Problem 23 - Chemistry and Chemical Reactivity

Question

The electrolysis of aqueous NaCl gives \(\mathrm{NaOH}, \mathrm{Cl}_{2},\) and \(\mathrm{H}_{2}\) (a) Write a balanced equation for the process. (b) In the United States, \(1.19 \times 10^{10} \mathrm{kg}\) of \(\mathrm{NaOH}\) and \(1.14 \times 10^{10} \mathrm{kg}\) of \(\mathrm{Cl}_{2}\) were produced in a recent year. Does the ratio of masses of \(\mathrm{NaOH}\) and \(\mathrm{Cl}_{2}\) produced agree with the ratio of masses expected from the balanced equation? If not, what does this tell you about the way in which \(\mathrm{NaOH}\) and \(\mathrm{Cl}_{2}\) are actually produced? Is the electrolysis of aqueous NaCl the only source of these chemicals?

Step-by-Step Solution

Answer

The ratio of NaOH to Cl₂ does not agree with the theoretical ratio, indicating other production methods are used.

Step 1: Write the Chemical Equation

The electrolysis of aqueous NaCl involves the decomposition of NaCl and water to form NaOH, Cl₂, and H₂ gas. The balanced chemical equation for this process is: \[ 2 ext{NaCl}_{(aq)} + 2 ext{H}_2 ext{O}_{(l)} ightarrow 2 ext{NaOH}_{(aq)} + ext{Cl}_2_{(g)} + ext{H}_2_{(g)} \] Here, two moles of NaCl react with two moles of water to produce two moles of NaOH, one mole of Cl₂, and one mole of H₂ gas.

Step 2: Determine Molar Masses

To find the theoretical mass ratio, we need to calculate the molar masses of NaOH and Cl₂. - The molar mass of NaOH is calculated as: \[ \text{NaOH} = 22.99 + 15.999 + 1.008 = 39.997 \text{ g/mol} \] - The molar mass of Cl₂ is calculated as: \[ \text{Cl}_2 = 2 \times 35.45 = 70.90 \text{ g/mol} \] With this information, we can find the mass ratio from the balanced equation.

Step 3: Calculate Theoretical Mass Ratio

According to the balanced equation, two moles of NaOH and one mole of Cl₂ are produced. Therefore, the mass of NaOH produced is \(2 \times 39.997\) and the mass of Cl₂ is \(1 \times 70.90\). Calculate the ratio: \[ \text{Mass ratio (NaOH to Cl}_2) = \frac{2 \times 39.997}{70.90} \approx 1.126 \] The theoretical mass ratio of NaOH to Cl₂ is approximately 1.126.

Step 4: Compare Real Mass Ratio

We now compare the theoretical mass ratio to the actual masses provided: - Actual NaOH mass = \(1.19 \times 10^{10} \) kg - Actual Cl₂ mass = \(1.14 \times 10^{10} \) kg Calculate the actual mass ratio: \[ \text{Actual mass ratio (NaOH to Cl}_2) = \frac{1.19 \times 10^{10}}{1.14 \times 10^{10}} \approx 1.044 \] This actual mass ratio of 1.044 is less than the theoretical ratio of 1.126.

Step 5: Analyze Results

The difference between the theoretical and actual mass ratios suggests that the electrolysis of aqueous NaCl is not the only method used to produce NaOH and Cl₂. Other processes must be involved in the production, particularly for NaOH, to account for the different ratio.

Key Concepts

Chemical Equation

The electrolysis of aqueous NaCl is a fascinating process that involves a chemical reaction to decompose sodium chloride and water. This reaction produces sodium hydroxide (NaOH), chlorine gas (Cl₂), and hydrogen gas (H₂). Understanding the balanced chemical equation is key to grasping the process:\[ 2 \text{NaCl}_{(aq)} + 2 \text{H}_2\text{O}_{(l)} \rightarrow 2 \text{NaOH}_{(aq)} + \text{Cl}_2_{(g)} + \text{H}_2_{(g)} \]This balanced equation tells us exactly how many moles of each substance are involved. Here, two moles of NaCl and two moles of water create two moles of NaOH, one mole of Cl₂, and one mole of H₂. Balancing the equation is essential, ensuring that the same number of atoms of each element appears on both sides. This forms the basis for calculating how much product you can expect from a given amount of reactant.

Molar Mass

Understanding molar mass is crucial when working with chemical reactions. Molar mass refers to the mass of one mole of a substance, measured in grams per mole (g/mol). For our reaction, we need to know the molar masses of NaOH and Cl₂ to calculate their mass production ratio.

• The molar mass of NaOH is calculated as follows:\[ \text{NaOH} = 22.99 + 15.999 + 1.008 = 39.997 \text{ g/mol} \]
• The molar mass of Cl₂ is:\[ \text{Cl}_2 = 2 \times 35.45 = 70.90 \text{ g/mol} \]

These molar masses help us understand how much each mole weighs and allow us to convert between moles and grams, which is fundamental in stoichiometry and comparing the amounts of substances involved in reactions.

Mass Ratio

The mass ratio is a critical concept when comparing theoretical possibilities with actual outcomes. In this electrolysis process, we derived the theoretical mass ratio from the balanced chemical equation:\[ \text{Theoretical mass ratio (NaOH to Cl}_2) = \frac{2 \times 39.997}{70.90} \approx 1.126 \]This means that for every 1.126 kg of NaOH, we expect 1 kg of Cl₂ to be produced based on the balanced equation. In comparison, the actual mass ratio is calculated using the provided weights:

• Actual NaOH mass = \(1.19 \times 10^{10} \) kg
• Actual Cl₂ mass = \(1.14 \times 10^{10} \) kg

The actual mass ratio of NaOH to Cl₂ calculated as:\[ \frac{1.19 \times 10^{10}}{1.14 \times 10^{10}} \approx 1.044 \]This discrepancy indicates a difference between expected theoretical outcomes and practical industrial results.

Chemical Production

Chemical production often involves multiple methods and sources. The difference between the calculated theoretical mass ratio and the actual mass ratio suggests that electrolysis might not be the sole method of producing NaOH and Cl₂. This insight encourages us to consider other industrial processes that might be contributing.

• Electrolysis is a common method for producing these chemicals, but other methods may be employed, particularly for NaOH.
• The presence of alternative production techniques could impact the efficiency and cost-effectiveness of the chemical industry.

Recognizing this helps in understanding not only the chemistry behind the reactions but also the broader industrial practices involved in chemical manufacturing.