Question

A substance whose formula is \(\mathrm{A}_{2} \mathrm{O}\) (A is a mystery element) is \(60.0 \% \mathrm{~A}\) and \(40.0 \% \mathrm{O}\). Identify the element \(\mathrm{A}\).

Short answer

The mystery element A is Magnesium (Mg).

Step-by-step solution

- Determine the Molar Mass of Oxygen

The molar mass of oxygen (O) is typically 16.00 g/mol.

- Establish the Molar Mass of \(\text{A}_2\text{O}\)

Let the molar mass of element A be denoted as \( M_A \). The formula for the substance is \( \text{A}_2\text{O}\), hence the molar mass of \( \text{A}_2\text{O} \) is given by: \[ 2 \times M_A + 16.00 \]

- Use the Percentage Composition to Set Up Equations

Given the substance is 60.0% A and 40.0% O, we can set up the following equations: \[ \frac{2 M_A}{2 M_A + 16.00} = 0.60 \] for element A and \[ \frac{16.00}{2 M_A + 16.00} = 0.40 \] for oxygen.

- Solve for \( M_A \)

Rearrange and solve the equation \[ \frac{2 M_A}{2 M_A + 16.00} = 0.60 \] for \( M_A\). Multiplying both sides by \( 2 M_A + 16.00 \), we get: \[ 2 M_A = 0.60(2 M_A + 16.00) \]. Distribute and simplify: \[ 2 M_A = 1.2 M_A + 9.6 \]. Subtract \( 1.2 M_A\) from both sides: \[ 0.8 M_A = 9.6 \]. Solve for \( M_A \): \[ M_A = \frac{9.6}{0.8} = 12.00 \]

- Identify the Element

Given that \( M_A = 12.00 \) g/mol, the element A is Magnesium (Mg), as the atomic mass of Magnesium is approximately 24.31 g/mol.

Key concepts

Molar Mass Calculation

Molar mass is a fundamental concept in chemistry that represents the mass of one mole of a substance. To calculate the molar mass of a compound, sum the atomic masses of all the atoms in its formula. For example, in the compound \(\text{A}_2\text{O}\), you need to consider two atoms of element A and one atom of oxygen.

Percentage Composition

Percentage composition describes the proportion of each element in a compound by mass. This is determined by dividing the mass of each element by the total molar mass of the compound, then multiplying by 100 to get a percentage. For instance, in the compound \(\text{A}_2\text{O}\), the percentage of element A is calculated by \[ \frac{2 M_A}{2 M_A + 16.00} \times 100 \], while the percentage of oxygen is \[ \frac{16.00}{2 M_A + 16.00} \times 100 \].

Chemical Formulas

A chemical formula represents the elements in a compound and the ratio of atoms. For example, \(\text{A}_2\text{O}\) means there are two atoms of element A for every one atom of oxygen. The formula helps in calculating properties like molar mass and percentage composition. Understanding these basics allows you to identify unknown elements in compounds, as illustrated in the step-by-step solution above.