Question

Balance each of the following equations that describe synthesis reactions. a. \(\mathrm{Fe}(s)+\mathrm{S}_{8}(s) \rightarrow \mathrm{FeS}(s)\) b. \(\mathrm{Co}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{Co}_{2} \mathrm{O}_{3}(s)\) c. \(\mathrm{Cl}_{2} \mathrm{O}_{7}(g)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{HClO}_{4}(a q)\)

Short answer

The balanced equations are: a. Fe(s) + S8(s) -> 8FeS(s) b. 4Co(s) + 3O2(g) -> 2Co2O3(s) c. Cl2O7(g) + 2H2O(l) -> 4HClO4(aq)

Step-by-step solution

a. Balancing Fe(s) + S8(s) -> FeS(s)

First, count the number of each type of atom on each side of the equation: Reactants side: 1 Fe, 8 S Products side: 1 Fe, 1 S We see that there is an imbalance in the number of sulfur atoms. To balance the equation, we need to change the coefficients so that there are an equal number of sulfur atoms on both sides. In this case, we can use a coefficient of 8 in front of FeS: Fe(s) + S8(s) -> 8FeS(s) Now the equation is balanced: Reactants side: 1 Fe, 8 S Products side: 8 Fe, 8 S

b. Balancing Co(s) + O2(g) -> Co2O3(s)

First, count the number of each type of atom on each side of the equation: Reactants side: 1 Co, 2 O Products side: 2 Co, 3 O We see that there is an imbalance in the number of cobalt and oxygen atoms. We can balance the cobalt atoms by putting a coefficient of 2 in front of Co: 2Co(s) + O2(g) -> Co2O3(s) Now count the atoms again: Reactants side: 2 Co, 2 O Products side: 2 Co, 3 O We still need to balance the oxygen atoms. In this case, we can use a coefficient of 3/2 in front of O2: 2Co(s) + \(\frac{3}{2}\)O2(g) -> Co2O3(s) However, having a fraction as a coefficient is not ideal, so we can multiply all the coefficients by 2 to get whole numbers: 4Co(s) + 3O2(g) -> 2Co2O3(s) The equation is now balanced: Reactants side: 4 Co, 6 O Products side: 4 Co, 6 O

c. Balancing Cl2O7(g) + H2O(l) -> HClO4(aq)

First, count the number of each type of atom on each side of the equation: Reactants side: 2 Cl, 7 O, 2 H Products side: 1 Cl, 4 O, 1 H We see that there is an imbalance in the number of chlorine, oxygen, and hydrogen atoms. We can balance the chlorine atoms by putting a coefficient of 2 in front of HClO4: Cl2O7(g) + H2O(l) -> 2HClO4(aq) Now count the atoms again: Reactants side: 2 Cl, 7 O, 2 H Products side: 2 Cl, 8 O, 2 H We still need to balance the oxygen atoms. In this case, we can use a coefficient of 1/2 in front of Cl2O7: \(\frac{1}{2}\)Cl2O7(g) + H2O(l) -> 2HClO4(aq) However, having a fraction as a coefficient is not ideal, so we can multiply all the coefficients by 2 to get whole numbers: Cl2O7(g) + 2H2O(l) -> 4HClO4(aq) The equation is now balanced: Reactants side: 2 Cl, 7 O, 4 H Products side: 2 Cl, 7 O, 4 H

Key concepts

Synthesis Reactions

Synthesis reactions, also known as combination reactions, involve two or more reactants joining together to form a single product. A classic example is when iron (Fe) and sulfur (S) combine to produce iron sulfide (FeS). These types of reactions can be represented with general chemical equations like:
\[ A + B \rightarrow AB \] Here, \(A\) and \(B\) are reactants that create a new product \(AB\). These reactions are fundamental in chemistry since they showcase how substances can amalgamate into more complex compounds.
To write a balanced chemical equation, it’s essential to ensure that the number of each type of atom on the reactants side equates to the number on the products side. This is crucial for obeying the law of conservation of mass, which dictates that matter cannot be created or destroyed in a chemical reaction.

Stoichiometry

Stoichiometry is the part of chemistry that quantifies the relationships between elements in chemical reactions. It involves calculations that focus on the amount of reactants and products. Essentially, stoichiometry tells us how much of each substance is needed or produced in a reaction.
In a synthesis reaction, stoichiometry helps determine how many moles of a reactant are required to entirely react with another, based on the coefficients in the balanced equation. For example, in the balanced equation for the reaction between hydrogen and oxygen to produce water:
\[ 2H_2(g) + O_2(g) \rightarrow 2H_2O(l) \] We can see that two moles of hydrogen react with one mole of oxygen to produce two moles of water. This proportional relationship is key to resolving problems involving reactants and products in a given reaction. It’s an analytical method that ensures precision when predicting the outcomes of a chemical reaction.

Reactants and Products

Reactants and products are the starting and ending substances respectively in a chemical reaction. Reactants are the chemicals you start with, and they undergo a transformation to yield products.
Identifying these components in a synthesis reaction is straightforward. For instance, in the equation for the reaction of chlorine dioxide \(\text{Cl}_2\text{O}_7\) and water \(\text{H}_2\text{O}\) to form perchloric acid \(\text{HClO}_4\), the reactants are \(\text{Cl}_2\text{O}_7\) and \(\text{H}_2\text{O}\), and the product is \(\text{HClO}_4\).
The transformation from reactants to products involves breaking chemical bonds in the reactants and forming new bonds to create the products. Thus, understanding the nature of reactants and products, and their quantities, is essential for balancing chemical equations accurately. This step ensures adherence to the principle of conservation of mass and supports efficient chemical synthesis.