Question

A $2.25-$ g sample of scandium metal is reacted with excess hydrochloric acid to produce 0.1502 g hydrogen gas. What is the formula of the scandium chloride produced in the reaction?

Short answer

The formula of the scandium chloride produced in the reaction is ScCl₃.

Step-by-step solution

Convert the mass of scandium and hydrogen to moles

We will use the molar mass of scandium and hydrogen to convert their respective mass given to moles. The molar mass of scandium (Sc) is 44.96 g/mol, and the molar mass of hydrogen (H) is 1.01 g/mol. Moles of Sc: ${\displaystyle \frac{2.25g}{44.96g/mol}}=0.0500\text{moles}$ Moles of H: ${\displaystyle \frac{0.1502g}{1.01g/mol}}=0.149\text{moles}$

Determine the mole ratio of Sc to H

To find the empirical formula of the scandium chloride, we need to determine the mole ratio of scandium to hydrogen. Mole ratio: ${\displaystyle \frac{0.0500molSc}{0.149molH}}={\displaystyle \frac{1}{2.98}}$ Since the mole ratio is approximately 1:3, it means there is one scandium atom for every three hydrogen atoms. Therefore, there should be three chloride (Cl) atoms for every scandium atom, as each hydrogen atom bonds with a chloride atom.

Write the formula of the scandium chloride

Knowing that there is one scandium atom for every three chloride atoms, the formula of the scandium chloride produced in the reaction is: ScCl₃

Key concepts

Understanding Molar Mass

Molar mass is a key concept in chemistry that helps you convert grams of a substance to moles, which are more universal for chemical equations. The molar mass is the weight of one mole of a substance, usually measured in grams per mole $ext(g/mol)$.Here's how it works:

• The molar mass of an element is its atomic weight from the periodic table.
• If you're dealing with a compound, add up the atomic weights of all the atoms in the formula.

In our exercise, you're given scandium with a mass of 2.25 grams. To convert this into moles, you'd divide by the molar mass of scandium, which is 44.96 g/mol. Likewise, for hydrogen, you have a mass of 0.1502 grams and a molar mass of 1.01 g/mol.Calculating these gets you the moles necessary to solve the problem:- Scandium: ${\displaystyle \frac{2.25extg}{44.96\text{g/mol}}}=0.0500\text{moles}$- Hydrogen: ${\displaystyle \frac{0.1502\text{g}}{1.01\text{g/mol}}}=0.149\text{moles}$Understanding molar mass helps in determining how much of each element you have in a chemical reaction.

Exploring Empirical Formulas

An empirical formula gives the simplest whole-number ratio of the atoms in a compound. It doesn't necessarily provide the precise number of atoms as they exist in the molecule (like a molecular formula does), but it opens the door to a deeper understanding of a compound's composition.To derive an empirical formula, you generally start by converting the mass of each element to moles, which you already have from the molar mass calculations. Then, you divide all the mole values by the smallest number of moles among them. This simplifies the ratios into whole numbers, which are then used as subscripts in the formula.In your problem: - After converting to moles, the next step is to compare scandium (0.0500 moles) and hydrogen (0.149 moles).- Dividing these by the smallest number of moles (0.0500 moles for scandium), will give you a simplified mole ratio of $1:2.98$, which rounds to $1:3$.This rounding leads to the empirical formula ScCl₃, indicating the simplest ratio of scandium to chloride based on the reaction data provided.

Insight into Mole Ratios

Mole ratios are crucial for understanding how substances react with one another in a chemical reaction. These ratios tell you the relationship between the amounts of reactants and products involved. In essence, they serve as a chemical recipe.To find the mole ratio, you look at the balanced chemical reaction equation or deduce it from experimental data by comparing the moles calculated from the molar mass of the reactants or products.In the given scenario:

• You start with moles from your molar mass calculations: 0.0500 moles of scandium and 0.149 moles of hydrogen.
• Dividing through by the smallest value, you discern a ratio of $1:2.98$, which rounds to $1:3$.

This implies one scandium atom pairs with three chloride atoms since each hydrogen atom represents a chloride in the formation of ScCl₃. Mole ratios like this dictate the stoichiometry of a reaction, allowing you to predict quantities of unknowns from knowns within complex chemical reactions.