Problem 17 - Chemistry: The Central Science

Question

At \(900^{\circ} \mathrm{C}\) titanium tetrachloride vapor reacts with molten magnesium metal to form solid titanium metal and molten magnesium chloride. (a) Write a balanced equation for this reaction. (b) What is being oxidized, and what is being reduced? (c) Which substance is the reductant, and which is the oxidant?

Step-by-Step Solution

Answer

(a) The balanced equation for the reaction is: \[ TiCl_4 + 2Mg \rightarrow Ti + 2MgCl_2 \] (b) Magnesium is being oxidized, and titanium is being reduced. (c) Magnesium is the reductant, and titanium tetrachloride is the oxidant.

Step 1: Write the unbalanced equation

Given the information in the problem, the unbalanced equation for the reaction can be written as: \[ TiCl_4 + Mg \rightarrow Ti + MgCl_2 \]

Step 2: Determine the oxidation numbers

Next, we need to determine the oxidation number of each element in the reactants and products: For \(TiCl_4\): - Titanium (Ti): +4 (because chlorine has an oxidation number of -1, and there are 4 chlorines in the compound, the oxidation number of Ti is +4) - Chlorine (Cl): -1 For \(Mg\): - Magnesium (Mg): 0 (because it is an elemental form) For \(Ti\): - Titanium (Ti): 0 (also in its elemental form) For \(MgCl_2\): - Magnesium (Mg): +2 (because chlorine has an oxidation number of -1 and there are 2 chlorines, the oxidation number of Mg is +2) - Chlorine (Cl): -1

Step 3: Balance the equation

Now that we have the oxidation numbers, let's balance the equation: \[ TiCl_4 + 2Mg \rightarrow Ti + 2MgCl_2 \] The equation is now balanced.

Step 4: Identify oxidation and reduction

To identify what is being oxidized and what is being reduced, we can look at the changes in the oxidation numbers for each element: - Titanium (Ti): Goes from +4 to 0, a reduction in oxidation number, meaning titanium is being reduced. - Magnesium (Mg): Goes from 0 to +2, an increase in oxidation number, meaning magnesium is being oxidized. So, titanium is being reduced, and magnesium is being oxidized.

Step 5: Identify the reductant and oxidant

The reductant is the substance that loses electrons (causing the reduction of another substance), so in this case, it's magnesium metal. The oxidant is the substance that gains electrons (causing the oxidation of another substance), in this case, it's titanium tetrachloride. In summary: (a) The balanced equation for the reaction is: \[ TiCl_4 + 2Mg \rightarrow Ti + 2MgCl_2 \] (b) Magnesium is being oxidized, and titanium is being reduced. (c) Magnesium is the reductant, and titanium tetrachloride is the oxidant.

Key Concepts

Oxidation-Reduction

Redox reactions, short for oxidation-reduction reactions, involve the transfer of electrons between substances. These reactions play a crucial role in chemistry because they describe how chemical elements change their oxidation states.
In a redox reaction:

• One substance loses electrons. This process is called "oxidation."
• Another substance gains those electrons, which is known as "reduction."

In our reaction between titanium tetrachloride and magnesium, magnesium gets oxidized as it loses electrons. Conversely, titanium within titanium tetrachloride gains those electrons, making it reduced.
Identifying these electron movements helps understand the behavior of reactants and products in a chemical reaction.

Chemical Equations

Chemical equations are a shorthand way of describing chemical reactions.
They show the substances involved as reactants on the left side, and products formed are shown on the right side. Consider our initial unbalanced equation:
\[ TiCl_4 + Mg \rightarrow Ti + MgCl_2 \]
This equation tells us that titanium tetrachloride and magnesium are the starting materials. They then transform into titanium metal and magnesium chloride as the final products. Each molecule or atom involved must also be accounted for to maintain what is known as the "law of conservation of mass."
This principle ensures that the same amount of matter exists before and after the reaction.

Oxidation Numbers

Oxidation numbers are a bookkeeping method in chemistry.
They help us track the movement of electrons in a chemical reaction. Each element is assigned a number that represents its 'oxidation state'.
To determine oxidation numbers:

• Elements in their elemental form have an oxidation number of zero.
• For molecules, we use electronegativity rules. For example, oxygen is typically -2, and hydrogen is +1.

In the example of titanium tetrachloride:
- Titanium has an oxidation number of +4, while chlorine is -1.
- When written for the reaction, we see titanium's oxidation number goes from +4 to 0. This decrease confirms its reduction.
Understanding oxidation numbers can be a powerful tool in predicting how substances will react under certain circumstances.

Balancing Reactions

Balancing chemical reactions is the process of ensuring that there are equal numbers of each type of atom on both sides of the equation.
It aligns with the law of conservation of mass.
In our example, unbalanced reaction:\[TiCl_4 + Mg \rightarrow Ti + MgCl_2\] was changed into:\[TiCl_4 + 2Mg \rightarrow Ti + 2MgCl_2\]When balancing, we follow these steps:

• Count the number of each atom on the reactant and product sides.
• Add coefficients to balance one type of atom at a time.
• Ensure all atoms match in number when completed.

By doing this, we ensure that no atoms are lost or created in the process.
This is crucial in making accurate predictions about the amount and identity of products formed.