Problem 77 - Chemistry: The Central Science in SI Units, Global Edition

Question

Write a balanced equation for the reaction that occurs in each of the following cases: (a) White phorphrous, \(\mathrm{P}_{4}(\mathrm{~s})\), reacts with chlorine gas. (b) Sodium metal reacts with water. (c) Hydrogen bromide gas reacts with chlorine gas. (d) Aluminum trichloride reacts with aqueous sodium hydroxide.

Step-by-Step Solution

Answer

The balanced chemical equations for the given reactions are: (a) \(P_4(s) + 6\, Cl_2(g) \rightarrow 4\, PCl_3\) (b) \(2\, Na(s) + 2\, H_2O(l) \rightarrow 2\, NaOH(aq) + H_2(g)\) (c) \(2\, HBr(g) + Cl_2(g) \rightarrow 2\, HCl(g) + Br_2(g)\) (d) \(AlCl_3 + 3\, NaOH(aq) \rightarrow Al(OH)_3(s) + 3\, NaCl(aq)\)

Step 1: (a) Identifying reactants and products for the reaction between phosphorous and chlorine

We are given that white phosphorus, \(P_4(s)\), reacts with chlorine gas, \(Cl_2(g)\). When these elements react, they form phosphorus trichloride, \(PCl_3\), as the product.

Step 2: (a) Balancing the chemical equation

The reactants are \(P_4(s)\) and \(Cl_2(g)\), and the product is \(PCl_3\). To balance this equation, we must adjust the stoichiometric coefficients: \(P_4(s) + 6\, Cl_2(g) \rightarrow 4\, PCl_3\) The balanced chemical equation for this reaction is: \(P_4(s) + 6\, Cl_2(g) \rightarrow 4\, PCl_3\)

Step 3: (b) Identifying reactants and products for the reaction between sodium metal and water

We are given that sodium metal, \(Na(s)\), reacts with water, \(H_2O(l)\). In this reaction, sodium reacts with water to produce sodium hydroxide, \(NaOH(aq)\), and hydrogen gas, \(H_2(g)\).

Step 4: (b) Balancing the chemical equation

The reactants are \(Na(s)\) and \(H_2O(l)\), and the products are \(NaOH(aq)\) and \(H_2(g)\). To balance this equation, we must adjust the stoichiometric coefficients: \(2\, Na(s) + 2\, H_2O(l) \rightarrow 2\, NaOH(aq) + H_2(g)\) The balanced chemical equation for this reaction is: \(2\, Na(s) + 2\, H_2O(l) \rightarrow 2\, NaOH(aq) + H_2(g)\)

Step 5: (c) Identifying reactants and products for the reaction between hydrogen bromide and chlorine

We are given that hydrogen bromide gas, \(HBr(g)\), reacts with chlorine gas, \(Cl_2(g)\). In this reaction, hydrogen chloride gas, \(HCl(g)\), and bromine gas, \(Br_2(g)\), are produced.

Step 6: (c) Balancing the chemical equation

The reactants are \(HBr(g)\) and \(Cl_2(g)\), and the products are \(HCl(g)\) and \(Br_2(g)\). To balance this equation, we must adjust the stoichiometric coefficients: \(HBr(g) + Cl_2(g) \rightarrow HCl(g) + Br_2(g)\) The balanced chemical equation for this reaction is: \(2\, HBr(g) + Cl_2(g) \rightarrow 2\, HCl(g) + Br_2(g)\)

Step 7: (d) Identifying reactants and products for the reaction between aluminum trichloride and sodium hydroxide

We are given that aluminum trichloride, \(AlCl_3\), reacts with aqueous sodium hydroxide, \(NaOH(aq)\). In this reaction, aluminum hydroxide, \(Al(OH)_3(s)\), and sodium chloride, \(NaCl(aq)\), are produced.

Step 8: (d) Balancing the chemical equation

The reactants are \(AlCl_3\) and \(NaOH(aq)\), and the products are \(Al(OH)_3(s)\) and \(NaCl(aq)\). To balance this equation, we must adjust the stoichiometric coefficients: \(AlCl_3 + 3\, NaOH(aq) \rightarrow Al(OH)_3(s) + 3\, NaCl(aq)\) The balanced chemical equation for this reaction is: \(AlCl_3 + 3\, NaOH(aq) \rightarrow Al(OH)_3(s) + 3\, NaCl(aq)\)

Key Concepts

Balancing Chemical Equations

Balancing chemical equations is like making sure a recipe has the right amount of each ingredient. When a chemical reaction occurs, it follows the law of conservation of mass, meaning no atoms are lost or gained.
Therefore, the number of atoms for each element must be the same on both sides of the equation.
To balance an equation, we adjust the stoichiometric coefficients, which are the numbers placed in front of chemical formulas. These coefficients ensure that the total mass of the reactants equals the total mass of the products.
For example, if you have a reaction where phosphorus reacts with chlorine to form phosphorus trichloride, you start with the unbalanced equation:

• \( P_4(s) + Cl_2(g) \rightarrow PCl_3 \)

After counting the atoms on each side, you'll find you need to adjust the coefficients to ensure both sides are equal:

• \( P_4(s) + 6 Cl_2(g) \rightarrow 4 PCl_3 \)

This balanced equation tells you that one molecule of tetra-phosphorus reacts with six molecules of chlorine, resulting in four molecules of phosphorus trichloride.
Balancing is a vital skill in chemistry as it reflects the stoichiometry of the reaction.

Reactants and Products

In any chemical reaction, we identify two main components: reactants and products. Reactants are the starting materials that react with each other, while products are the substances formed as a result of the reaction.
By identifying these components, we can write a chemical equation which serves as a map of the reaction.For instance, when sodium metal reacts with water, sodium (Na) and water (H₂O) are the reactants, while sodium hydroxide (NaOH) and hydrogen gas (H₂) are the products:

• Reactants: \( 2 Na(s) + 2 H_2O(l) \)
• Products: \( 2 NaOH(aq) + H_2(g) \)

Understanding the difference between reactants and products helps us to comprehend the transformation that occurs during a reaction.
This categorization not only helps in writing and balancing chemical equations but also is crucial for predicting the amount of product formed from given quantities of reactants.

Stoichiometric Coefficients

Stoichiometric coefficients are numbers placed before the chemical formulas in a chemical equation to indicate the ratios of reactants and products involved in the reaction.
They play a critical role in the balancing process and are vital for calculating reactants and products in quantitative terms.The coefficients indicate the proportions of substances that participate in a reaction.
For example, in the reaction where hydrogen bromide reacts with chlorine:

• \( 2 HBr(g) + Cl_2(g) \rightarrow 2 HCl(g) + Br_2(g) \)

The coefficient "2" in front of \(HBr\) and \(HCl\) means that two molecules of hydrogen bromide react with one molecule of chlorine to produce two molecules of hydrogen chloride and one molecule of bromine.
This provides the essential information needed to calculate how much of each reactant is needed, or how much product will be formed.By using stoichiometric coefficients, chemists ensure that chemical equations accurately reflect the reality of chemical processes, thus facilitating the understanding of a vast array of chemical phenomena.