Problem 65 - Chemistry and Chemical Reactivity

Question

What volume of \(0.750 \mathrm{M} \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2},\) in milliliters, is required to react completely with \(1.00 \mathrm{L}\) of \(2.25 \mathrm{M} \mathrm{NaCl}\) solution? The balanced equation is \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})+2 \mathrm{NaCl}(\mathrm{aq}) \rightarrow\) $$ \mathrm{PbCl}_{2}(\mathrm{s})+2 \mathrm{NaNO}_{3}(\mathrm{aq}) $$

Step-by-Step Solution

Answer

1500 mL of \(0.750 \mathrm{M} \mathrm{Pb}(\mathrm{NO}_{3})_{2}\) is required.

Step 1: Understand the Reaction

The balanced chemical equation is \( \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq}) + 2 \mathrm{NaCl}(\mathrm{aq}) \rightarrow \mathrm{PbCl}_{2}(\mathrm{s}) + 2 \mathrm{NaNO}_{3}(\mathrm{aq}) \). This shows that 1 mole of \( \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2} \) reacts with 2 moles of \( \mathrm{NaCl} \).

Step 2: Calculate Moles of NaCl

The given concentration of \( \mathrm{NaCl} \) is \( 2.25 \mathrm{M} \) and the volume is \( 1.00 \mathrm{L} \). Moles of \( \mathrm{NaCl} = 2.25 \, \mathrm{mol/L} \times 1.00 \, \mathrm{L} = 2.25 \, \mathrm{mol} \).

Step 3: Determine Moles of Pb(NO3)2 Needed

According to the balanced equation, the mole ratio of \( \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2} \) to \( \mathrm{NaCl} \) is 1:2. Therefore, the moles of \( \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2} \) needed are \( \frac{2.25 \, \mathrm{mol} \, \mathrm{NaCl}}{2} = 1.125 \, \mathrm{mol} \).

Step 4: Calculate Volume of Pb(NO3)2 Solution

Given that the concentration of \( \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2} \) solution is \( 0.750 \, \mathrm{M} \), use the formula \( \text{Volume (L)} = \frac{\text{Moles}}{\text{Concentration (Molarity)}} \). Therefore, the volume is \( \frac{1.125 \, \mathrm{mol}}{0.750 \, \mathrm{M}} = 1.50 \, \mathrm{L} \).

Step 5: Convert Volume to Milliliters

Convert the volume from liters to milliliters to get the final answer. \( 1.50 \, \mathrm{L} = 1.50 \times 1000 \, \mathrm{mL/L} = 1500 \, \mathrm{mL} \).

Key Concepts

Molarity

Molarity is an essential concept in chemistry when dealing with solutions. It is a way to express the concentration of a solute in a solution. Specifically, molarity is defined as the number of moles of solute per liter of solution. The unit of measurement is moles per liter (mol/L), often denoted as M.
Understanding the molarity helps us not only to know how much of a substance is in a given volume of solution but also to make predictions and calculations about chemical reactions that involve solutions. For example, if you have 2.25 M NaCl in an exercise, it means there are 2.25 moles of sodium chloride in every liter of that solution. This information becomes critical when calculating how the solution will react with other chemicals.
To calculate molarity, use the formula:

• Molarity (M) = Moles of solute / Volume of solution (L)

This formula enables you to solve problems like determining how much of a particular solution is needed to completely react with another, as seen in the given exercise.

Chemical Reactions

Chemical reactions are the processes in which substances (reactants) are transformed into new substances (products). These reactions are indicated by chemical equations, which show the reactants on the left and the products on the right. In a chemical reaction, the bonds between atoms in the reactants are broken, and new bonds are formed to create the products.
Each reaction is governed by specific stoichiometry, meaning the exact ratio in which reactants combine and products form. Understanding stoichiometry is fundamental to predicting the amounts of products formed from given reactants.

• In the case of our exercise, the reaction involves Pb(NO3)2 and NaCl reacting to form PbCl2 and NaNO3.
• The chemical equation helps us understand that one molecule of Pb(NO3)2 combines with two molecules of NaCl.

This relationship is crucial for calculating how much Pb(NO3)2 is needed to react with a certain amount of NaCl, as it establishes the mole ratio between the reacting substances.

Balanced Equations

A balanced chemical equation is a representation of a chemical reaction that has the same number of each type of atom on both the reactant and product sides. Balancing equations is essential because it complies with the law of conservation of mass, which states that matter cannot be created or destroyed in a closed system.
In a balanced equation, the coefficients (the numbers in front of molecules) indicate the ratio in which each substance participates in the reaction. The coefficients are necessary for stoichiometric calculations and ensure that the equation accurately reflects the reaction.
For example, in the reaction:

• \( \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq}) + 2 \mathrm{NaCl}(\mathrm{aq}) \rightarrow \mathrm{PbCl}_{2}(\mathrm{s}) + 2 \mathrm{NaNO}_{3}(\mathrm{aq}) \)

The equation shows that one mole of \( \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2} \) combines with two moles of \( \mathrm{NaCl} \), forming one mole of \( \mathrm{PbCl}_{2} \) and two moles of \( \mathrm{NaNO}_{3} \). This balanced equation allows us to relate the quantities of the reactants and products, which is vital for determining how much of each reactant is needed and the expected amount of product.