moles of the compound \( \mathrm{ECl}_{4} \) is \( 385 \, \mathrm{g} \). We need to find the molar mass of \( \mathrm{ECl}_{4} \) and identify the element \( \mathrm{E} \).

Step 2: Calculate Molar Mass of ECl₄

To find the molar mass, we use the formula: \( \text{Molar Mass} = \frac{\text{Total Mass}}{\text{Number of Moles}} \). Thus, the molar mass of \( \mathrm{ECl}_{4} \) is \( \frac{385}{2.50} \approx 154 \, \mathrm{g/mol} \).

Step 3: Determine Molar Mass of Chlorine x 4

The molar mass of chlorine (\( \mathrm{Cl} \)) is approximately \( 35.5 \, \mathrm{g/mol} \). Since the compound contains four chlorine atoms, the total molar mass of chlorine in the compound is \( 4 \times 35.5 = 142 \, \mathrm{g/mol} \).

Step 4: Calculate Molar Mass of E

Subtract the molar mass of chlorine from the molar mass of the compound to find the molar mass of element \( \mathrm{E} \): \( 154 - 142 = 12 \, \mathrm{g/mol} \).

Step 5: Identify Element E

The element with a molar mass of approximately \( 12 \, \mathrm{g/mol} \) is carbon (\( \mathrm{C} \)). Therefore, the element \( \mathrm{E} \) is carbon.

Key Concepts

Chemical Compounds

Chemical compounds form the basis of many chemical reactions and are composed of two or more different elements. In our exercise, we have a compound with the formula \( \text{ECl}_4 \), where \( \text{E} \) represents a nonmetallic element. This means that \( \text{ECl}_4 \) is a molecule made of one element \( \text{E} \) bonded with four chlorine (\( \text{Cl} \)) atoms.
The study of chemical compounds involves understanding how these atoms interact and bond to form new substances. Each chemical compound has a unique chemical formula that tells us the number of different atoms present in a single molecule. Here, the subscript "4" indicates that there are four chlorine atoms for every one atom of \( \text{E} \) in the compound.

• Compounds are often categorized by the types of bonds they have, such as ionic or covalent bonds.
• Knowing the chemical formula helps in predicting the properties and reactions of the compound.

Understanding chemical compounds like \( \text{ECl}_4 \) requires recognizing how different elements come together to form a substance with characteristics distinct from its individual elements.

Mole Concept

The mole concept is at the heart of many chemical calculations. A mole refers to \( 6.022 \times 10^{23} \) of anything, often atoms or molecules. It simplifies the counting of large numbers of small particles. In the given exercise, we have 2.50 moles of \( \text{ECl}_4 \), which is substantial when considering individual molecules.
Calculating molar mass involves the use of moles, as we saw with the formula \( \text{Molar Mass} = \frac{\text{Total Mass}}{\text{Number of Moles}} \). This formula helps us find the mass of one mole of a substance rather than just a portion of it.

• Moles provide a bridge between the atomic world and the macro world we can measure.
• Mole calculations are fundamental for stoichiometry in chemistry, allowing predictions of product amounts.

Mastering the mole concept aids in determining quantities and proportions in chemical reactions, ensuring accurate calculations and conclusions.

Element Identification

In chemistry, identifying elements means determining which atoms make up a compound. In our scenario, element \( \text{E} \) in \( \text{ECl}_4 \) needed identification. We know the molar mass of the whole compound is \( 154 \text{ g/mol} \).
By subtracting the mass contribution of known chlorine atoms from this total, we isolate the molar mass of \( \text{E} \), calculated as \( 12 \text{ g/mol} \). This corresponds to carbon (\( \text{C} \)) on the periodic table.

• The periodic table is essential for matching molar masses to elements.
• Knowing molar masses helps confirm elemental identity and purity in compounds.

Identifying an element involves both mathematical calculations and referencing the periodic table, enabling chemists to understand the makeup and characteristics of compounds.