Virgo Moon Man Cancer Moon Woman, Grange Hill Filming Locations, Religion Anthropology Quizlet, Matt Kaulig Biography, Articles I

Is a solution with OH- = 3.7 x 10-10 M acidic or basic? Solved Write equations showing how each of the following By expressing your answer in a chemical formula you are defining the composition a class of (The value of Kb for . Is a solution with OH- = 8.74 x 10-11 M acidic, basic, or neutral? Design a buffer that has a pH of 11.43 using one of the weak base/conjugate acid systems shown below. When it reacts with an acid such as lemon juice, buttermilk, or sour cream in a batter, bubbles of carbon dioxide gas are formed from decomposition of the resulting carbonic acid, and the batter rises. Baking powder is a combination of sodium bicarbonate, and one or more acid salts that react when the two chemicals come in contact with water in the batter. A. Is a solution with H+ = 9.52 x 10-2 M acidic, basic, or neutral? A compound that can donate protons are considered acids but here in Methanol; as a result, water is a better proton donor, which makes Methanol a weak acid. Illustrative of the drugs prepared from aniline is paracetamol (acetaminophen, Tylenol). Explain. salts. A solution has OH- = 1.3 x 10-2 M. Is this solution acidic, basic, or neutral? These derivatives are of importance in the color industry. HClO4. How can I identify conjugate acids and bases? Pickling is a method used to preserve vegetables using a naturally produced acidic environment. What is it conjugate base? The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. HCO + HO HCO + OH. The reaction, \[CaCO_3(s)+2HCl(aq)CaCl_2(aq)+H_2O(l)+CO_2(g) \nonumber \]. The lactic acid eventually increases the acidity of the brine to a level that kills any harmful bacteria, which require a basic environment. This causes a disturbance to the equilibrium, and causes a response predicted by the Le Chatelier Principle - more of the acid molecules dissociate to increase the concentration of H + ions back to near the original concentration. When base is added it reacts with the H + ions in the buffer, and this (temporarily) reduces the concentration of the H + ion. Students also viewed . You're left with an amine and the hydronium ion for products. The molecule shown is anilinium fluoride. 96% Satisfaction rate 49547 Orders Deliver x. c6h5nh2 express your answer as a chemical formula. Strong bases completely dissociate in aq solution (Kb > 1, pKb < 1). Acids are molecular covalent compounds which you don't expect to ionize (release an #H^+# and leave behind the conjugate base, or #Cl^-# for example). Is a solution with H3O+ = 9.45 x 10-9 M acidic, basic, or neutral? Kauna unahang parabula na inilimbag sa bhutan? However, practically all hydrated metal ions other than those of the alkali metals ionize to give acidic solutions. What are the answers to studies weekly week 26 social studies? Is an aqueous solution of NH4NO2 acidic, basic, or neutral? Large. It is a strong base. What is the conjugate acid of #HSO_4^-2#? The aluminum hydroxide tends to cause constipation, and some antacids use aluminum hydroxide in concert with magnesium hydroxide to balance the side effects of the two substances. Is an aqueous solution with H+ = 6.9 x 10-4 M acidic, basic, or neutral? Will NH4ClO form a solution that is acidic, basic, or neutral? After World War II, Cornelius P. Rhoads introduced the chemotherapeutic approach to cancer treatment. Aniline is an amine that is used to manufacture dyes. Smith, Michael Abbott, Provider & Carrier MGMT Test 1 - Not Terms. 4, acid Ammonia, NH 3 Nitrite NO 2-, base Nitrous acid, HNO 2 H 2 PO 4-2** Dihydrogen phosphate ion, acid and base HPO 4 -, base H 3 PO 4, acid OCl-Hypochlorite ion, base Hypochlorous acid, HClO C 6 H 5 NH 2 Aniline, base C 6 H 5 NH 3 + CH 3 NH 2 Methylamine, base CH 3 NH 3 + C 5 H 5 N (pyridine) Pyridine, base C 5 H 5 NH+ Problem #2 . The equilibrium equation for this reaction is simply the ionization constant. Is a solution with H3O+ = 8.39 x 10-9 M acidic, basic, or neutral? 