Question

A \(2.25-g\) sample of scandium metal is reacted with excess hydrochloric acid to produce \(0.1502 \mathrm{~g}\) 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 ScCl2.

Step-by-step solution

Balance the chemical equation of the reaction

The general formula for the reaction of scandium metal and hydrochloric acid is: Sc + HCl -> ScClx + H2 But, we don't know the number of "x" chloride ions in the product, ScClx, so we cannot balance this equation yet. We will determine the value of "x" later.

Calculate moles of hydrogen produced

First, we need to convert the mass of hydrogen gas (H2) produced to moles. The molar mass of H2 is 2.02 g/mol. Therefore, Moles of H2 = mass / molar mass = 0.1502 g / 2.02 g/mol = 0.0744 mol

Calculate moles of scandium reacted

Similarly, we need to convert the mass of scandium (Sc) reacted to moles. The molar mass of Sc is 44.96 g/mol. Therefore, Moles of Sc = mass / molar mass = 2.25 g / 44.96 g/mol = 0.0500 mol

Determine the mole ratio of H2 to Sc

Divide the moles of H2 by the moles of Sc to deduce the mole ratio: Mole ratio = moles of H2 / moles of Sc = 0.0744 mol / 0.0500 mol = 1.488 We will round this ratio to the nearest whole number, which is 1.

Balance the chemical equation and determine the formula of scandium chloride

Now that we know the mole ratio of H2 to Sc is 1, we can balance the chemical equation: Sc + 2HCl -> ScCl2 + H2 So, the formula of scandium chloride produced in the reaction is ScCl2.

Key concepts

Balancing Chemical Equations

Balancing chemical equations involves making sure that the same number of each type of atom appears on both sides of a chemical reaction. This is crucial because of the conservation of mass. You cannot create or destroy atoms in a chemical reaction. Instead, atoms simply rearrange to form new compounds.

In the exercise you're studying, scandium (\( \text{Sc} \)) is reacting with hydrochloric acid (\( \text{HCl} \)) to produce scandium chloride and hydrogen gas (\( \text{H}_2 \)). Initially, we have an unknown number of chloride ions in the product, represented as \( \text{ScCl}_x\).

Initially, the equation looks like this:

• \( \text{Sc} + \text{HCl} \rightarrow \text{ScCl}_x + \text{H}_2 \)

This is unbalanced because we don’t know \( x \), the number of chloride ions combining with scandium. After determining the mole ratio, you find that \( x = 2 \), resulting in the balanced equation:

• \( \text{Sc} + 2\text{HCl} \rightarrow \text{ScCl}_2 + \text{H}_2 \)

Now each side of the reaction contains the same number of each type of atom, fulfilling the guiding principle of balancing equations.

Mole Concept

The mole concept is a fundamental chemical principle that allows chemists to count atoms, molecules, and ions in a given mass of a substance. One mole is defined as exactly 6.022 x 10^23 particles of that substance, which is Avogadro's number. It simplifies working with chemical quantities, as you can translate between mass and the number of atoms or molecules more easily.

In the exercise, the mass of hydrogen gas (\( \text{H}_2 \)) and scandium (\( \text{Sc} \)) is converted to moles. For hydrogen:

• The molar mass of \( \text{H}_2 \) is 2.02 g/mol.
• Number of moles in 0.1502 g of hydrogen: \[ \frac{0.1502}{2.02} = 0.0744 \text{ mol} \]

For scandium:

• The molar mass is 44.96 g/mol.
• Number of moles in 2.25 g of scandium: \[ \frac{2.25}{44.96} = 0.0500 \text{ mol} \]

The ratio of moles plays a crucial role in balancing the equation and highlights the power of the mole concept in practical chemistry applications.

Chemical Formula

A chemical formula is a symbolic way to represent the composition of a chemical compound. It indicates the types and numbers of atoms involved. For example, water is represented as \( \text{H}_2\text{O} \), showing two hydrogen atoms and one oxygen atom.

In the context of this exercise, the chemical formula we're trying to find is for scandium chloride. Initially, it's unknown, represented as \( \text{ScCl}_x \). Through the course of balancing the equation and using the mole ratio from the reaction, it is determined that \( x = 2 \), leading to the chemical formula \( \text{ScCl}_2 \).

This formula indicates that each scandium atom pairs with two chloride ions, representing the simplest whole number ratio of these atoms in the compound. Knowing how to interpret and write chemical formulas is central to understanding chemical reactions and compounds.