Problem 149 - 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 \(\mathrm{ECl}_{4} ?\) What is the identity of E?

Step-by-Step Solution

Answer

The molar mass of \( \text{ECl}_4 \) is 154 g/mol and \( \text{E} \) is carbon (C).

Step 1: Calculate Molar Mass of Compound

To find the molar mass of the compound \(\text{ECl}_4\), we use the formula: \[ M = \frac{\text{mass}}{\text{moles}} \] Given the mass of 2.50 mol of \(\text{ECl}_4\) is 385 g, we substitute into the formula: \[ M = \frac{385 \text{ g}}{2.50 \text{ mol}} = 154 \text{ g/mol} \].

Step 2: Molar Mass of Chlorine in Compound

We need to find the contribution of the chlorine atoms to the molar mass. Since there are four chlorine atoms, we calculate: \[ 4 \times M_{\text{Cl}} = 4 \times 35.5 = 142 \text{ g/mol} \].

Step 3: Determine Molar Mass of Element E

Subtract the total mass of chlorine from the molar mass of the compound to find the molar mass of \(\text{E}\): \[ M_E = 154 \text{ g/mol} - 142 \text{ g/mol} = 12 \text{ g/mol} \].

Step 4: Identify Element E

The molar mass of \(\text{E}\) is 12 g/mol, which corresponds to carbon (C) on the periodic table.

Key Concepts

Element Identification

In chemistry, identifying elements in a compound is an intriguing yet simple task with the right approach. Every element has a unique property called molar mass. This attribute helps us pinpoint which element we're dealing with.
In this exercise, our target is the element "E" in the compound \( \text{ECl}_4 \). First, we calculate the total molar mass of this compound, which turns out to be 154 g/mol. The role of the element "E" becomes apparent when we consider the entire composition of the compound.
We subtract the known contribution of the chlorine atoms (142 g/mol) to find the molar mass of the mysterious element "E." As the result is 12 g/mol, a quick look at the periodic table tells us that this molar mass matches that of carbon (C). Thus, the enigmatic "E" is indeed carbon.

Chemical Formula Analysis

Understanding chemical formulas is like deciphering a coded message that tells us about the composition of a compound. The formula \( \text{ECl}_4 \) reveals significant information.
Each letter and number in a formula has deep chemical significance, indicating the type and number of atoms in the compound.

• "E" represents a non-metal element whose identity we are tasked to uncover.
• "Cl" stands for chlorine, a well-known non-metal element.
• The subscript "4" indicates there are four chlorine atoms attached to our unknown element "E."

Through chemical formula analysis, we discern that chlorine contributes significantly to the compound's mass due to its repetition in the formula. This lays the groundwork for determining the molar mass separation between "E" and the chlorine found through calculations.

Periodic Table Interpretation

The periodic table is not just a chart; it's a powerful tool for identifying elements based on their properties, such as molar mass. In our exercise, once we determined that element "E" had a molar mass of 12 g/mol, the periodic table guided us to the identity of this element.
To interpret a periodic table:

• Locate the section where elements are listed with increasing molar mass from left to right.
• Each element's entry provides a wealth of information including molar mass, symbol, and atomic number.
• Match the calculated molar mass of the unknown to the listed values.

Our calculated molar mass of 12 g/mol directly matches the molar mass of carbon, whose symbol is "C" on the periodic table. Thus, periodic table interpretation played a crucial role in identifying "E" as carbon. This approach simplifies the process, offering clarity through methodical deduction.