Question

Balance the following chemical equation. $$\operatorname{LiAlH}_{4}(s)+\mathrm{AlCl}_{3}(s) \rightarrow \mathrm{AlH}_{3}(s)+\mathrm{LiCl}(s)$$

Short answer

The balanced chemical equation for the given reaction is: \( 3LiAlH_4(s) + AlCl_3(s) \rightarrow 2AlH_3(s) + 3LiCl(s) \).

Step-by-step solution

Count the atoms for each element on both sides of the equation

First, let's count the number of atoms of each element on the left-hand side (reactants) and the right-hand side (products) of the equation. On the reactants side: - Li (Lithium): 1 - Al (Aluminum): 1 + 1 = 2 - H (Hydrogen): 4 - Cl (Chlorine): 3 On the products side: - Li (Lithium): 1 - Al (Aluminum): 1 - H (Hydrogen): 3 - Cl (Chlorine): 1 Now that we have the atom count, we can identify which elements are unbalanced: The Aluminum (Al) and Chlorine (Cl) elements are unbalanced.

Balance the unbalanced elements

To balance these elements, we can add coefficients in front of the chemical formulas. We will add coefficients to make the number of Aluminum and Chlorine atoms equal on both sides of the equation. - Since we have 2 Aluminum atoms on the reactants side and only 1 on the products side, let's add a coefficient of 2 in front of the \(AlH_3\) on the products side to balance the Aluminum atoms: \( LiAlH_4(s) + AlCl_3(s) \rightarrow 2AlH_3(s) + LiCl(s) \) Now let's recount the Hydrogen atoms on the products side: - H (Hydrogen): 2 x 3 = 6 To balance the Chlorine atoms, the reactants side has 3 Chlorine atoms, and we will need to add a coefficient of 3 in front of the LiCl on the products side: \( LiAlH_4(s) + AlCl_3(s) \rightarrow 2AlH_3(s) + 3LiCl(s) \) Now, we see that the Lithium atoms are unbalanced as well. We need a total of 3 Lithium atoms on the reactants side. We can achieve this by adding a coefficient of 3 in front of the \(LiAlH_4\): \( 3LiAlH_4(s) + AlCl_3(s) \rightarrow 2AlH_3(s) + 3LiCl(s) \)

Verify that the equation is balanced

Lastly, let's check to ensure that all elements are balanced in the equation by counting the atoms on both sides again: On the reactants side: - Li (Lithium): 3 - Al (Aluminum): 1 + 1 = 2 - H (Hydrogen): 3 x 4 = 12 - Cl (Chlorine): 3 On the products side: - Li (Lithium): 3 - Al (Aluminum): 2 x 1 = 2 - H (Hydrogen): 2 x 3 = 6 - Cl (Chlorine): 3 The balanced chemical equation is: \( 3LiAlH_4(s) + AlCl_3(s) \rightarrow 2AlH_3(s) + 3LiCl(s) \) As we can see, the atoms' count matches for each element on both sides of the equation, and the exercise is complete.

Key concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It's like the recipe of chemistry, ensuring that you have just the right amount of each ingredient to complete a reaction without anything extra leftover. When balancing chemical equations, stoichiometry is key. You must make sure that the number of atoms for each element is equal on both sides of the equation.
For example, in the original exercise, we balanced the equation by adjusting coefficients to get equal numbers of lithium ( Li ), aluminum ( Al ), hydrogen ( H ), and chlorine ( Cl ) atoms.

• This process involves counting atoms on both sides.
• Next, you adjust coefficients to balance any discrepancies.
• Finally, you recheck to ensure the atom counts are equal for each element!

By following these steps, you can confidently balance equations and solve stoichiometry tasks accurately.

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, transform into new substances, known as products. Represented by chemical equations, these reactions see bonds breaking and forming.
Imagine you are arranging Lego blocks—taking some apart and snapping others together to create a new structure.
Chemical reactions follow this pattern, where the structure of molecules changes through bonding.

• A chemical reaction is signified by a change, such as a color difference, temperature change, or gas formation.
• Equations illustrating these reactions must be balanced to reflect what truly occurs at the molecular level.
• In the given reaction, we start with lithium aluminum hydride ( LiAlH_4 ) and aluminum chloride ( AlCl_3 ) as reactants transforming into aluminum hydride ( AlH_3 ) and lithium chloride ( LiCl ) as products.

Understanding chemical reactions helps us grasp how substances interact and change, forming the foundation of chemistry.

Conservation of Mass

The conservation of mass principle asserts that in a closed system, mass is neither created nor destroyed in a chemical reaction. It means the mass of reactants equals the mass of products. Antoine Lavoisier, a French chemist, introduced this principle in the 18th century.
In a balanced chemical equation, confirmation of the conservation of mass comes when the number of each type of atom is equal on both sides of the equation.

• Every chemical reaction must obey the conservation of mass.
• This is achieved by balancing the equation, ensuring each element has the same number of atoms in the products as it does in the reactants.
• In our balanced equation, mass is conserved as the numbers of lithium, aluminum, hydrogen, and chlorine atoms all match on both sides.

This principle is foundational in understanding chemical processes, reflecting the unchanging nature of matter in reactions.