If you had placed 50mL of 0.1M HCl in a 150mL beaker,then the [H3O+] in the 50mL solution would be the same as the [H3O+] in the 25mL solution. Therefore, option 3 is correct.
What is the solution ?Any mixture of one or more solutes that have been dissolved in a solvent is referred to as a solution. To create a homogenous mixture, a solute must dissolve in a solvent. To create a homogenous mixture, a solute must dissolve in a solvent.
A homogenous mixture of two or more components with particles smaller than 1 nm is referred to as a solution. Solutions come in many forms, including soda water, salt and sugar solutions, and others. Every element in a solution appears as a single phase.
Thus, option 3 is correct.
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consider the structure of the amino acid aspartic acid. indicate the hybridization about each interior atom.
They are known as the s p 3 hybrid orbitals because they are made up of ones atomic orbital and three p atomic orbitals. Aspartic acid's structural formula is C4H7NO4, as shown in the image below:
The concept of hypothetical orbitals mixing to produce new orbitals with the same energy is referred to as hybridization. The orbitals are shown with hybrid orbitals. Only sigma bonding makes use of hybrid orbitals. Hybridization is the process of combining atomic orbitals to create new hybridized orbitals. These recently hybridized orbitals are known as hybrid orbitals. The total number of atomic orbitals fused will always equal the total number of hybrid orbitals. For example, one s atomic orbital and three p atomic orbitals may combine.
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as the term "peroxide" is used in chapter 10, it can refer to which structure(s)?
The RCOOCR structure can be referred to because the word "peroxide" is mentioned in Chapter 10. Carboxylic acid: A molecule with a carboxyl group (RCOOH; RCO2H).
Because of how easily the carboxyl group gives up a proton, carboxylic acids get their name (pKa usually in the range of 0-5). Structure of carboxylic acids in general. A carbon atom or group or a hydrogen atom is X. The carbonyl group (C=O) and Carboxylic group are what give the carboxyl (COOH) group its name. The acidity of the carboxylic acids is their primary chemical property. The major carrier was found to be carboxylic acids (RCOOH).
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imagine the reaction in model 1 starts with zero molecules of a and 100 molecules of b. will the concentration of substance b increase or decrease as the reaction proceeds? explain.
Imagine the reaction in model 1 starts with zero molecules of a and 100 molecules of b is the concentration of b decreases .
The model 1 starts with zero molecules of a and 100 molecules of b. if we start with the zero molecules of a the concentration of b will decreases as it will turn to the reactant. The chemical reaction occurs when the two or substance reactant to form a new product. so the reaction is given as :
A ⇄ B
so, if in the reaction it start with the molecules of a and the b is 100 molecules than the concentration of b decreases as the b turns in to the reactant.
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pressure has little effect on the solubility of liquids and solids because they are almost incompressible. This state of True Or False
- True
- False
Pressure has little effect on the solubility of liquids and solids because they are almost incompressible. This statement is True. Solid solubility hardly gets affected by changes in pressure.
A substance's physical and chemical characteristics affect how soluble it is. A few other factors and circumstances can also influence it. A few of them are: temperature, pressure, type of binding, and forces between the particles.
Pressure has a significantly greater impact on gases than it does on solids and liquids. The likelihood of a gas's solubility also increases as its partial pressure rises. One instance of how CO2 is stored under high pressure is in a soda bottle.
In like, like dissolves.
Each molecule has a unique set of intermolecular forces and connections. The likelihood of solubility between two dissimilar compounds is less likely than that between like substances. For instance, ethanol is highly soluble in water, a polar solvent, whereas water is not.
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predict whether, to any significant extent, ag(s) will react with 1 m hcl(aq).
Under normal conditions, Ag does not react with hydrochloric acid. However, if the HCl is concentrated and heated, it can dissolve silver to form silver chloride.
To determine whether Ag(s) will react with 1 M HCl(aq), we can consult a table of standard reduction potentials to see if the reaction is thermodynamically favorable. If the standard reduction potential for the reaction Ag(s) + [tex]H^+[/tex] (aq) -> [tex]Ag^+[/tex] + H(aq) is positive, then the reaction is not thermodynamically favorable and will not occur to a significant extent. If the standard reduction potential for the reaction is negative, then the reaction is thermodynamically favorable and will likely occur to a significant extent.
