As a result, the solution's freezing point is between 1.86 and 1.86 Celsius.
How is the freezing point determined?The molal freezing point depression constant KF and the solute's molality, m, are used to calculate the freezing point depression, which is given by T = KFm. Rearranging results in: Molecules of a solute are equal to (m) x (kg of solvent), where kg of solvent is the mass of lauric acid, the solvent in the mixture.
Can water at one degree Celsius freeze?The Process Of Water Freezing
When it approaches zero degrees, it begins to freeze. Ice crystals begin to develop from water molecules in the first stage. The size of the ice crystals increases in the second stage.
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The solution's freezing point is between 1.86 and 1.86°C.
How is the freezing point determined?The molal freezing point depression constant KF and the solute's molality, m, are used to calculate the freezing point depression, which is given by T = KFm. Rearranging results in: Molecules of a solute are equal to (m) x (kg of solvent), where kg of solvent is the mass of acid, the solvent in the mixture. This provides the solute's moles.
How is freezing point calculated?Assuming that there is no association or dissociation of the solute in solution.
ΔTb=kb×m
T′b−Tb=0.512×0.575
T′b−100=0.512×0.575
T′b=0.2944+100=100.2944
Boiling point of that solution will be 100.2944℃.
ΔT f=kf×m
T f−T′f=1.86×0.575
0−T′f=1.86×0.575
T′f=−1.0695
Freezing point of that solution will be -1.0695℃
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What happens if an element has 3 valence electrons?
Answer:
If an element has 3 valence electrons, it means that it can form chemical bonds with other atoms by sharing or transferring those 3 valence electrons. The resulting compound will have a chemical formula and properties that depend on the specific elements involved in the bonding and the arrangement of the atoms in the compound. Some elements with 3 valence electrons include boron (B), aluminum (Al), and phosphorus (P). These elements are commonly found in compounds such as borax (Na2B4O7), alum (KAl(SO4)2), and phosphoric acid (H3PO4), respectively.
What special equipment did aristotle use to develop and support his atomic model?
Answer: He thought that all materials on Earth were not made of atoms, but of the four elements, Earth, Fire, Water, and Air.
Explanation: Aristotle did not believe in the atomic theory and he taught so otherwise. He thought that all materials on Earth were not made of atoms, but of the four elements, Earth, Fire, Water, and Air. He believed all substances were made of small amounts of these four elements of matter.
When 50g of sugar is dissolved in 100g mL of water there is no increase in volume what characteristics is illustrated by this observation?
This observation illustrates the concept of a solution's solubility, which is the amount of solute that can be dissolved in a given amount of solvent at a certain temperature. In this case, the sugar is said to be highly soluble in water, as it was able to dissolve completely in the given volume.
What is solubility?Solubility is the property of a substance to dissolve in a solvent to form a homogeneous solution. It is a measure of the maximum amount of solute that can be dissolved in a given amount of solvent at a given temperature and pressure. Solubility is an important factor in many areas of science, including chemistry, pharmacy and environmental science.
This observation also shows that the sugar does not take up any additional volume when dissolved, as its molecules are small enough to disperse evenly throughout the solvent.
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The table indicates that nitrogen and oxygen are the main components of the atmosphere by volume. Together these two gases make up approximately 99% of the dry atmosphere. Why are these gases important?.
Answer:
Explanation:
Nitrogen and oxygen are important components of the atmosphere because they are essential for life on Earth.
Nitrogen makes up about 78% of the Earth's atmosphere by volume, and it is an important component of proteins, nucleic acids, and other biomolecules. It is also a vital component of the Earth's nitrogen cycle, which is the process by which nitrogen is converted into various forms and transported through the environment.
Oxygen makes up about 21% of the Earth's atmosphere by volume, and it is essential for respiration and the production of energy in living organisms. It is also a key component of the Earth's carbon cycle, which is the process by which carbon is exchanged between living organisms, the atmosphere, and the Earth's surface.
Together, nitrogen and oxygen play important roles in the functioning of the Earth's ecosystems and the support of life on the planet.
Which of the components of the box model is transparent and does not take a background color?.
The components of the box model is transparent and does not take a background color is Margin
Whatever color is allocated to the container that the elements are in will be used as the margin color. Therefore, simply set the parent element's color as needed.