286 Math Specialists. Suppose a solution has (H3O+) = 1 x 10-2 M and (OH-) = 1 x 10-12 M. Is the solution acidic, basic, or neutral? Calculate the pH of a 5.4010-1 M aqueous solution of aniline hydrochloride (C6H5NH3Cl). In this case, C5H5N accepts a hydrogen ion, becoming a conjugate acid and the species left over is OH-, making it the conjugate base. . What are the Physical devices used to construct memories? The conjugate acid of KOH is K + which is too weak to function as an acid in water. When the conjugate acid and the conjugate base are of unequal strengths, the solution can be either acidic or basic, depending on the relative strengths of the two conjugates. Is a solution with OH- = 1 x 10-9 M acidic, basic, or neutral? A triprotic acid, H 3 A has the following K a s: K a1 = 3.37 x 10-4 , . Choosing an acid or base where pK a is close to the pH needed gives the best results. This is sometimes true, but the salts that are formed in these reactions may have acidic or basic properties of their own, as we shall now see. In this example, sulfuric acid (#H_2SO_4#) is an acid because it "donates" #H^+# to the water. The conjugate base of an acid remains after the acid has donated what? Other aniline dyes followed, such as fuchsin, safranin, and induline. Name. Explain. (CH 3) 3 NH and N 2 H 5 + 4. [16] Oxidation with persulfate affords a variety of polyanilines. What is the conjugate base? Is a solution with OH- = 4.00 x 10-5 M acidic, basic, or neutral? A conjugate base contains one less H atom and one more - charge than the acid that formed it. The fourth column has the following: 0, x, x. Explain. Is an aqueous solution with H+ = 5.55 x 10-5 M acidic, basic, or neutral? February 27, 2023 endeavor air pilot contract No Comments . 18.6 Calculating pH in Strong Acid or Strong Base Solutions (Video) 18.7 Conjugate Acid-Base Pairs (Video) 18.8 Calculating the pH of Weak Acids and Weak Bases (Video) 18.9 Solving when X is not Small (Video) Chapter 18: Acid / Base Chemistry is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. Get access to this video and our entire Q&A library, Acidic & Basic Salt Solutions: Explanation & Examples. Now we have the ionization constant and the initial concentration of the weak acid, the information necessary to determine the equilibrium concentration of H3O+, and the pH: With these steps we find [H3O+] = 2.3 103 M and pH = 2.64, \(K_a\ce{(for\:NH4+)}=5.610^{10}\), [H3O+] = 7.5 106 M. \(\ce{C6H5NH3+}\) is the stronger acid (a) (b) . [30], In the late 19th century, derivatives of aniline such as acetanilide and phenacetin emerged as analgesic drugs, with their cardiac-suppressive side effects often countered with caffeine. K a is the equilibrium constant for the dissociation reaction of a weak acid.A weak acid is one that only partially dissociates in water or an aqueous solution. What is the pH of a 0.233 M solution of aniline hydrochloride? However, even if we mix stoichiometrically equivalent quantities, we may find that the resulting solution is not neutral. PLEASE HELP!!! HNO2 + OH- -----> H2O + NO2- I know that HNO2 is a weak acid and NaOH is a strong base . What is the conjugate acid of C6H5NH2 What formula do you use to calculate pH when given the molarity of an acid? ; Base generates OH - in aqueous solutions. Identify the following compounds as strongly acidic, weakly acidic, weakly basic, strongly basic, or pH-neutral in water at #25^@ "C"#? Calculate the pH of a 0.10-M solution of aluminum chloride, which dissolves completely to give the hydrated aluminum ion \(\ce{[Al(H2O)6]^3+}\) in solution. The arithmetic checks; when 1.2 103 M is substituted for x, the result = Ka. In this reaction primary aromatic amine reacts with sodium nitrile and with 2 moles of HCl which is known as Ice cold mixture because the temperature use to be 0.5C and it forms benzene diazonium salt as major product and water and sodium chloride. A teacher walks into the Classroom and says If only Yesterday