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

The balanced chemical equation for the decomposition of aqueous solutions of NaCl is given as: $$ 2 \mathrm{NaCl}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) $$

We are given that the plant produces \(1.5 \times 10^{6} \mathrm{kg}\) of Cl₂ daily. To find the moles of Cl₂, we can use the following formula: $$ \text{moles of Cl₂} = \frac{\text{mass of Cl₂}}{\text{molar mass of Cl₂}} $$ The molar mass of Cl₂ is \(2 \times 35.45 \thinspace \mathrm{g/mol}\) (since there are two chlorine atoms, each with a molar mass of \(35.45 \thinspace \mathrm{g/mol}\)). First, convert the mass of Cl₂ from kg to g: $$ 1.5 \times 10^{6} \thinspace \mathrm{kg} \times \frac{1000 \thinspace \mathrm{g}}{1 \thinspace \mathrm{kg}} = 1.5 \times 10^{9} \thinspace \mathrm{g} $$ Next, calculate the moles of Cl₂ produced daily: $$ \text{moles of Cl₂} = \frac{1.5 \times 10^{9} \thinspace \mathrm{g}}{2 \times 35.45 \thinspace \mathrm{g/mol}} = \frac{1.5 \times 10^{9} \thinspace \mathrm{g}}{70.9 \thinspace \mathrm{g/mol}} = 2.12 \times 10^{7} \thinspace \mathrm{mol} $$

From the balanced equation, we can see that for each mole of Cl₂ produced, one mole of H₂ is produced, and two moles of NaOH are produced. Therefore: Moles of H₂ produced daily = Moles of Cl₂ produced daily = \(2.12 \times 10^{7} \thinspace \mathrm{mol}\) Moles of NaOH produced daily = \(2 \times\) Moles of Cl₂ produced daily = \(2 \times 2.12 \times 10^{7} \thinspace \mathrm{mol} = 4.24 \times 10^{7} \thinspace \mathrm{mol}\)

Now we can calculate the mass of H₂ and NaOH produced daily using their respective molar masses: Molar mass of H₂ = \(2 \times 1.01 \thinspace \mathrm{g/mol}\) (since there are two hydrogen atoms, each with a molar mass of \(1.01 \thinspace \mathrm{g/mol}\)) Molar mass of NaOH = \(22.99 \thinspace \mathrm{g/mol} + 15.999 \thinspace \mathrm{g/mol} + 1.01 \thinspace \mathrm{g/mol}\) (Na, O, and H) Mass of H₂ produced daily: $$ (2.12 \times 10^{7} \thinspace \mathrm{mol}) \times (2.02 \thinspace \mathrm{g/mol}) = 4.28 \times 10^{7} \thinspace \mathrm{g} = 4.28 \times 10^{4} \thinspace \mathrm{kg} $$ Mass of NaOH produced daily: $$ (4.24 \times 10^{7} \thinspace \mathrm{mol}) \times (39.998\thinspace \mathrm{g/mol}) = 1.69 \times 10^{9} \thinspace \mathrm{g} = 1.69 \times 10^{6} \thinspace \mathrm{kg} $$

The chemical plant produces approximately \(4.28 \times 10^{4} \thinspace \mathrm{kg}\) of hydrogen gas (H₂) and \(1.69 \times 10^{6} \thinspace \mathrm{kg}\) of sodium hydroxide (NaOH) daily, along with the given \(1.5 \times 10^6 \thinspace \mathrm{kg}\) of chlorine gas (Cl₂).