It requires a background color because the margin is completely transparent and lacks a background color. It is made clear what area the piece is in.
It is the area surrounding a component. On a page, margins can be used to move an element left, right, up, and down.
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What i the difference between expanion and contraction? Chapter - Mattter
Cla - 6
Expansion is the process of an object increasing its size or volume, while contraction is the process of an object decreasing its size or volume. Both expansion and contraction occur in response to a change in temperature.
When an object is heated, it expands as the molecules within it begin to move faster. This increases the distance between the molecules, causing the object to increase in size and volume. Conversely, when an object is cooled, the molecules within it slow down, and the distance between them decreases. This causes the object to contract and decrease in size and volume.
Expansion and contraction are both physical properties of matter. Expansion and contraction occur in all states of matter, including solids, liquids, and gases. Expansion and contraction can also occur in non-matter objects, such as air and water.
Expansion and contraction have practical applications in everyday life. For instance, in construction, expansion and contraction are taken into account when designing bridges and other structures. The expansion and contraction of metal, concrete, and other materials due to changes in temperature must be taken into account in order to prevent structural failure.
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How do you know if sanitizer is too strong or too weak?
If sanitizer is added to the water, it won't be enough to adequately eliminate the microorganisms that cause foodborne disease. If there is an excessive amount of sanitizer added to the water, it may dry on dining tables and kitchen countertops.
How should one go about figuring out whether a sanitizer is too strong or too weak?Using test strips, verify that the sanitizer is neither either too strong or too weak. The sanitising combination should only receive the precise amount of water.
How can you tell if the concentration of the cleaning solution is correct?Over time, a chlorine bleach sanitising solution starts to lose part of its effectiveness. The sanitising solution must therefore be evaluated using test strips.
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What are the 4 main sectors that contribute to carbon emissions?
The four main sectors that contribute to carbon emissions are Energy, Industrial Processes, Agriculture, and waste.
Energy: This sector includes the production, distribution, and use of energy from fossil fuels such as coal, oil, and natural gas.Industrial processes: This sector includes the production of goods such as cement, steel, and chemicals, which emit GHGs during the manufacturing process.Agriculture, forestry, and other land use: This sector includes activities such as the cultivation of crops, raising livestock, and the clearing of forests, which can emit GHGs due to the decomposition of organic matter.Waste: This sector includes the collection, treatment, and disposal of waste, which can emit GHGs due to the decomposition of organic matter in landfills.These four sectors are responsible for the majority of GHG emissions globally. Reducing emissions in these sectors is essential for mitigating climate change and achieving net-zero emissions. This can be done through a variety of measures, such as increasing energy efficiency, transitioning to renewable energy sources, adopting more sustainable land use practices, and reducing waste.
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What is the freezing point in degrees Celsius of a 1.33 molal solution of C 6 H 14 in benzene? The boiling point of benzene is 80.1 degrees Celsius and the boiling point elevation constant for benzene is 2.65 degrees Celsius per molal. Give your answer to the thousandths place.
The freezing point of pure benzene is 5.48 °C. The depression in freezing point is calculated to be 6.80. Thus, the freezing point of the 1.33 molal solution is -1.32 °C.
What is freezing point ?Freezing point of a substance is the temperature at which its liquid state converts to its solid state where, the solid phase and liquid phase are in equilibrium.
The addition of a non - volatile solute to the solvent decreases the freezing point of the solution from that of the pure solvent. This decrease is a colligative property.
The depression in freezing point ΔTf = kf m
kf or depression constant of benzene = 5.12 °C /molal
freezing point of pure benzene = 5.48 °C
ΔTf = 5.12 °C /molal × 1.33 = 6.80
Therefore, the freezing point of the 1.33 molal solution is :
T (soln) = 5.48 - 6.80 = -1.32 °C
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for n2 at 298 k, what fraction of molecules has a speed between 200 and 300 m/s?
For N2 at 298 K, 0.071 fraction of molecules has a speed between 200 and 300 m/s.
Molecular speed is defined as the speed of a group of molecules in an ideal gas. The concept of molecular speed is critical in gas kinetic theory. According to the kinetic theory of gases, the molecules of a gas are constantly moving and follow a straight route until they collide with another molecule.