was Tomorrow Today would have been a Saturday Which Day did the Teacher make this Statement? Explain. Acidic. ________________is the period of development from document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Address: 9241 13th Ave SW [40] Although the base excision repair pathway was also activated, its activity was not sufficient to prevent the accumulation of 8-OHdG. Count the number of atoms of each element on each side of the equation and verify that all elements and electrons (if there are charges/ions) are balanced. Is a solution with OH- = 1.0 x 10-15 M acidic, basic, or neutral? Explain. THANKS! Salts of Weak Acids and Strong Bases. Why is the conjugate base of a strong acid weak? Explain. When aluminum nitrate dissolves in water, the aluminum ion reacts with water to give a hydrated aluminum ion, \(\ce{Al(H2O)6^3+}\), dissolved in bulk water. Completa las oraciones con la forma correcta del presente de subjuntivo de los verbos entre parntesis.? Is an aqueous solution with H+ = 3.1 x 10-6 M acidic, basic, or neutral? What happens to the charge of the overall base? Explain. pH of Solution. For a given strong acid #HA#, is the concentration of #A^-# likely to be high or low at equilibrium? Is a solution with OH- = 9.00 x 10-8 M acidic, basic, or neutral? Is a solution with OH- = 0.00070 M acidic, basic, or neutral? The acetate ion behaves as a base in this reaction; hydroxide ions are a product. It ignites readily, burning with a smoky flame characteristic of aromatic compounds. OC6H5- 1. One of the most common antacids is calcium carbonate, CaCO3. Is an aqueous solution with H+ = 2.45 x 10-8 M acidic, basic, or neutral? Top. We see that HCO becomes HCO. . Answer (1 of 5): Is the salt C5H5NHBr acidic, basic, or neutral? An idealized equation is shown: The resulting diamine is the precursor to 4,4'-MDI and related diisocyanates. Calculate the ionization constant for each of the following acids or bases from the ionization constant of its conjugate base or conjugate acid: a. HTe (as a base) b. Use the Bronsted-lowry model to label the acid-base pairs in the following equation for the ionization of water: H_2O(L) + H_2O(L) to H_3O^+(Aq) + OH^-(Aq). Question = Is IF4-polar or nonpolar ? C6H5NH3+ Weak acid. What is the conjugate base of oxalic acid, #HO(O=)C-C(=O)OH#? Aniline is a weak base. Explain. Therefore, it's conjugate base wouldn't be C6H5NH2 2+, rather, it would be C6H5NH2 and would have a neutral charge. However, the ammonium ion, the conjugate acid of ammonia, reacts with water and increases the hydronium ion concentration: \[\ce{NH4+}(aq)+\ce{H2O}(l)\ce{H3O+}(aq)+\ce{NH3}(aq) \nonumber \]. Deltoid muscle _____ 2. We will not find a value of Ka for the ammonium ion in Table E1. There are a number of examples of acid-base chemistry in the culinary world. Water can act as an acid or base depending on the other reactant. If you add acid (even weak acetic acid) they fizz. Thats not exactly C6H5NH3+ dissociating but I dont understand how a positively charged thing can react with water. Is a solution with pOH = 3.34 acidic, basic, or neutral? Determine the acetic acid concentration in a solution with \(\ce{[CH3CO2- ]}=0.050\:M\) and [OH] = 2.5 106 M at equilibrium. The second column is blank. Like most volatile amines, it has the odor of rotten fish. Here, the conjugate base of CHOH is CHO. ), How to make a New Post (submit a question) and use Equation Editor (click for details), How to Subscribe to a Forum, Subscribe to a Topic, and Bookmark a Topic (click for details), Multimedia Attachments (click for details), Accuracy, Precision, Mole, Other Definitions, Bohr Frequency Condition, H-Atom , Atomic Spectroscopy, Heisenberg Indeterminacy (Uncertainty) Equation, Wave Functions and s-, p-, d-, f- Orbitals, Electron Configurations for Multi-Electron Atoms, Polarisability of Anions, The Polarizing Power of Cations, Interionic and Intermolecular Forces (Ion-Ion, Ion-Dipole, Dipole-Dipole, Dipole-Induced Dipole, Dispersion/Induced Dipole-Induced