Problem 40 - General Chemistry: Principles and Modern Applications

Question

The element \(X\) forms the compound \(X O C l_{2}\) containing 59.6\% Cl. What is element X?

Step-by-Step Solution

Answer

The element X in the compound \(X O C l_{2}\) is Aluminium (Al).

Step 1: Determine the percentage of each element in the compound

Start by breaking the compound \(X O C l_{2}\) into its components. Since the compound contains 59.6% chlorine (Cl), it must also contain 40.4% of element X and oxygen (O), because the percentages of all elements in a compound must add up to 100%.

Step 2: Calculate the Percentage of Oxygen

Firstly, map out the atomic masses of each element present in the compound. The atomic mass of oxygen (O) is around 16g/mol and Chlorine (Cl) is 35.45g/mol. Since there are two Chlorines in the compound, the total mass contributed by Chlorine is \(2 \times 35.45g/mol = 70.9g/mol\). Substituting this value into the percentage formula \(\frac{70.9}{70.9+16+massX} \times 100% = 59.6%\), we can solve for \(massX\), which is the atomic mass of element X.

Step 3: Solve for the Atomic Mass of Element X

Rearranging the formula in step 2 and substituting all known quantities, we get \(massX = (\frac{59.6}{100} \times (70.9 + 16)) - 70.9\). Calculating the result yields an approximate atomic mass of X of ~27g/mol.

Step 4: Identify Element X

Consulting the periodic table, the element with atomic mass close to 27g/mol is Aluminium (Al). It’s approximately 26.98g/mol which is close to the computed 27g/mol. Therefore, the element X in the compound \(X O C l_{2}\) is Aluminium (Al).

Key Concepts

Chemical Formula Interpretation

In chemistry, understanding a chemical formula allows us to understand the composition of a compound. Each formula is like a recipe, giving us the exact number and identity of different elements bonded together in a compound. For example, in the formula \( X O C l_{2} \), each letter represents an element from the periodic table. The subscript numbers indicate the number of each type of atom in a molecule.

Here's how it works:

• "\( X \)" represents an unknown element, which is what we are trying to identify.
• "\( O \)" stands for Oxygen, a common non-metal.
• "\( Cl_{2} \)" means there are two Chlorine atoms included in the compound.

By understanding these basic symbols and numbers, chemists can determine what elements a compound contains and in what proportions they exist. Therefore, interpreting a chemical formula is essential for calculating the relative amounts of each element in a compound.

In this specific case, we have a task of breaking down the compound \( X O C l_{2} \) to find out how much of each element is present in the molecular structure.

Element Identification

Element identification involves pinpointing which element an unknown component in a compound might be. Through the use of atomic masses and the periodic table, we can achieve this.To identify element \( X \) in the compound \( X O C l_{2} \), we analyze its percentage composition. Since 59.6% of the compound is Chlorine, the remaining 40.4% is composed of element \( X \) and Oxygen. With this data, we can begin solving for the identity of \( X \).By understanding the formula setup and being aware of the typical atomic masses of elements, locating the unidentified element becomes manageable:

• Determine the percent composition rule that total element percentages must equal 100%.
• Use given percentages and atomic masses from the periodic table to solve for the unknown element's possible atomic mass.
• Cross-reference this atomic mass with known values on the periodic table to deduce the specific element.

Using these steps, we find that the unknown element, with an atomic mass close to \( 27\)g/mol, is Aluminum, a lightweight and commonly utilized element.

Atomic Mass Calculation

Atomic mass calculation is a pivotal process in identifying unknown substances in chemistry. It's similar to a balancing act where the known and unknown masses must be compared to maintain equilibrium.The steps involve using a formula to combine known and unknown masses, which for the compound \( X O C l_{2} \) gives us:

• Calculate the total known mass of Chlorine: \( 2 \times 35.45 \text{g/mol} = 70.9 \text{g/mol} \).
• Apply the mass percent formula to find the mass of element \( X \):\[massX = \left( \frac{59.6}{100} \times (70.9 + 16) \right) - 70.9\]
• Perform algebraic rearrangements followed by calculations to isolate and solve for \( massX \).
• Utilize the periodic table to find the closest atomic weight to the calculated \( massX \).

This analytic method allows chemists to correctly identify the unknown element's atomic mass, and ultimately, its identity, based on accurate calculations and comparisons.