Alternatively, you can also perform a simple experiment to see if the reaction occurs. Simply mix a sample of Ag(s) with 1 M HCl(aq) and observe if any reaction occurs. If the solution becomes cloudy or if the silver metal appears to dissolve or change color, then a reaction has occurred.
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calculate the depth below the surface of water at which the pressure due to the weight of water equals 2 atm?
The depth below the surface of water at which the pressure due to the weight of water equals 2 atm is 10.2m.
Calculation:-
Entering the known values into the expression for h gives
h = 1.01 × 105N/m2(2.00×103kg/m3)(9.80m/s2) = 10.2m.
Force normal to the surface of an object per unit area over which that force is distributed. At a point in the gas, pressure acts in all directions. At the surface of a gas, compressive forces act perpendicular to the surface. If the gas is moving as a whole, the measured pressure will be different in the direction of movement.
Pressure is defined as the physical force exerted on an object. The force applied is normal to the surface of the object per unit area. The basic formula for pressure. The unit of pressure is Pascal. Pressure types include absolute, atmospheric, differential, and gauge. Pressure is a measure of the force exerted on a surface per unit area.
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which of the following is true for the solubility of nacl(s) and ch4(g) in water?
Sodium chloride will be soluble in water because it is polar molecule.
A polar molecule was one who has a slight positive charge on one end and a slight negative charge on the other. A polar molecule would be a diatomic compound, such as HF, that contains a polar covalent link.
We refer to something as being polar when it differs at either end. Some molecules also contain positive as well as negative ends; these are known as polar molecules. If not, we refer to them as non-polar. Polar objects can both attract and repel one another.
Pyramidal and V-shaped molecules were typically considered to be polar. Linear molecules, on the other hand, are thought to be non-polar through nature. Because the oxygen and hydrogen atoms have different electronegativities, water would be considered to be a polar molecule.
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you have 100 grams of rubidium bromide (rbbr). how many moles do you have? responses 0.61 mol 0.61 mol 1.00 mol 1.00 mol 1.22 mol 1.22 mol 2.00 mol
If you have 100 grams of rubidium bromide (rbbr) then no of moles you have is 0.61 mol.
What in chemistry is an A mole?The International Unit System uses the mole (symbol: mol) as the unit of material quantity. How so many basic entities of a particular substance are present in an item or sample is determined by the quantity of that material. One molecule or atom possesses the same weight in grams as one mole of the substance does in units of atomic mass.
Briefing:as we know that
165.3718 g Rubidium Bromide = 1 mol
according to the question-
100 g of Rubidium Bromide = (1/165.3718 ) x 100
= 0.61 mol
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Occaionally, you will ee a few white flower on a plant that normally ha purple flower. Explain what caue flower color and how ome white flower could appear on a purple-flowered plant
You will see a few white flowers on a plant that normally has purple flowers due to mutations.
Flower color is determined by pigments in the flower petals. The pigments responsible for the purple flower color are anthocyanins. A mutation in the genetic code responsible for producing anthocyanins could cause some of the petals to be white.
If this mutation is inheritable, then it could be passed down to future generations, resulting in some white flowers appearing on a plant that normally has purple flowers.
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not all of the orbitals in the n = 4 shell are shown in this figure.which subshells are missing?
The 4d and 4f subshells of the orbitals are not shown in the figure when n=4.
Subshell energies are determined by examining orbital diagrams showing how the subshells are arranged. The 1s orbital has the lowest energy, the 2s orbital has slightly higher energy than her 1s orbital, and so on. Electrons in orbits farther from the nucleus have higher energies.
The closer the orbitals, the greater the nuclear charge experienced by the electrons in them. 4d experiences a larger nuclear charge than 4f because 4d is closer to the nucleus.
Inside the subshell are orbitals. The s subshell contains 1 orbital, the p subshell contains 3 orbitals, the d subshell has 5 orbitals, and the f subshell has 7 orbitals. Every orbital can hold up to 2 electrons.
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2. The illustration here shows rock layers in their original order, along with a fracture in some rock
layers caused by an earthquake. Based on the evidence in the illustration, an earthquake occurred -
Caused by earthquake
A before layer W was deposited.