Dipole/London Forces, Hydrogen Bonding), *Liquid Structure (Viscosity, Surface Tension, Liquid Crystals, Ionic Liquids), *Molecular Orbital Theory (Bond Order, Diamagnetism, Paramagnetism), Coordination Compounds and their Biological Importance, Shape, Structure, Coordination Number, Ligands, *Molecular Orbital Theory Applied To Transition Metals, Properties & Structures of Inorganic & Organic Acids, Properties & Structures of Inorganic & Organic Bases, Acidity & Basicity Constants and The Conjugate Seesaw, Calculating pH or pOH for Strong & Weak Acids & Bases, Chem 14A Uploaded Files (Worksheets, etc. Is a solution with H+ = 1.0 x 10-7 acidic, basic, or neutral? (CH,)2NH" (as an acid) c. HASO4 (as a base) d. HOZ (as a base) e. CH_NH (as an acid) f. HSO3 (as a base) What is the conjugate base for #"H"_2"S"#? The constant of dissociation is calculated as K a = c ( C 6 H 5 N H 2) c ( H 3 O +) c ( C 6 H 5 N H 3 +). For example: 7*x^2. We frequently see the formula of this ion simply as Al3+(aq), without explicitly noting the six water molecules that are the closest ones to the aluminum ion and just describing the ion as being solvated in water (hydrated). Answer: B2 2-is a Diamagnetic What is Paramagnetic and Diamagnetic ? However, in this case, the hydrated aluminum ion is a weak acid (Figure \(\PageIndex{2}\)) and donates a proton to a water molecule. Let us first write the equation of dissociation C 6 H 5 N H 3 + ( a q) + H 2 O ( l) C 6 H 5 N H 2 ( a q) + H 3 O + ( a q). Explain. In the following acid-base reaction, how would you identify the acid, base, and their conjugate acids and bases: NH4+ + HCO3- --> NH3 + H2CO3? Calculate the pH of a solution of 0.157 M pyridine. A force has the dependence Fx(x)=kx4F_x(x)=-k x^4Fx(x)=kx4 on the displacement xxx, where the constant k=20.3N/m4k=20.3 \mathrm{~N} / \mathrm{m}^4k=20.3N/m4. According to the equations below, what is the conjugate base of #HCO_3^-# ? NaHCO3 is a base. The constants for the different stages of ionization are not known for many metal ions, so we cannot calculate the extent of their ionization. Example \(\PageIndex{1}\): pH of a Solution of a Salt of a Weak Base and a Strong Acid, Example \(\PageIndex{2}\): Equilibrium of a Salt of a Weak Acid and a Strong Base, Equilibrium in a Solution of a Salt of a Weak Acid and a Weak Base, Example \(\PageIndex{3}\): Determining the Acidic or Basic Nature of Salts, Example \(\PageIndex{4}\): Hydrolysis of [Al(H2O)6]3+, status page at https://status.libretexts.org, Predict whether a salt solution will be acidic, basic, or neutral, Calculate the concentrations of the various species in a salt solution, Describe the process that causes solutions of certain metal ions to be acidic, A strong acid and a strong base, such as HCl(. Does this mean addressing to a crowd? Work Plz. Who were the models in Van Halen's finish what you started video? What is the conjugate base of #"bisulfite ion"#, #HSO_3^(-)#? [40] Rats exposed to aniline in drinking water, showed a significant increase in oxidative DNA damage to the spleen, detected as a 2.8-fold increase in 8-hydroxy-2-deoxyguanosine (8-OHdG) in their DNA. The nitrogen is described as having high p character. to the empployees was very informative. These polymers exhibit rich redox and acid-base properties. Determine whether a 0.0100 M C6H5NH3F solution is acidic, basic, or neutral. As we noted previously, acids and bases react chemically with each other to form. Possibilities: Conjugate Acid: C6H5NH3+ | Conjugate Base: C6H5NH Conjugate Acid: C6H5NH3 | Conjugate Base: C6H5NH Conjugate Acid: C6H5N2 | Conjugate Base: C6H5NH2 Conjugate Acid . Question = Is C2Cl2polar or nonpolar ? What are the 4 major sources of law in Zimbabwe? Which of the following compounds should have the strongest conjugate acid? The vegetable, such as a cucumber, is placed in a sealed jar submerged in a brine solution. Is a solution with OH- = 5.3 x 10-12 M acidic, basic, or neutral? All other acids are weak acids and ionize to a much lesser