Problem 47 - Chemistry Matter and Change

Question

When hydrochloric acid solution reacts with lead(II) nitrate solution, lead(II) chloride precipitates and a solution of nitric acid is produced. \begin{equation} \begin{array}{l}{\text { a. Write the balanced chemical equation for the reaction. }} \\ {\text { b. Interpret the equation in terms of molecules and }} \\ {\text { formula units, moles, and mass. }}\end{array} \end{equation}

Step-by-Step Solution

Answer

The balanced equation is \(2\text{HCl} + \text{Pb(NO}_3)_2 \rightarrow \text{PbCl}_2 + 2\text{HNO}_3\). This means 2 moles of HCl react with 1 mole of Pb(NO_3)_2 to form 1 mole of PbCl_2 and 2 moles of HNO_3.

Step 1: Write the Unbalanced Reaction Equation

Identify the reactants and products in the reaction. The reactants are hydrochloric acid (HCl) and lead(II) nitrate \((\text{Pb(NO}_3)_2)\). The products formed are lead(II) chloride \((\text{PbCl}_2)\) and nitric acid \((\text{HNO}_3)\). Write the unbalanced chemical equation: \[\text{HCl} + \text{Pb(NO}_3)_2 \rightarrow \text{PbCl}_2 + \text{HNO}_3\].

Step 2: Balance the Chemical Equation

To balance the chemical equation, ensure there are equal numbers of each type of atom on both sides. Start with lead (Pb) and check that there's 1 Pb on each side. Next, balance the chloride ions (Cl): \(2\) HCl are needed for \(\text{PbCl}_2\). Now balance the nitrate ions (NO_3): 2 molecules of \(\text{HNO}_3\) are required. The balanced equation is: \[2\text{HCl} + \text{Pb(NO}_3)_2 \rightarrow \text{PbCl}_2 + 2\text{HNO}_3\].

Step 3: Interpret the Equation in Molecules and Formula Units

The balanced equation \(2\text{HCl} + \text{Pb(NO}_3)_2 \rightarrow \text{PbCl}_2 + 2\text{HNO}_3\) shows that 2 molecules (or formula units) of hydrochloric acid react with 1 formula unit of lead(II) nitrate to produce 1 formula unit of lead(II) chloride and 2 molecules of nitric acid.

Step 4: Interpret the Equation in Moles

Interpret the balanced equation in terms of moles: 2 moles of HCl react with 1 mole of Pb(NO_3)_2 to produce 1 mole of PbCl_2 and 2 moles of HNO_3.

Step 5: Interpret the Equation in Mass

Calculate the molar masses of the substances involved: HCl has a molar mass of 36.5 g/mol, Pb(NO_3)_2 is 331.2 g/mol, PbCl_2 is 278.1 g/mol, and HNO_3 is 63.0 g/mol. Using these values, in terms of mass: \(2 \times 36.5\) g of HCl reacts with 331.2 g of lead(II) nitrate to produce 278.1 g of lead(II) chloride and \(2 \times 63.0\) g of nitric acid.

Key Concepts

balanced equations

Chemical reactions must obey the law of conservation of mass, which states that matter cannot be created or destroyed in an isolated system. To reflect this, we use **balanced equations**. Start by identifying all reactants and products in the reaction. Then, ensure that the number of each type of atom on the reactants' side equals the number on the products' side. For instance, in the reaction between hydrochloric acid (HCl) and lead(II) nitrate - The unbalanced equation: \[ \text{HCl} + \text{Pb(NO}_3)_2 \rightarrow \text{PbCl}_2 + \text{HNO}_3 \] To balance this equation:- Find the molecules with the greatest number of different atoms. - Adjust coefficients to balance the most complex molecules first. - The balanced form is: \[ 2\text{HCl} + \text{Pb(NO}_3)_2 \rightarrow \text{PbCl}_2 + 2\text{HNO}_3 \] This equation now reflects an equal number of each type of atom on both sides of the equation, maintaining the conservation of mass principle.

stoichiometry

**Stoichiometry** involves calculating the relative quantities of reactants and products in chemical reactions. It is based on the balanced equation of the reaction. The coefficients in a balanced equation indicate the ratio of moles of each substance involved. In our balanced equation: - \[ 2\text{HCl} + \text{Pb(NO}_3)_2 \rightarrow \text{PbCl}_2 + 2\text{HNO}_3 \] The coefficients

• 2 in front of HCl means 2 moles of HCl,
• 1 in front of Pb(NO₃)₂ means 1 mole of Pb(NO₃)₂,
• 1 in front of PbCl₂ means 1 mole of PbCl₂,
• 2 in front of HNO₃ means 2 moles of HNO₃.

This ratio guides calculations for determining how much of a reactant is needed or a product is formed in a chemical reaction. Start with moles of a known substance and use this ratio to find the unknown. Stoichiometry is an essential tool in answering questions such as: "How much product can be formed from a given amount of reactant?"

molecule interpretation

Interpreting chemical equations in terms of molecules helps in understanding how substances interact at the molecular level in a chemical reaction. A balanced equation tells us not just about the number of moles involved but also about the specific molecules or formula units interacting in the reaction. Consider \[ 2\text{HCl} + \text{Pb(NO}_3)_2 \rightarrow \text{PbCl}_2 + 2\text{HNO}_3 \].- It implies:

• 2 molecules of HCl combine with
• 1 formula unit of Pb(NO₃)₂ to produce
• 1 formula unit of PbCl₂ and
• 2 molecules of HNO₃.

This interpretation is crucial, especially when predicting the outcomes of reactions at the molecular level in laboratory settings. Understanding molecule interactions aids in visualizing how substances combine to form new products, emphasizing that chemical reactions are a "molecular shuffle" rather than mere arithmetic.

mass calculation

Mass calculation is the process of determining the mass of reactants and products in a chemical reaction. Knowing the molar mass of each compound involved in the reaction is essential. For our balanced equation:- Calculate the molar masses:

• HCl = 36.5 g/mol
• Pb(NO₃)₂ = 331.2 g/mol
• PbCl₂ = 278.1 g/mol
• HNO₃ = 63.0 g/mol

Using these, compute the actual mass involved in the reaction: - Total for HCl: \(2 \times 36.5 = 73.0\) g - For Pb(NO₃)₂: 331.2 g- For PbCl₂: 278.1 g- Total for HNO₃: \(2 \times 63.0 = 126.0\) gMass calculations are vital in chemical engineering and laboratory experiments, where precise measurements ensure successful reactions and safety. By understanding these calculations, you can ensure that chemical reactions comply with the law of conservation of mass, which is fundamental in chemistry.