Problem 63 - Chemistry and Chemical Reactivity

Question

When an electric current is passed through an aqueous solution of NaCl, the valuable industrial chemicals \(\mathrm{H}_{2}(\mathrm{g})\) \(\mathrm{Cl}_{2}(\mathrm{g}),\) and \(\mathrm{NaOH}\) are produced. $$2 \mathrm{NaCl}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \mathrm{H}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})+2 \mathrm{NaOH}(\mathrm{aq})$$ What mass of NaOH can be formed from \(15.0 \mathrm{L}\) of \(0.35 \mathrm{M}\) NaCl? What mass of chlorine is obtained?

Step-by-Step Solution

Answer

209.98 g of NaOH and 186.13 g of Cl2 are produced.

Step 1: Calculate moles of NaCl

First, we need to find the number of moles of NaCl in the solution. Use the formula \( n = C \times V \), where \( C \) is the concentration of the solution and \( V \) is the volume in liters. Here, \( C = 0.35 \, \text{M} \) and \( V = 15.0 \, \text{L} \). Thus, the moles of NaCl is \( 0.35 \, \text{mol/L} \times 15.0 \, \text{L} = 5.25 \text{ mol} \).

Step 2: Determine moles of NaOH formed

The balanced chemical equation shows that 2 moles of NaCl produce 2 moles of NaOH. Hence, the moles of NaOH produced is equal to the moles of NaCl. Therefore, 5.25 moles of NaCl will produce 5.25 moles of NaOH.

Step 3: Calculate mass of NaOH

To find the mass of NaOH produced, use the formula \( \text{mass} = \text{moles} \times \text{molar mass} \). The molar mass of NaOH is \( 22.99 \, \text{g/mol} \) for Na + \( 15.999 \, \text{g/mol} \) for O + \( 1.008 \, \text{g/mol} \) for H, totaling \( 39.997 \, \text{g/mol} \). Thus, the mass of NaOH is \( 5.25 \, \text{mol} \times 39.997 \, \text{g/mol} = 209.98 \, \text{g} \).

Step 4: Determine moles of Cl2 formed

For every 2 moles of NaCl, 1 mole of Cl2 is produced according to the balanced equation. Therefore, \( 5.25 \text{ moles} \) of NaCl will produce \( 5.25 \div 2 = 2.625 \text{ moles} \) of Cl2.

Step 5: Calculate mass of Cl2

The molar mass of Cl2 is \( 70.906 \, \text{g/mol} \). Thus, the mass of Cl2 formed is \( 2.625 \text{ moles} \times 70.906 \text{ g/mol} = 186.13 \text{ g} \).

Key Concepts

Chemical Reactions

Chemical reactions involve the rearrangement of atoms to transform reactants into products. In an electrolysis process, like the one for NaCl solution, an electric current drives a non-spontaneous chemical reaction.
In this specific reaction, electrical energy is used to decompose NaCl and water into valuable chemicals:

• Hydrogen gas
• Chlorine gas
• Sodium hydroxide (NaOH).

The balanced equation for this process shows it requires two moles of NaCl and two moles of water to produce one mole of hydrogen gas, one mole of chlorine gas, and two moles of NaOH. Understanding the stoichiometry of this reaction is essential for calculating how much product can be formed from given reactants.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative aspects of chemical reactions, i.e., the measurements of reactants and products. In our example, stoichiometry helps us calculate how much product (NaOH and Cl2) can be produced from a certain amount of NaCl.
The balanced chemical equation shows a 1:1 molar relationship between NaCl and NaOH, and a 2:1 relationship between NaCl and Cl2. By understanding these ratios, we can determine the amount of NaOH and Cl2 produced.
For instance, starting with 5.25 moles of NaCl, since the ratio is 1:1, you get 5.25 moles of NaOH. The same amount of NaCl will produce half as many moles of Cl2 (2.625 moles) because of the 2:1 ratio.

Industrial Chemistry

Industrial chemistry applies chemical knowledge to produce and process the materials that society needs. The electrolysis of NaCl is an excellent example of industrial chemistry because it helps produce essential materials like chlorine gas and NaOH on a large scale for various applications.

• Chlorine gas is vital in water purification, disinfectants, and the manufacture of plastics.
• Sodium hydroxide is crucial for making soap, paper, and as a general cleaning agent.

By electrochemically decomposing saltwater, industries can efficiently and economically generate these necessary compounds, showcasing how industrial chemistry transforms basic chemistry knowledge into practical uses.

Molar Mass Calculation

Molar mass is the mass of a given substance (chemical element or chemical compound) divided by the amount of substance. Calculating molar mass is key to determining the amount of a substance present in moles, which can then relate to grams.
For NaOH, the molar mass is calculated by summing up the molar masses of its constituent elements:

• Sodium (Na): 22.99 g/mol
• Oxygen (O): 15.999 g/mol
• Hydrogen (H): 1.008 g/mol

Totaling these gives us a molar mass of 39.997 g/mol. This value enables us to convert between moles and mass in a chemical calculation. For example, to find the grams of NaOH in a certain number of moles, multiply the number of moles by this molar mass. This method also applies to Cl2, where its molar mass allows us to calculate its produced mass from the amount in moles obtained through stoichiometry.