B. before layer X was deposited.
C. after layer Y was deposited.
D. after layer Z was deposited.
Rock Layer Z
Rock Layer Y
Rock Layer X
Rock Layer W
Rock Layer V
after the limestone's placement. demonstrates the sequence of the rock layers as well as parts of the layers' fractured due to an earthquake. According to the evidence in the graphic, there was an earthquake.
Explain what an earthquake is:
An earthquake is a quick movement of geological materials beneath the earth's surface that causes the ground to shake violently or weakly. The tectonic plate border is where the earthquakes start.
How is earthquake caused?
Although the tectonic plates are constantly moving slowly, friction causes them to become impermeable at their borders. An earthquake occurs when the stress on the edge exceeds the friction, releasing energy in waves that flow through the earth's crust and produce the shaking we experience.
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an element compound has 82 protons, 82 electrons, and 123 neutrons. write its isotopic symbol including both the mass number and the atomic number.
With an atomic number of 82, the chemical element lead has 82 protons and 82 electrons in its atomic structure. Lead has the chemical symbol Pb.
Lead's neutron number and mass number Lead's usual isotopes have masses between 204 and 208. Lead's (pb) atomic number is 82. The quantity of protons in an element's nucleus is indicated by the element's atomic number. Only lead displays no Thomson effect in a metal. In other words, neither heat is emitted nor absorbed when an electrical current is transmitted through a sample of lead. Lead has a molecular weight of 207. Natural bluish-gray metal called lead may be found in trace levels in the earth's crust. Every area of our is filled with lead environment.
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When does a metallic bond present
Answer:
Metallic bonds occur among metal atoms.
the basic units of matter, the smallest units that maintain the chemical properties of an element, are called a. atoms. b. lipids. c. compounds. d. molecules.
Why might Pacific Ocean be more conducive to volcanic activity?
Answer:
The movement of tectonic plates in the area, causes more volcanoes.
They call it the Pacific Ring of Fire
Answer:
The Pacific Ocean is more likely to experience volcanic activity because the Ring of Fire, an area in which several volcanos and earthquakes occur, is located within it.
What is the difference between the collision theory and the transition state theory? How do they explain the factors that affect the rate of a chemical reaction?
The basic differences between the collision theory and the transition state theory are-
Collision theory assumes a collision between reactants needs to happen before a reaction can take place. But on the other hand, during a reaction, an increase in potential energy corresponds to an energy barrier over which the reactant molecules must pass if the reaction is to proceed.The majority of collisions do not lead to a reaction, but only those in which the colliding species have: kinetic energy greater than a certain minimum called the activation energy, Ea, and the correct special orientation with respect to each other. Whereas the transition state occurs at the maximum of this energy barrier.Collision theory states that chemical reactions (in the gas phase) occur due to collisions between reactants. But transition state theory states that chemical reactions occur via going through a transition state.According to collision theory, chemical reactions occur only due to successful collisions. Although according to transition state theory, a chemical reaction will happen if and only if the reactants can overcome the activation energy barrier.The factors that affect the rate of a chemical reaction:
Temperature: With increasing temperature reaction rate will also increase.Concentration: In a solution, if the amount of reactants increases then the reaction rate increases.Pressure: Increasing pressure increases reaction rate.State of matter: Gases react more readily than liquids, whereas liquids react more readily than solids.Catalysts: A catalyst lowers the activation energy, then the reaction rate increases.Mixing: Mixing reactants improves reaction rate.To learn more about this topic,
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Help please as fast as possible. What is an example of mutualism between three organisms in the forest. thankyou
An example of mutualism is between the ants and the acacia plants in the forest.
What is mutualism?Mutualism can be described as the interaction between two or more species where each species has a net benefit. Mutualism is a general type of ecological interaction. Examples include vascular plants engaged with mycorrhizae in mutualistic interactions, flowering plants pollinated by animals, and corals with zooxanthellae, among many others.
Mutualism can be contrasted with competition, in which each species experiences decreased fitness, and exploitation, in which one species benefits at the expense of the other.
Mutualism can be described as conflated with two other kinds of ecological phenomena which are cooperation and symbiosis. Cooperation can be described as an increase in fitness through within-species interactions, although it has been used to refer to mutualistic interactions.
Symbiosis includes two species living in physical contact over a long period of their existence.
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if the ea for the forward reaction is 25 kj/mol and the enthalpy of reaction is -95 kj/mol, what is ea for the reverse reaction?
