Question

When \(1.00 \mathrm{~g}\) of metallic chromium is heated with elemental chlorine gas, \(3.045 \mathrm{~g}\) of a chromium chloride salt results. Calculate the empirical formula of the compound.

Short answer

The empirical formula of the compound is CrCl3.

Step-by-step solution

Convert masses to moles

To do this, we need to use the molar masses of Chromium (Cr) and the given mass of the compound. The molar mass of Chromium is 51.996 g/mol. For Chromium: Moles of Cr = mass / molar mass Moles of Cr = \( \frac{1.00 \mathrm{~g}}{51.996 \mathrm{~g/mol}} \) = 0.0192 mol Now, we determine the moles of chlorine (Cl) in the compound: Mass of Cl = Total mass of the compound - mass of Cr Mass of Cl = 3.045 g - 1.00 g = 2.045 g The molar mass of Chlorine is 35.453 g/mol. For Chlorine: Moles of Cl = mass / molar mass Moles of Cl = \( \frac{2.045 \mathrm{~g}}{35.453 \mathrm{~g/mol}} \) = 0.0577 mol

Find the mole ratio of Cr to Cl

To find the mole ratio, divide each element's moles by the smaller number of moles (in this case, the moles of Cr). Mole ratio (Cr:Cl) = \( \frac{0.0192}{0.0192} \):\( \frac{0.0577}{0.0192} \) Mole ratio (Cr:Cl) = 1:3

Determine the empirical formula of the compound

Now that we have the mole ratio (Cr:Cl) as 1:3, this is our simplest whole number ratio. Therefore, the empirical formula of the compound is: CrCl3

Key concepts

Mole Calculation

Mole calculation is a fundamental step in chemistry that helps us determine the quantity of a substance. It involves converting the mass of an element or compound into moles using its molar mass. The mole is a convenient unit in chemistry that allows chemists to count particles like atoms or molecules by weighing.

• To calculate moles, use the formula: \[ \text{Moles} = \frac{\text{Mass of substance}}{\text{Molar mass}} \]

For example, in the given exercise, we calculate moles of Chromium (Cr) and Chlorine (Cl) using their respective molar masses.
This step is crucial as it lays the groundwork for finding relationships between quantities in a chemical reaction.

Chemical Reaction

In chemistry, a chemical reaction represents the transformation of reactants into products. During a chemical reaction, bonds are broken and new bonds form, resulting in different substances. Recognizing a chemical reaction helps us understand how elements combine and rearrange.
In the exercise, Chromium reacts with Chlorine gas to form a chromium chloride compound.
This reaction changes Chromium into a new compound, showing the dynamic nature of matter. Understanding the concept of chemical reactions is essential for predicting how different elements and compounds will interact.

Mole Ratio

The mole ratio is a key concept in chemistry that shows the relationship between the amounts of reactants and products in a chemical equation. It is determined by the coefficients in a balanced chemical equation and is used to ensure that the chemical equation follows the law of conservation of mass.

• It is calculated by dividing the moles of each element by the smallest number of moles present in the reaction.

In the given exercise, the mole ratio of Cr to Cl is 1:3.
This means that for every mole of chromium, three moles of chlorine react to form the compound. Understanding mole ratios helps predict the quantity of products formed and ensures balanced reactions.

Elemental Analysis

Elemental analysis is a technique used to determine the composition of a compound in terms of its constituent elements. It provides insight into the proportion of different elements within a substance based on mass.
In the exercise, we use elemental analysis to determine how much of each element is present in the compound formed from Chromium and Chlorine.

• This involves calculating the masses and using molar masses to find moles.
• The results help us derive the empirical formula, which represents the simplest ratio of atoms in the compound.

Elemental analysis is essential for identifying unknown compounds and verifying the composition of known substances.