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Chapter 3: Problem 40

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

Short Answer

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

Step by step solution

01

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%.
02

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.
03

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.
04

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).

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