The Ea of the reverse reaction is 120 kJ/mol, that is calculated by using the enthalpy of reaction.
The Activation energy of a reverse reaction is the difference between the energy of the Activated complex and the energy of the products. The activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction.
Ea of the forward reaction is 25 kJ/mol.
The enthalpy of reaction is -95 kJ/mol.
No, the activation energy for a forward reaction is not equal to the activation energy for the reverse of the same reaction.
Ea = 95 + 25 = 120 KJ/mol
Therefore, the Ea of the reverse reaction is 120 kJ/mol.
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If the temperature of a fixed amount of an ideal gas is increased, it NECESSARILY follows that?
a. the pressure of the gas will increase.
b. the volume of the gas will increase.
c. the average kinetic energy will increase
d. All of the above statements are correct.
The volume of an ideal gas must obviously rise if the temperatures of a fixed sum of the gas is raised.
Explain what an ideal gas is.The phrase "ideal gas" describes a fictitious gas made up of molecules that adhere to the following principles: No attraction or repellence exists between the molecules of ideal gases. Only an unbalanced force upon impact would occur between molecules of a perfect gas.
What is the ideal gas worth?Because when pressure is expressed in kPa, the real gases characteristic is found to be 8.314J/Kmol. The pressure, area, temperature, & number of moles of an ideal gas are all related by a single equation known as the ideal gas law. Pressure, density, & temperature of a gas are related by the combined gas law.
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the overall efficiency of the formation of retinal from beta-carotene is estimated at approximately what percentage?
The total effectiveness of producing retinal from beta-carotene is thought to be around 50%.
The most significant provitamin A is beta carotene, a precursor to vitamin A (retinol). It splits into two molecules of retinal, one of which undergoes further metabolic processing to provide retinol and retinoic acid. Carotene has three isomers: beta, alpha, and gamma, with beta being the most active. There are two ways that carotenoids can be converted into retinal. In the central cleavage process, -carotene 15,15′-mono-oxygenase catalyzes the cleavage of -carotene to produce one molecule of retinal from other provitamin A carotenoids or two molecules of retinal from -carotene.
complete question:
The overall efficiency of the formation of retinal from beta-carotene is estimated at approximately what percentage?
a. 20% b. 35% c. 50% d. 65%
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What is the difference between theoretical yield and actual yield? How do you calculate the percent yield of a chemical reaction?
The difference between theoretical yield and actual yield is that theoretical yield is what is calculated while the actual yield is what you actually get in a chemical reaction.
What is actual and theoretical yield?Actual yield is the quantity of a product that is obtained from a chemical reaction while the calculated or theoretical yield is the amount of product that could be obtained from a reaction if all of the reactant converts to product.
This depicts that theoretical yield is based on the limiting reactant. The relationship between actual yield and theoretical yield is used to calculate percent yield:
Percent yield = (actual yield ÷ theoretical yield) x 100%
The difference between actual yield and theoretical yield is illustrated above.
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a copper, cu(s) , electrode is immersed in a solution that is 1.00 m in ammonia, nh3 , and 1.00 m in tetraamminecopper(ii), [cu(nh3)4]2 . if a standard hydrogen electrode is used as the cathode, the cell potential, ecell , is found to be 0.057 v at 298 k . part a based on the cell potential, what is the concentration of cu2 in this solution?
A copper electrode is immersed in the solution that is 1 M in the ammonia and 1.00 M in tetrammine copper(ii). the concentration of the Cu²⁺ in the solution is 3.3 × 10¹¹ M.
given that :
concentration of ammonia = 1 M
concentration of the tetramine copper = 1 M
cell potential = 0.057 V
temperature = 298 K
the reaction
at cathode :
Cu²⁺ + 2e⁻ ----> Cu E° cathode = 0.337 V
at anode :
2H⁺ + 2e⁻ ---> H₂ E° anode = 0.00 V
electrode potential = E° cathode - E° anode
= 0.337 - 0.00
= 0.0337 V
Nernst equation :
E cell = E° cell - (0.0591 / n ) log Q
0.055 V = 0.337 V - ( o.0591 / 2 ) log Q
log Q = 0.282 / 0.029
Q = 2.95 × 10⁻¹⁰
concentration of Cu²⁺ = 1 / Q
= 1 / 2.95 × 10⁻¹⁰
= 3.3 × 10¹¹ M
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Question 1 of 10
What information does a reaction rate give?