The speed of molecules in a gas is proportional to temperature and inversely proportional to the molar mass of the gas. In other words, when the temperature of a gas sample rises, the molecules accelerate, and so does the root mean square molecular speed. To determine a molecular speed, multiply three times the gas constant by the temperature, divide by the molar mass, and then square the result.
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What form of energy keeps your hands warm when you hold a glass of hot chocolate?
Your hands receive a heat transfer from the hot chocolate. Heat energy is exchanged between two objects when their temperatures differ. When the two items reach the same temperature, the cooler object becomes warmer.
How much energy is in hot chocolate?The vibrations of the hot chocolate's particles provide thermal energy. Some of this energy is transmitted from the chocolate to the milk's granules when you add cold milk to hot chocolate.
Your hands are getting warm from what kind of heat transfer?A fire emits thermal energy that warms a person's hands. One of the three ways that thermal energy can be delivered is by thermal radiation. Convection and conduction are the other two methods, both of which require matter to transfer energy.
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Is Gibbs free energy 0 for elements?
Yes, for pure elements the Gibb's free energy is equivalent to 0.
The Gibbs free energy is a concept in chemistry specially of thermodynamics. The maximum amount of work that can be accomplished at a constant temperature and pressure by a closed system can be calculated using the Gibbs free energy (also known as Gibbs energy; symbol: denoted as delta G). Additionally, it offers a prerequisite for any processes like chemical reactions that might take place in such circumstances.
When a system achieves equilibrium without being pushed by an input electrolytic voltage, the Gibbs energy is the thermodynamic potential that is reduced. At the equilibrium point, its derivative w.r.t. the system's reaction coordinate vanishes.
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Classify the following as intensive or extensive properties of zinc. Drag the appropriate items to their respective bins. View Available Hint(s) Reset Help bluish gray in color has a mass of 63.74 g begins to melt at 419.58 degrees Celsius has a volume of 8.94 mL has a density of 7.13 g/mL Intensive Extensive Submit Part B You are given a sample resembling zinc. Which of the following properties could be used to help determine whether the sample is really zinc? Check all that apply. View Available Hint(s) the melting point of the sample the volume of the sample the density of the sample Submit
(A): Bluish-gray in color, (C): begins to melt at 419.58 degrees Celsius,and (E): has a density of 7.13 g/mL are classified as intensive properties of zinc; while (B): has a mass of 63.74 g, and (D): has a volume of 8.94 mL are characterized by extensive properties of zinc.
An intensive property is a property of matter that is dependent only on the type of matter in a certain sample and not on the quantity. Color, density, solubility, and temperature are examples of intensive properties. On the other hand, an extensive property refers to a property that depends on the quantity of matter in a sample. Volume and are examples of extensive properties.
Answer to the question number 2 is as follows:
(A): The melting point of the sample and (B): the density of the sample help to determine if a given sample is really zinc.
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Is 20% NaCl hypertonic?
20% NaCl is hypertonic.
What is hypertonic solution?
A hypertonic solution is any external solution that has a high solute content and a low water concentration compared to body fluids. In a hypertonic solution, water will often transfer from the body into the solution.
A solution that is hypertonic includes more solute particles (such as salts and other electrolytes) is frequently found in blood plasma and cells. Osmotic pressure of the interior of cell is equals to 0.9 % NaCl solution, which is called physiological saline.
Therefore, 20% NaCl is hypertonic.
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Why are the elements at the bottom of the periodic table?
Answer:
Electron configurations
Explanation:
answer
How many atoms of magnesium are in 1.00 g?
Answer:
2
Mg has a molar mass of 24.3 g/mol. Hence, the number of atoms of Mg in 1.00 g is 2.
2.47 x [tex]10^{22}[/tex] atoms are there in 1.00 g. In chemistry, atoms are the fundamental building blocks of matter.
Atoms are the fundamental constituents of matter and the smallest units of an element that nevertheless retain its chemical characteristics. As they come together to create molecules, which then give rise to more complex structures, atoms are the subject of research in chemistry. Protons, neutrons, and electrons are the three primary subatomic particles that make up an atom. Neutrons have no charge, protons have a positive charge, and electrons have a negative charge. The quantity of protons determines an element's atomic number and establishes its identity.