amount. [24][25] In 1842, Nikolay Nikolaevich Zinin reduced nitrobenzene and obtained a base that he named benzidam. Re: 12.3 6th edition. ClO 4 -Perchlorate ion. Through these intermediates, the amine group can be converted to a hydroxyl (OH), nitrile (CN), or halide group (X, where X is a halogen) via Sandmeyer reactions. What is the conjugate acid of C6H5NH2 What formula do you use to calculate pH when given the molarity of an acid? Is a solution with OH- = 1.99 x 10-7 M acidic, basic, or neutral? Relative to benzene, it is electron-rich. (Its conjugate base is the weak base aniline, C6H5NH2.) The first azo dye was aniline yellow. Your email address will not be published. [11], The amine in anilines is a slightly pyramidalized molecule, with hybridization of the nitrogen somewhere between sp3 and sp2. Ka, for the acid \(\ce{NH4+}\): \[\ce{\dfrac{[H3O+][NH3]}{[NH4+]}}=K_\ce{a} \nonumber \]. Suppose a solution has (H3O+) = 1 x 10-10 M and (OH-) = 1 x 10-4 M. Is the solution acidic, basic, or neutral? You'll get a detailed solution from a subject matter expert that helps you learn core concepts. In the equation -ClO 4 + HNO 3 HClO 4 + NO 3- the order, from left to right, for Brnsted-Lowry acids and bases is A. acid + base base + acid B. acid + base acid + base C. base + acid base + acid Expert Answer. Explain. This is the most complex of the four types of reactions. Adding Base to the Buffer. Business Studies. Strong acid. Being a standard reagent in laboratories, aniline is used for many niche reactions. 2.Find the volume of the solid obtained by rotating the region bounded by the curve y=e^x^2(that is ee with a power of x^2) and the x-axis, where 0x7, about the y-axis. Explain. What are the #"conjugate acids"# of #HO^-#, #HCO_3^(-)#, #HPO_4^(2-)#, and #CO_3^(2-)# ions? Explain. The reaction of converting primary aromatic amine into diazonium salt is called diazotisation. pH of Solution. 3. {/eq} solution is acidic, basic, or neutral. It is also dense, and can be stored for extended periods. Identify the following solution as acidic, basic, or neutral. Will Al(NO3)3 form a solution that is acidic, basic, or neutral? (a) KCN (b) CH_3COONH_4, How to classify solution either acidic, basic, or neutral? Is a solution with H3O+ = 4.21 x 10-6 M acidic, basic, or neutral? Explain. What is the conjugate base of #"phosphoric acid"#, #H_3PO_4#? So HCO is the conjugate acid of HCO. HNO3. How do you determine the formula for the conjugate base of #HSO_4^(-)#? A salt is a general chemical term for any ionic compound formed from an acid and a base. You can find the polarity of a compound by finding electronegativities (an atoms desire for an electron) of the atoms; Carbon has an electronegativity of 2.5, compared to Fluorines A) Enter the the Ksp expression for the solid AB2 in terms of the molar solubility x. F. F. Runge (1834) "Ueber einige Produkte der Steinkohlendestillation" (On some products of coal distillation), N. Zinin (1842). The early manufacture of aniline resulted in increased incidents of bladder cancer, but these effects are now attributed to naphthylamines, not anilines. This reduces the odor of the fish, and also adds a sour taste that we seem to enjoy. Hint: We will probably need to convert pOH to pH or find [H3O+] using [OH] in the final stages of this problem. Register Alias and Password (Only available to students enrolled in Dr. Lavelles classes. Explain. 4. acid: C6H5NH3+" base: H2O conjugate acid: H30+ conjugate base: C6H5NH2 Am I correct? How do you identify conjugate acid base pairs? Some salts formed in neutralization reactions may make the product solutions slightly acidic or slightly basic. Is a solution with H+ = 1.2 x 10-4 M acidic, basic, or neutral? The following four situations illustrate how solutions with various pH values can arise following a neutralization reaction using stoichiometrically equivalent quantities: Our stomachs contain a solution of roughly 0.03 M HCl, which helps us digest the food we eat. The acid can be titrated with