A. It indicates the concentrations of products formed.
B. It indicates the equilibrium position of the reaction.
O
C. It indicates if products or reactants are preferred.
D. It indicates how fast reactants become products.
The rate of reaction is the rate at which the reactants disappear or the rate at which the products appear. Option D.
What is the rate of reaction?The rate of a chemical reaction can be defined in a variety of ways. Some of them are:
It is the rate of disappearance of reactantsIt is the rate of appearance of productsIt is an indication of how fast reactants become products.Before the beginning of a reaction, only reactants are present in reaction vessels. Once the reaction starts, the reactants start reacting to form products. Thus, the rate of reaction is the rate at which the reactants are being converted into products.
This can be measured by either of or a combination of the rate of disappearance of the reactants or the rate of appearance of the products.
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compute repeat unit molecular weights for the following: (a) poly(vinyl chloride), (b) poly(ethylene terephthalate), (c) polycarbonate, and (d) polydimethylsiloxane.
Repeat unit molecular weights for the poly(ethylene terephthalate, polyvinyl chloride, polycarbonate, and polydimethylsiloxane are 62.494 g/mol, 192.164 g/mol, and 74.158 g/mol, respectively.
The mass of a molecule is its molecular weight. Gram/mole is a fundamental unit. It is the result of adding the atomic weights and atom counts of all the molecules' constituent elements.
Basic formulas for calculating molecular weight include:
Some of the most well-known elements' atomic masses are as follows:
Atomic Weight (g/mole) = Element
C = 12.01 for carbon
H - Hydrogen = 1.008
O = 16.00 for oxygen.
CI = 35.45 for chlorine.
1.
Type the chemical formula for poly vinyl chloride in the following format: H Cl C C H
Polymer's monomer unit is
Calculate the poly vinyl chloride repeat unit molecular weight.
MW = 2 (C's atomic weight) + 3 (H's atomic weight) + 4 (Cl's atomic weight) = 2 (12.01) + 3 (1.008) + 35.45
=62.494 g/mol
For poly vinyl chloride, molecular weight is calculated as the sum of the atomic weight and the number of atoms. Monomer is the name for the polymer's repeating unit
2. Compose the polyethylene terephthalate chemical equation.
The polymer's monomer unit will
Determine the polyethylene terephthalate repeat unit molecular weight.
MW = 10 (C's atomic weight) + 8 (H's atomic weight) + 4 (Atomic weight of O
=10(12.01)+8(1.008)+4(16.00)
=192.164 g/mole
For polyethylene terephthalate, the atomic weight and number of atoms are multiplied to get the molecular weight.
Write the polycarbonate chemical equation
Determine the polycarbonate repeat unit molecular weight.
MW = 16 (C's atomic weight) + 14 (H's atomic weight) + 3 (Atomic weight of O)
=16(12.01)+14(1.008)+3(16)
=254.272 g/mole
For polycarbonate, molecular weight is calculated as the sum of the atomic weight and the number of atoms.
4. Compose the polydimethylsiloxane chemical equation.
The polymer's monomer unit is
Calculate the polydimethylsiloxane repeat unit molecular weight
MW = 2 (C's atomic weight) + 6 (H's atomic weight) + (Si's atomic weight) + (Atomic weight of O)
=2(12.01)+6(1.008)+28.09+16
=74.158 g/mol
For polydimethylsiloxane, molecular weight is calculated as the sum of the atomic weight and the number of atoms.
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the empirical formula for a compound containing 26.0 % n and 74.0 % o by mass is selected answer: a. n2o5 correct answer: a. n2o5
The empirical formula for a compound is N2O5, that can be calculated by considering the masses of elements.
The simplest whole number ratio of atoms present in a compound. The mass composition for both the elements is given which is as follows:
N = 26g and O = 74g
Now we will divide the above masses with respect to the Molecular mass of each element;
N = 26/14 = 1.857 moles and for O = 74/16 = 4.625 moles
Now as we have molar ratio of each species;
We will divide the mole ratio by smallest number and round off to nearest decimal;
1.857/4.625 ~ 2/5 (say divide by 0.9 approx.)
Which will give a composition of N2O5.
