Question

A metal (M) forms a compound with the formula \(\mathrm{MCl}_{3}\). If the compound contains \(65.57 \% \mathrm{Cl}\) by mass, what is the identity of the metal?

Short answer

The metal (M) has a molar mass of 34.43 g/mol. The closest element by atomic mass is Aluminum (Al), with a molar mass of approximately 27 g/mol. Thus, the metal is likely to be Aluminum (Al).

Step-by-step solution

Calculate the mass of chlorine in the compound

To find the identity of the metal (M), we first need to calculate the mass of chlorine in one mole of the compound MCl3. Since the compound is 65.57% chlorine by mass, for every 100 g of MCl3, there are 65.57 g of chlorine.

Calculate the mass of the metal in the compound

The mass of M in one mole of MCl3 must be the remainder of the mass not attributed to chlorine. If the compound is 100 g, the mass of the metal M is 100 g - 65.57 g = 34.43 g.

Use the molar mass of chlorine to find moles of chlorine

One mole of chlorine atoms has a mass of approximately 35.45 g (from the periodic table). Since the compound MCl3 has three chlorine atoms, we calculate the mass of chlorine in the compound as 3 times the molar mass of one chlorine atom, which is 3 * 35.45 g/mol = 106.35 g/mol.

Calculate the molar mass of the metal (M)

To find the molar mass of the metal M, we use the total molar mass of MCl3, which is the molar mass of M plus the molar mass of three chlorine atoms. Since we calculated 106.35 g/mol for the chlorine part, the molar mass of M is 34.43 g/mol (the mass of the metal from Step 2).

Identify the metal by its molar mass

We compare the molar mass calculated for the metal, which is 34.43 g/mol, with known molar masses of elements from the periodic table. The element with a molar mass closest to this value is likely to be the metal that forms MCl3.

Key concepts

Molar Mass Calculation

Understanding the molar mass of a substance is fundamental in chemistry, as it provides a bridge between the mass of a material and the number of particles it contains. The molar mass, often measured in grams per mole (g/mol), is numerically equivalent to the average mass of one molecule of the substance in atomic mass units (amu).

For compounds, the molar mass is calculated by adding up the molar masses of all the atoms in a single molecule of the compound. For instance, in a compound like MCl₃, we would need to know the molar mass of the metal (M) and chlorine (Cl). Since the molar mass of chlorine is approximately 35.45 g/mol, for three chlorine atoms, it would be tripled, resulting in 106.35 g/mol. Subtracting this from the total mass of the compound gives the molar mass of the metal (M), which can then be compared against the periodic table to identify the element.

Percent Composition

Percent composition is a crucial concept that relates to the composition of a compound, indicating the percentage by mass of each element within it. It provides a quick way to understand the proportion of each component in a chemical compound. To calculate the percent composition, one must know the mass of each element and the total mass of the compound.

To illustrate, if a compound like MCl₃ is 65.57% chlorine by mass, this implies that for every 100 g of MCl₃, there are 65.57 g of chlorine. By deduction, the remaining percentage and mass would belong to the metal (M). This information can lead us to further calculations or assessments about the identity of (M) when combined with molar masses.

Empirical Formula Determination

The empirical formula represents the simplest whole-number ratio of elements in a compound, providing a fundamental insight into the chemical composition without conveying information about the arrangement of atoms. Determining an empirical formula requires knowing the percent composition or mass of each element in the compound.

To find the empirical formula, it's necessary to convert the mass of each element to moles by dividing by its molar mass. Then, we find the simplest whole-number ratio of the moles of elements present. For a compound like MCl₃, if chlorine makes up 65.57% of the mass, we can calculate the moles of chlorine and the remaining metal to determine the mole ratio. The question initially provided was seeking to identify the metal (M) based on the known percentage of chlorine, which is an indirect path to determining an empirical formula, in this case, confirming the 1:3 ratio of metal to chlorine as outlined by the formula MCl₃.