Number of moles of Mg = (1.00 g) / (24.305 g/mol)
= 0.0411 mol
Number of atoms = (0.0411 mol) x (6.022 x [tex]10^{23 }[/tex]atoms/mol)
= 2.47 x [tex]10^{22}[/tex] atoms
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Suggest one reason why Newlands placed hydrogen in the octave shown
Answer:
because H (hydrogen) is very reactive with other elements
Explanation:
calculate the amount of daughter isotope that has been produced after 1, 2, 3, and 4 half-lives. include 4 decimal places in your answers daughter present: 0.0000 unit (i.e., no daughter isotope is present) after 1 half-life: 0.5000 units
The amount of daughter isotope that has been produced after 1, 2, 3, and 4 half-lives is 0.9375.
remaining after 1 half life = 1.0000/2 = 0.5000
remaining after 2 half lives = 0.5000/2 = 0.2500
remaining after 3 half lives = 0.2500/2 = 0.1250
remaining after 4 half lives = 0.1250/2 = 0.0625
For parent isotope:
In each half life the amount of remaining parent isotope will be half of the remaining of previous half life.
Therefore,
Parent present = 1.0000
present after 1 half life = 0.0000+ (1.0000 - 0.5000)=0.5000
present after 2 half lives = 0.5000+ (0.5000 -0.2500) = 0.7500
present after 3 half lives = 0.7500+ (0.2500 -0.1250) = 0.8750
remaining after 4 half lives = 0.8750+ (0.1250 - 0.0625)=0.9375
For daughter isotope:
The amount of daughter isotopes will be found by adding the value by which the number of parent isotope is decreased by in the relevant half life to the available daughter isotopes.
Daughter isotopes initially present: 0.0000
Daughter isotope Parent isotope Daughter to
present remaining parent ratio
Starting state: 0.0000 1.0000 0.0000/1.0000 =0
After 1 half life: 0.5000 0.5000 0.5000/0.5000=1
After 2 half lives: 0.7500 0.2500 0.7500/0.2500=3
After 3 half lives: 0.8750 0.1250 0.8750/ 0.1250=7
After 4 half lives: 0.9375 0.0625 0.9375/0.0625=15
the amount of daughter isotope that has been produced after 1, 2, 3, and 4 half-lives is 0.9375.
and Ratio of the amount of daughter to the amount of parent isotope is 15.
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Diphenylmethanol Infrared Spectrum 1.005 1.000 0.995 0.990 Transmitance чалгү 0.985 0.980 0.975 3750 3500 3250 3000 2750 2500 2250 2000 1750 1500 1250 1000 750 Wavenumbers (cm-1)
Interpret the IR spectrum of Diphenylmethanol.
Absorption of free OH bonds occurs at about 3650 cm⁻¹ Since it is a free hydroxyl group, the frequency range is high. This result indicates that there are no hydrogen bonds.In the IR spectrum, we see that the peak is around 3100–3000 cm⁻¹, telling us that this range represents the range of aromatic CH molecules (sp 2 CH).In addition, we see a peak around 2900 cm⁻¹, which is the presence of the Sp 3 CH bond band.The aromatic part of the compound contains an asymmetric C=C bond with an IR absorption peak of about 1630 cm⁻¹The compound contains CO bonds, for a frequency this voltage is detected at about 1050 cm⁻¹.Diphenylmethanol is an organic compound with the formula (C₆H₅)₂CHOH. Also known as benzhydryl, it is a white solid and the parent member of the large class of diary alcohols.
Infrared (IR) spectroscopy is a method that observes the interaction of molecules with electromagnetic radiation in the wavelength region of 0.75 – 1,000 µm or at wave numbers of 13,000 – 10 cm⁻¹
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Classify the following species as aromatic, nonaromatic, or antiaromatic: Sort these molecular species into the proper categories Reset Help CH2 :N ёнг 9 Nonaromatic Aromatic Antiaromatic
The classification of the following species as aromatic, nonaromatic, or antiaromatic is attached.
Aromatic refers to a class of chemical compounds that have a cyclic rotation of (4n+2) electrons. These chemicals are significantly more stable than other compounds in their class. Where, n = 0,1,2,3.......
Anti-aromatic compounds are those that have a cyclic rotation of 4n+ electrons in their electronic configuration. The stability of these compounds is significantly lower than that of typical compounds.
The term "nonaromatic" refers to any other kind of compound outside aromatic ones. The classification of the given compounds according to the nature of the aromatic ring is attached as a picture.
The proper question is attached.