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What is the total dose required for a 140 lb patient if the amount required is 28 mg/kg bodyweight? Given: 1.00 kg = 2.20 lb. Group of answer choices 1.8 mg 11 mg 28 mg 1.8 g 8.6 g 26)How many O atoms are in the formula unit GaO(NO2)2?
The many O atoms are in the formula unit GaO(NO2)2 as the total dose required are 63.5 kg.
You get lb and mg/k*g need to know mg
63.5 kg^ * 28 mg/k * g = 1778 mg1.8g is the next answerWhenNeed to convert lb to kg: 140 lb^ * 1kg / 2.205 * lb = 63.5kg.The total dose required for a 140 lb patient if the amount required is 28 mg/kg bodyweight is 63.5kg.
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A person runs 1 km. How does his speed affect the total energy needed to cover this distance?A. A faster speed requires less total energy.B. A faster speed requires more total energy.C. The total energy is about the same for a fast speed and a slow speed.
A person runs 1 km. Then his speed affects the total energy needed to cover this distance: A faster speed requires more total energy.
In everyday life, of course, you have seen vehicles running, fans spinning, and balls rolling. However, do you realize that we are actually witnessing a kinetic energy event firsthand.
What is kinetic energyUnderstanding kinetic energy Kinetic energy is the energy possessed by an object caused by the force of motion. The term kinetic comes from the Greek, 'kinetikos', which means to move. Therefore, an object moving at a certain speed must have kinetic energy, while an object that is not moving does not have kinetic energy.
Kinetic energy is also called motion energy, where the movement of an object can produce other energy. For example, motion energy can be turned into electrical energy, eventually that electrical energy can be utilized by humans.
Types of kinetic energyKinetic energy is divided into two types which are classified based on the movement of an object, namely:
Translational kinetic energyThis type of translation is kinetic energy produced by objects moving in a straight line with the same direction and speed. For example, a car driving on a highway and a bullet moving in a straight line.
Rotational kinetic energyThis is a condition when an object rotates. When rotating, the amount of energy in it can change. For example, the rotation of the earth around the sun, a spinning top that rotates on its axis, and a Ferris wheel.
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in a metallic substance, electrons are shared among all of the metal atoms in the sample. how does this explain why metals are more malleable and ductile than ionic and covalent compounds?
Answer:
In a metallic substance, electrons are shared among all of the metal atoms in the sample, forming a "sea" of electrons that surrounds the metal ions. This electron sea is responsible for many of the unique properties of metals, including their high conductivity, malleability, and ductility.
The electron sea in a metallic substance allows the metal ions to slide past one another easily, making it easier to deform the metal without breaking it. In contrast, ionic and covalent compounds are held together by strong chemical bonds, which makes it more difficult to deform these materials without breaking the bonds. This is why metals are generally more malleable and ductile than ionic and covalent compounds.
what is the leaving group when acetic anhydride is reacted with ethanol in a nucleophilic acyl substitution reaction?
BH3/THF with H2O2/NaOH is the leaving group when acetic anhydride is reacted with ethanol in a nucleophilic acyl substitution reaction
Corn and other plant resources are used to make ethanol, a sustainable fuel. In the United States, ethanol is widely used and is present in more than 98% of gasoline. E10 (10% ethanol, 90% gasoline) is the most widely used ethanol mix. The production of medicines, polymers, lacquers, polishes, plasticizers, and cosmetics all need ethanol. In medicine, ethanol is employed as a topical anti-infective and as an antidote for methanol or ethylene glycol overdose. More than two billion people consume ethanol (also known as ethyl alcohol) daily.
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what is a semiconductor whose electrical properties are dictated by the impurity atoms in the semiconductor?
Whose electrical properties are dictated by the impurity atoms in the semiconductor is extrinsic semiconductor.
Any member of the family of crystalline solids known as a semiconductor falls into the range of conductors and insulators in terms of electrical conductivity. Diodes, transistors, and integrated circuits are just a few of the electrical devices that use semiconductors in their production. Due to their portability, dependability, energy efficiency, and affordability, these gadgets are widely used. They have been utilized as discrete components in solid-state lasers, optical sensors, and power devices. They are capable of tolerating a wide range of current and voltage, and more importantly, they are well suited for integration into intricate but easily fabricated microelectronic circuits. They are and will continue to be the primary components of the vast majority of electronic systems, supporting applications in communications, signal processing, computation, and control.
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