a strong base such as NaOH. answer (1 of 5): no2 is an acidic oxide. conjugate base of c2h5oh. Anilinium Cation - C 6 H 5 NH 3 + Anilinium Ion C6H5NH3{+} Molar Mass C6H5NH3{+} Oxidation Number. What is \(\ce{[Al(H2O)5(OH)^2+]}\) in a 0.15-M solution of Al(NO3)3 that contains enough of the strong acid HNO3 to bring [H3O+] to 0.10 M? Is a solution with H+ = 2.7 x 10-9 M acidic, basic, or neutral? The brine solution favors the growth of beneficial bacteria and suppresses the growth of harmful bacteria. [16], Boiled with carbon disulfide, it gives sulfocarbanilide (diphenylthiourea) (CS(NHC6H5)2), which may be decomposed into phenyl isothiocyanate (C6H5CNS), and triphenyl guanidine (C6H5N=C(NHC6H5)2).[16]. Determine whether the following salt solution is acidic, basic, or neutral: Sr(ClO_4)_2. \(\ce{Al(H2O)6^3+}(aq)+\ce{H2O}(l)\ce{H3O+}(aq)+\ce{Al(H2O)5(OH)^2+}(aq) \hspace{20px} K_\ce{a}=1.410^{5}\). 3.Find the volume of the solid obtained by rotating the region bounded by y=8x^2, x=1, and y=0 . Aniline, a weak base, reacts with water according to the reaction. So OH is the conjugate base of HO. Aniline (from Portuguese anil 'indigo shrub', and -ine indicating a derived substance) is an organic compound with the formula C 6 H 5 NH 2.Consisting of a phenyl group (C 6 H 5) attached to an amino group (NH 2), aniline is the simplest aromatic amine.It is an industrially significant commodity chemical, as well as a versatile starting material for fine chemical synthesis. Kim Tran 1J Posts: 62 Joined: Fri Sep 28, 2018 7:24 am. Determine whether the following salt solution is acidic, basic, or neutral: NH_4I. Is a solution with H+ = 7.0 x 10-13 acidic, basic, or neutral? (c) During an acid-base reaction the lone pair on the base fills the A-H . Explain. Answer = if4+ isPolar What is polarand non-polar? [7], Aniline has been implicated as one possible cause of forest dieback. How many nieces and nephew luther vandross have? Why are weak acids and bases poor electrical conductors? Conjugate acids (cations) of strong bases are ineffective bases. NO2-, conjugate acid is a weak acid, therefore the salt is also potentially basic. Explain why different parts of the Earth have different climates. CH3NH3+ Weak acid (CH3)2NH2+ Weak acid (CH3)3NH+ Weak acid. Post by Kim Tran 1J Fri Dec 07, 2018 3:35 am . Thus, I-will lose H+ ions easier than Cl-, although both are strong acids. C6H5NH3+, conjugate base is a weak base, therefore it is potentially acidic NO2-, conjugate acid is a weak acid, therefore the salt is also potentially basic However, since the Ka > Kb, the solution must be acidic So it has both nature acidic on basic in its constituent, it will act as a neutral soul. The hydrogen oxalate ion is amphoteric. Is a solution with H+ = 1.0 x 10-3 M acidic, basic, or neutral? Industrial aniline production involves two steps. Is a solution with H3O+ = 0.000635 M acidic, basic, or neutral? Explain. Explain. Re: HW Question 11.3. For example, reaction of aniline with sulfuric acid at 180C produces sulfanilic acid, H2NC6H4SO3H. Calculate the pH a. before titration begins b. at E. P c. at the midpoint d. after 20 mL of NaOH e. after 30 mL of NaOH Answer true or false to the following statements about the mechanism of acid-base reactions. Salt of a Weak Base and a Strong Acid. Is an aqueous solution with H+ = 0.00014 M acidic, basic, or neutral? They often are prepared by nitration of the substituted aromatic compounds followed by reduction. [22] He called it Crystallin. The constituent ions that makes up an ionic (salt) compound may potentially have acidic/basic properties. Es ridculo que t ______ (tener) un resfriado en verano. Answer = C2H6O is Polar What is polarand non-polar? All rights reserved. fertilization to birth, whereas is the period of C6H5NH3+ + H2O > C6H5NH2 + H3O+. Sketch the region enclosed by y=27x and y=8x^4. As you may know, hydrogen ions (H +) are found in acids and hydoxide ions (OH -) are found in bases.. Arrhenius in the 1890's made the following discovery:.