Problem 29 - Chemistry The Molecular Science

Question

(a) Write the balanced chemical equation for the electrolysis of aqueous \(\mathrm{NaCl}\). (b) In \(2002,8.98 \times 10^{9} \mathrm{~kg} \mathrm{NaOH}\) and \(1.14 \times 10^{10} \mathrm{~kg}\) chlorine were produced in the United States. Does the ratio of these masses agree with the ratio of masses from the balanced chemical equation? If not, what does that suggest about the ways that \(\mathrm{NaOH}\) and \(\mathrm{Cl}_{2}\) are produced?

Step-by-Step Solution

Answer

The mass ratio does not agree, suggesting additional methods of production.

Step 1: Identify the Electrolysis Reaction

The electrolysis of aqueous sodium chloride (\( \text{NaCl} \)) involves breaking down \( \text{NaCl} \) in water to form sodium hydroxide \( \text{NaOH} \), chlorine gas \( \text{Cl}_2 \), and hydrogen gas \( \text{H}_2 \). The products are formed as follows due to the chemical reactions at the electrodes during electrolysis.

Step 2: Write the Balanced Chemical Equation

The balanced chemical equation for the electrolysis of aqueous \( \text{NaCl} \) is:\[2 \text{NaCl} (\text{aq}) + 2 \text{H}_2\text{O} (\text{l}) \rightarrow 2 \text{NaOH} (\text{aq}) + \text{H}_2 (\text{g}) + \text{Cl}_2 (\text{g})\]This equation shows that two moles of NaCl react with two moles of water to produce two moles of NaOH, one mole of \(\text{H}_2\), and one mole of \(\text{Cl}_2\).

Step 3: Calculate the Theoretical Mass Ratio

From the balanced equation, consider the molar masses: - \( \text{NaOH}: 40 \) g/mol - \( \text{Cl}_2: 71 \) g/mol Looking at the mole ratio from the equation, we have \( 2 \text{NaOH} : 1 \text{Cl}_2 \). Thus, the mass ratio is:\[\text{Mass ratio} = \frac{2 \times 40}{71} \approx 1.13\]

Step 4: Compare Given Masses from 2002

The mass ratio based on the given production values is:- \( \text{Mass of NaOH} = 8.98 \times 10^9 \text{ kg}\)- \( \text{Mass of Cl}_2 = 1.14 \times 10^{10} \text{ kg}\)The ratio is:\[\frac{8.98 \times 10^9}{1.14 \times 10^{10}} \approx 0.788\]This calculated ratio of 0.788 doesn't match the theoretical mass ratio of 1.13.

Step 5: Interpret the Results

Since the ratio from the masses produced in 2002 (0.788) does not match the theoretical ratio of the balanced equation (1.13), it suggests that methods other than the electrolysis of NaCl are used to produce either NaOH or \(\text{Cl}_2\), or both, affecting the production proportions based on their more global industrial synthesis methods.

Key Concepts

Balanced Chemical Equation

Understanding a balanced chemical equation is crucial for the electrolysis of aqueous NaCl. In this process, sodium chloride (\( \text{NaCl} \)) is decomposed in water to produce sodium hydroxide (\( \text{NaOH} \)), chlorine gas (\( \text{Cl}_2 \)), and hydrogen gas (\( \text{H}_2 \)). The equation for this reaction is carefully balanced to reflect the conservation of mass and moles.
The balanced equation is:\[2 \text{NaCl} (\text{aq}) + 2 \text{H}_2\text{O} (\text{l}) \rightarrow 2 \text{NaOH} (\text{aq}) + \text{H}_2 (\text{g}) + \text{Cl}_2 (\text{g})\]Balancing a chemical equation means ensuring that the number of atoms for each element is the same on both sides of the equation. This equation shows that two moles of NaCl and two moles of water are needed to produce two moles of NaOH, one mole of \( \text{H}_2 \), and one mole of \( \text{Cl}_2 \).
This balanced equation is fundamental for understanding the stoichiometry of electrolysis, which determines how much product is generated from given amounts of reactants.

Sodium Hydroxide Production

Sodium hydroxide (\( \text{NaOH} \)) is a key product of the electrolysis of NaCl. In the reaction, for every two moles of sodium chloride and two moles of water, two moles of sodium hydroxide are produced. This product is essential in many industrial processes.

• Manufacture of paper and pulp
• Petroleum refining
• Production of soaps and detergents

The mass of \( \text{NaOH} \) can be calculated using its molar mass, which is 40 g/mol. This knowledge is important for determining how much starting material is needed and what the yield of the reaction will be.
The theoretical ratio of \( \text{NaOH} \) to \( \text{Cl}_2 \) based on the balanced equation is approximately 1.13 when considering their molar masses. However, the industrial production in the U.S. in 2002 showed a different ratio of 0.788, indicating that not all NaOH is produced by this method alone.

Chlorine Production

Chlorine gas (\( \text{Cl}_2 \)) is another vital product from the electrolysis of NaCl. For every two moles of sodium chloride and two moles of water consumed, one mole of chlorine gas is produced.
Chlorine is crucial for several applications:

• Disinfection of water supplies
• Production of PVC and other plastics
• Manufacturing of solvents

The molar mass of chlorine is 71 g/mol. This helps in calculating the mass of chlorine produced from a known quantity of NaCl. The discrepancy between the real production ratio (0.788) and the theoretical ratio (1.13) suggests additional production methods or uses outside the scope of NaCl electrolysis. This deviation implies varying industrial practices and the necessity of various methods for ensuring an adequate supply of chlorine globally.