Question

A chemical plant uses electrical energy to decompose aqueous solutions of \(\mathrm{NaCl}\) to give \(\mathrm{Cl}_{2}, \mathrm{H}_{2}\), and \(\mathrm{NaOH}\) : \(2 \mathrm{NaCl}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \underset{2 \mathrm{NaOH}(a q)}{\longrightarrow}+\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g)\) If the plant produces \(1.5 \times 10^{6} \mathrm{~kg}\left(1500\right.\) metric tons) of \(\mathrm{Cl}_{2}\) daily, estimate the quantities of \(\mathrm{H}_{2}\) and \(\mathrm{NaOH}\) produced.

Short answer

The estimated daily production of H₂ is approximately \(4.26299 \times 10^4\ kg\) (42.63 metric tons), and the estimated daily production of NaOH is approximately \(1.6925 \times 10^6\ kg\) (1692.5 metric tons).

Step-by-step solution

Calculate the moles of Cl₂ produced

Since we are given the mass of Cl₂ produced daily, we can calculate the moles of Cl₂ by dividing the mass by the molar mass of Cl₂. The molar mass of Cl₂ is approximately 70.9 g/mol. First, convert the daily production of Cl₂ to grams: \(1.5 \times 10^{6}\ kg \times \frac{1000\ g}{1\ kg} = 1.5 \times 10^9\ g\) Next, calculate the moles of Cl₂: \(\frac{1.5 \times 10^9\ g}{70.9\ g/mol} = 2.11563 \times 10^7\ moles\)

Determine the moles of H₂ and NaOH produced

Now, use the stoichiometry of the balanced equation to determine the moles of H₂ and NaOH produced. From the balanced equation, we can see that for every 1 mole of Cl₂ produced, 1 mole of H₂ and 2 moles of NaOH are produced: \(2 \mathrm{NaCl}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \underset{2 \mathrm{NaOH}(a q)}{\longrightarrow}+\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g)\) So, the moles of H₂ produced will be equal to the moles of Cl₂: \(2.11563 \times 10^7\ moles\ H₂\) And the moles of NaOH produced will be twice the moles of Cl₂: \(2 \times 2.11563 \times 10^7\ moles\ NaOH \approx 4.23126 \times 10^7\ moles\)

Calculate the mass of H₂ and NaOH produced

Finally, we'll use the molar mass of H₂ and NaOH to convert the moles calculated in Step 2 to mass: Molar mass of H₂ = 2.016 g/mol Molar mass of NaOH = 40 g/mol Calculate the mass of H₂ produced: \((2.11563 \times 10^7\ moles\ H₂) \times \frac{2.016\ g}{1\ mole\ H₂} \approx 4.26299 \times 10^7\ g\) Convert to kg: \(\frac{4.26299 \times 10^7\ g\ H₂}{1000\ g/kg} \approx 4.26299 \times 10^4\ kg\ H₂\) Calculate the mass of NaOH produced: \((4.23126 \times 10^7\ moles\ NaOH) \times \frac{40\ g}{1\ mole\ NaOH} \approx 1.6925 \times 10^9\ g\ NaOH\) Convert to kg: \(\frac{1.6925 \times 10^9\ g\ NaOH}{1000\ g/kg} \approx 1.6925 \times 10^6\ kg\ NaOH\) So, the estimated daily production of H₂ and NaOH is: H₂: \(4.26299 \times 10^4\ kg\) (approximately 42.63 metric tons) NaOH: \(1.6925 \times 10^6\ kg\) (approximately 1692.5 metric tons)

Key concepts

Mole Concept

The mole concept is a fundamental principle in chemistry that functions as the bridge between the atomic world and the macroscopic world we experience. It allows chemists to count particles by weighing. In essence, a mole represents a fixed number of particles—specifically, Avogadro's number, which is approximately 6.022 x 10²³ particles.

Think of it like a 'chemist's dozen,' similar to how a dozen represents 12 of something, a mole represents 6.022 x 10²³ particles. This is incredibly useful, as it means that if we know the molar mass of a substance (the mass of one mole of particles), we can easily convert between the mass of a substance and the number of particles or moles it represents. In the chemical reaction from our exercise, knowing the mole concept helps us calculate how much raw material is needed or how much product can be obtained.

Molar Mass Calculation

Molar mass calculation is simply determining the mass of one mole of a substance. The unit for molar mass is grams per mole (g/mol). It can be calculated by summing the atomic masses of all the atoms in a molecule. For instance, water (H₂O) has a molar mass of approximately 18.015 g/mol because it has two hydrogen atoms (each with a molar mass of about 1.008 g/mol) and one oxygen atom (with a molar mass of about 15.999 g/mol).

In the example, the molar mass of Cl₂ was used to convert the mass of chlorine gas produced into moles, a necessary step to then use our stoichiometric ratios. Accurate molar mass calculations are vital to stoichiometry since they ensure that the math regarding the number of particles involved in a reaction is correct.

Stoichiometric Calculations

Stoichiometric calculations involve using the balanced chemical equation to understand the proportions of reactants to products. It's all about the ratios in which substances react or form products. The balanced equation tells us the mole ratio, in this case, that for every 2 moles of NaCl and 2 moles of H₂O, we get 2 moles of NaOH, 1 mole of H₂, and 1 mole of Cl₂.

With stoichiometry, once we know the amount of one substance in a reaction, we can calculate the amounts of all the other substances involved in the reaction. For the chemical plant problem, by knowing the daily production of Cl₂, we estimated the quantities of H₂ and NaOH produced. This is crucial, not just for assignments, but in real-world applications where chemists need to predict how much of each chemical is needed or will be produced in a reaction.