Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Problem 100

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

Short Answer

Expert verified
In conclusion, using stoichiometric calculations, we found that the chemical plant produces daily approximately 2.14 x 10⁴ kg (21.4 metric tons) of H₂ and 8.48 x 10⁵ kg (848 metric tons) of NaOH.

Step by step solution

01

Calculate moles of Cl₂ produced daily

First, we must convert the mass of Cl₂ produced daily (1.5 x 10⁶ kg) into moles, using the molar mass of Cl₂ (70.90 g/mol). Remember, we have to convert from kg to grams before the conversion: 1.5 x 10⁶ kg * 1000 g/kg = 1.5 x 10⁹ g. Now, we can find the moles of Cl₂ produced: \[\frac{1.5 \times 10^{9} \mathrm{~g} \mathrm{Cl}_{2}}{70.90 \mathrm{~g/mol}} \approx 2.12 \times 10^{7} \mathrm{~moles} \mathrm{Cl}_{2}\]
02

Determine moles of H₂ produced daily

From the balanced chemical equation, we can see that one mole of H₂ is produced for every two moles of Cl₂: 2 NaCl + 2 H₂O → 2 NaOH + H₂ + Cl₂. So, the moles of H₂ produced daily are half the amount of moles of Cl₂ produced daily: \[2.12 \times 10^{7} \mathrm{~moles} \mathrm{Cl}_{2} \times \frac{1 \mathrm{~mole} \mathrm{H}_{2}}{2 \mathrm{~moles} \mathrm{Cl}_{2}} = 1.06 \times 10^{7} \mathrm{~moles} \mathrm{H}_{2}\]
03

Calculate the mass of H₂ produced daily

Now, we need to convert the moles of H₂ to mass, using the molar mass of H₂ (2.02 g/mol). \[1.06 \times 10^{7} \mathrm{~moles} \mathrm{H}_{2} \times \frac{2.02 \mathrm{~g/mol}}{1 \mathrm{~mole} \mathrm{H}_{2}} \approx 2.14 \times 10^{7} \mathrm{~g}\] To convert to metric tons (kg), we divide by 1000: \[2.14 \times 10^{7} \mathrm{~g} \mathrm{H}_{2} \times \frac{1 \mathrm{~kg}}{1000 \mathrm{~g}} \approx 2.14 \times 10^{4} \mathrm{~kg}\]
04

Determine moles of NaOH produced daily

From the balanced chemical equation, we know that for every one mole of Cl₂ produced, one mole of NaOH is also produced. So, the moles of NaOH produced daily is equal to the moles of Cl₂ produced daily (2.12 x 10⁷ moles).
05

Calculate the mass of NaOH produced daily

We can now convert the moles of NaOH to mass by using the molar mass of NaOH (40.00 g/mol). \[2.12 \times 10^{7} \mathrm{~moles} \mathrm{NaOH} \times \frac{40.00 \mathrm{~g/mol}}{1 \mathrm{~mole} \mathrm{NaOH}} \approx 8.48 \times 10^{8} \mathrm{~g}\] To convert to metric tons (kg), we divide by 1000: \[8.48 \times 10^{8} \mathrm{~g} \mathrm{NaOH} \times \frac{1 \mathrm{~kg}}{1000 \mathrm{~g}} \approx 8.48 \times 10^{5} \mathrm{~kg}\]
06

Final quantities

In conclusion, using the stoichiometric calculations, we found that the chemical plant produces daily: - About 2.14 x 10⁴ kg (21.4 metric tons) of H₂. - About 8.48 x 10⁵ kg (848 metric tons) of NaOH.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The molecular formula of saccharin, an artificial sweetener, is \(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{NO}_{3} \mathrm{~S} .(\mathbf{a})\) What is the molar mass of saccharin? (b) How many moles of sachharin are in $2.00 \mathrm{mg}\( of this substance? (c) How many molecules are in \)2.00 \mathrm{mg}\( of this substance? (d) How many C atoms are present in \)2.00 \mathrm{mg}$ of saccharin?

Washing soda, a compound used to prepare hard water for washing laundry, is a hydrate, which means that a certain number of water molecules are included in the solid structure. Its formula can be written as $\mathrm{Na}_{2} \mathrm{CO}_{3} \cdot \mathrm{xH}_{2} \mathrm{O},\( where \)x$ is the number of moles of \(\mathrm{H}_{2} \mathrm{O}\) per mole of $\mathrm{Na}_{2} \mathrm{CO}_{3} .$ When a 2.558-g sample of washing soda is heated at \(125^{\circ} \mathrm{C},\) all the water of hydration is lost, leaving $0.948 \mathrm{~g}\( of \)\mathrm{Na}_{2} \mathrm{CO}_{3} .\( What is the value of \)\chi ?$

Calculate the percentage by mass of oxygen in the following compounds: (a) vanillin, \(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{3} ;(\mathbf{b})\) isopropyl alcohol, \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}\); (c) acetaminophen, \(\mathrm{C}_{8} \mathrm{H}_{9} \mathrm{NO}_{2} ;\) (d) cyclopropanone, \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}\); (e) dioxin, \(\mathrm{C}_{12} \mathrm{H}_{4} \mathrm{Cl}_{4} \mathrm{O}_{2} ;\) (f) penicillin, $\mathrm{C}_{16} \mathrm{H}_{18} \mathrm{~N}_{2} \mathrm{O}_{4} \mathrm{~S}$.

When benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) reacts with bromine \(\left(\mathrm{Br}_{2}\right),\) bromobenzene $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Br}\right)$ is obtained: $$ \mathrm{C}_{6} \mathrm{H}_{6}+\mathrm{Br}_{2} \longrightarrow \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Br}+\mathrm{HBr} $$ (a) When \(30.0 \mathrm{~g}\) of benzene reacts with \(65.0 \mathrm{~g}\) of bromine, what is the theoretical yield of bromobenzene? (b) If the actual yield of bromobenzene is \(42.3 \mathrm{~g}\), what is the percentage yield?

The complete combustion of octane, \(\mathrm{C}_{8} \mathrm{H}_{18}\), produces \(5470 \mathrm{~kJ}\) of heat. Calculate how many grams of octane is required to produce \(20,000 \mathrm{~kJ}\) of heat.
See all solutions

Recommended explanations on Chemistry Textbooks

Making Measurements

Read Explanation

Kinetics

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Chemistry Branches

Read Explanation

Chemical Reactions

Read Explanation

The Earths Atmosphere

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free