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question content area what are its electron-pair and molecular geometries? what is the hybridization of the nitrogen atom? what orbitals on and overlap to form bonds between these elements? electron-pair geometry
Molecular geometry refers to how atoms are arranged within a molecule, typically in relation to a single center atom. Because the nitrogen is sp3 hybridized, it possesses four sp3 hybrid orbitals.
What are the definitions of the electron pair and molecule geometries?By taking into account both lone pairs and bond pairs, electron pair geometry can forecast the form of a molecule. By merely taking into account bond pairs, molecular geometry may predict the form of a molecule.
N2 sp2 hybridization is it possible?The nitrogen atom likewise hybridizes in the sp2 configuration, but unlike the carbon atom, it has a "lone pair" of remaining electrons that are not involved in the bonding. As a result, the geometry of nitrogen with three bonded ligands is trigonal pyramidal.
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what number of moles of o2 is needed to produce 14.2 grams of p4o10 from p? (molecular weight p4o10
0.25 moles of O2 is needed to produce 14.2 grams of P4O10 from P.
In order to calculate the number of moles of O2 needed to produce 14.2 grams of P4O10 from P, we need to use the equation for the reaction:
P + 5O2 → P4O10
We can calculate the number of moles of O2 needed by using the molar mass of P4O10, which is 284 g/mol. First, we need to calculate the number of moles of P4O10 present in 14.2 grams:
14.2 g/ 284 g/mol
= 0.05 mol.
Now, we can use the mole ratio between P and O2 to calculate the number of moles of O2 needed. The mole ratio is 5:1, meaning that for every 5 moles of O2, 1 mole of P is needed. Therefore, to get 0.05 moles of P4O10 from P, we need 0.05 x 5 = 0.25 moles of O2.
In conclusion, 0.25 moles of O2 is needed to produce 14.2 grams of P4O10 from P.
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Write a balanced chemical equation for the formation of NaHSO4
Answer:
2 NaOH + H2SO4 -> Na2SO4 + 2 H2O
If you react H2SO4 with NaOH, then NaHSO4 is formed.
H2SO4+NaOH - NaHSO4+H2O
which of the statements below correctly describes an achiral molecule? group of answer choices the molecule might be a meso form. the molecule exhibits optical activity when it interacts with plane-polarized light. none of the above the molecule has a nonsuperimposable mirror image. the molecule has an enantiomer.
A description of an achiral molecule as having optical activity when it interacts with plane-polarized light is accurate.
Of the following, which one is an achiral molecule?A few of examples of achiral compounds are (meso)-2,3-dibromobutane and trans-1,2-dichloro-1,2-ethanediol.
Regarding a pair of enantiomers, which of the following propositions is true?They rotate the polarized light plane in the same direction and by the same amount, but in different directions. The polarized light plane is rotated in the same direction and by the same amounts. The melting point and boiling point are among the physical characteristics shared by a pair of enantiomers. Meso compounds are numerous chiral centers in achiral molecules.
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What’s the correct sorting function to list Colors in alphabetical order (A to Z)? What value would be returned based on the formula in Cell A49? A B 29 Color Number 30 Red 100 31 Orange 112 32 Yellow 90 33 Green 85 34 Blue 120 Image not displaying? ASCENDING DESCENDING EQUAL TO A TO Z А 43 npab 44 npce 45 npfo 46 npbb 47 norp 48 49 =COUNTIF(A43:A47,"NP*") Image not displaying? 0 1 O 2 03 04 05
The correct sorting function to list Colors in alphabetical order is Ascending.
The value would be returned based on the formula in Cell A49 is 4.
What is the function?A function is simply the code that one can use over and over again, rather than writing it out multiple times. In this case, it'll be illustrated in an ascending order.
Also, the formula: =COUNTIF(range;"*"). Range is defined cell range where you want to count the text in Excel and wildcard * is criteria for all text occurrences in the defined range.
The answer is 4, there were four instances of Np in the given range of five cells.
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Classify the following solvents as either protic or aprotic solvents.
The protic solvents include NH3, HCONH2, and (CH3)2CHOH.
The aprotic solvents include N(CH3)3, CH3NO2, and CH2Cl2.
An oxygen (O), nitrogen (N), or fluoride atom is bonded to a hydrogen atom in a protic solvent (F). Protic solvents are generally any solvents that have a labile H+.
(CH3) (CH3) Because one of the hydrogens in 2CHOH is linked to oxygen, it is a protic solvent (O)
CH3NO2 is an aprotic (i.e not a protic solvent) solvent because all the hydrogens are bound to carbon.
CH2Cl2 is an aprotic solvent because all the hydrogens are bound tocarbon.
NH3 is a protic solvent because all the hydrogens are bound to Nitrogen (N)
N(CH3)3 is an aprotic solvent because all the hydrogens are bound to carbon
HCONH2 is a protic solvent because two of the hydrogens are bound to Nitrogen (N)
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complete question:
Classify each solvent as protic or aprotic. a. (CH3)2CHOH c. CH2Cl2 e. N(CH3)3 b. CH3NO2 d. NH3 f. HCONH2
draw a stepwise mechanism for the following reaction
In the reaction described, the OH group accepts the proton of sulfuric acid. Consequently, one water molecule is eliminated,ans further the process was done to get the desired result.
After the elimination, a secondary carbocation is produced. This carbocation then goes through a 1, 2-hydrogen shift to produce a more stable tertiary carbocation. A cyclic molecule is produced as a result of the alkene's addition of electrons to the tertiary carbocation.
Carbonation is the addition of carbon dioxide gas to a beverage to give it sparkle and a tangy flavor while also preventing spoilage. Under pressure, the liquid is chilled and cascaded down in an enclosure containing carbon dioxide (either as dry ice or as a liquid). Gas absorption is maximized by increasing pressure and decreasing temperature. Pasteurization is not required for carbonated beverages.
Below is a diagram of the mechanism:
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What would happen if there was no H+ gradient created in the mitochondrial membrane?
If protons (H+) were able to freely move across the mitochondrial membrane, cellular respiration will not occur.
Mitochondria are encased in a double-membrane system made up of inner and outer mitochondrial membranes separated by an intermembranous space. The inner membrane has numerous folds (cristae) that extend into the organelle's interior. In the critical process of oxidative phosphorylation, the electrochemical proton gradient across the inner mitochondrial membrane drives ATP synthesis. This is made possible by the previously mentioned membrane-bound enzyme ATP synthase.
The electron transport chain creates a proton gradient across the inner mitochondrial membrane, causing chemiosmosis to drive ATP synthesis. The proton gradient across the cristae membrane is produced by three large membrane protein complexes of the respiratory chain in the cristae, known as complexes I (NADH/ubiquinone oxidoreductase), III (cytochrome c reductase), and IV (cytochrome c reductase) (cytochrome c oxidase).
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Draw the Lewis structure of CHO, that obeys the octet rule. (Assign lone pairs, radical electrons, and alorric charges where appropriate.) Marvin JS Help C. :O: Edit drawing Calculate the electrons required (ER), valence electrons (VE), shared pairs (SP), and lone pairs (LP). ER 26 VE 18 SP 4 LP 5
The Lewis structure of CHO, which obeys the octet rule is attached as a picture. electrons required (ER) = 26, valence electrons (VE) = 18, shared pairs (SP) = 4, and lone pairs (LP) = 5.
The total number of valence electrons in the molecule, which is present in each individual atom, is represented by that atom.
The valence electrons in the CHO- = 4 + 6 + 1 + 1 = 12.
Since C, O, and H are group IVA, VIA, and IA elements, their valence electrons are 4, 6, and 1, respectively. For every negative charge, an additional electron is added.
Electrons required (ER) = 26
Valence electrons (VE) = 18
Shared pairs (SP) = 2 + 2 + 4 =8 (means 4 shared pairs)
Lone pairs (LP) = 3 + 2 = 5
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Suppose you had four spoons, the same size and shape, made out of glass plastic steal and wood which spoon handle would get hot the quickest when the spoons are placed in a pan of hot water.
Steel spoons heat up the fastest of all other spoons. This is because steel is primarily composed of metals with metallic properties such as heat conduction.
Why do metals conduct heat so quickly?The specific heat capacity of metals is small. H. Amount of heat required to raise 1 g of substance by 1°C.
This is how metals conduct heat very quickly. Delocalized electrons around the central nucleus play a very important role. Other properties derived from metallurgical bonding include ductility, malleability, and luster.
Therefore, of the four spoons of the same size and shape, the iron spoon heats up the fastest.
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