how does changing the alkyl halide from ch3ch2br to (ch3)2chbr affect the rate of an e2 reaction? select the single best answer. rate increases no change rate fluctuates rate decreases

Answer:
The splitting is going to be larger for CO.

Explanation:

"The ligand field splitting in a coordination complex is determined by the strength of the interaction between the metal center and the ligands, which is affected by various factors, including the ligands' identity. CO ligands are stronger field ligands than H2O ligands, meaning that they interact more strongly with the metal center and cause a larger ligand field splitting. Therefore, if H2O ligands are replaced with CO ligands in this experiment, we would expect the ligand field splitting to be larger for CO."

Ammonia ionizes only partially in water. Option 4 is correct.

When ammonia dissolves in water, it reacts with water to form ammonium ions (NH₄⁺) and hydroxide ions (OH⁻), according to the equation: NH₃ + H₂O ⇌ NH₄⁺ + OH⁻. However, this reaction is reversible and only a small fraction of ammonia molecules ionize to form ions. As a result, ammonia is classified as a weak electrolyte, meaning that it only conducts electricity weakly in solution.

Weak electrolytes are characterized by their partial ionization in solution, and they have relatively low electrical conductivity compared to strong electrolytes, which ionize completely in solution. Hence Option 4 is correct.

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Explanation:

Moles in the 20 ml  

   .020 L   *   1.5  moles/L = .03 moles

now in 50 ml   (which is  .05 liters )

      .03 moles / .05 L   = .6 m

1) 5.1167 x 10²⁴atoms of chlorine. 2) 248.00 g. 3) 4.8825 x 10⁷ moles of helium. 4) 2.7757 x 10²⁴ atoms of sulfur.  5) Molar mass of Co (cobalt) is 58.93 g/mol.  6) Formula mass =  310.18 g/mol.

Sum of the atomic masses of all the atoms in chemical formula is called formula mass

1.)  Number of atoms = 8.500 moles x 6.022 x 10²³ atoms/mole = 5.1167 x 10²⁴ atoms of chlorine.

2.) Molar mass of oxygen is 16.00 g/mol. Therefore:

Mass of 15.50 moles of oxygen = 15.50 moles x 16.00 g/mol = 248.00 g.

3.) Molar mass of helium is 4.00 g/mol. Therefore, the number of moles of helium in 1.953 x 10⁸ g is:

Number of moles = 1.953 x 10⁸ g / 4.00 g/mol = 4.8825 x 10⁷ moles of helium.

4.) Molar mass of sulfur is 32.06 g/mol. Therefore, the number of moles of sulfur in 147.82 g is:

Number of moles = 147.82 g / 32.06 g/mol = 4.6084 moles of sulfur.

To find the number of atoms, we can use Avogadro's number again:

Number of atoms = 4.6084 moles x 6.022 x 10²³ atoms/mole = 2.7757 x 10²⁴ atoms of sulfur.

5.) Molar mass of Co (cobalt) is 58.93 g/mol.

6.) Ca₃(PO₄)₂ contains 3 calcium atoms, 2 phosphorus atoms, and 8 oxygen atoms.

Atomic masses of these elements are:

Calcium (Ca) = 40.08 g/mol

Phosphorus (P) = 30.97 g/mol

Oxygen (O) = 16.00 g/mol

Therefore, formula mass of Ca₃(PO₄)₂ is:

Formula mass = (3 x 40.08 g/mol) + (2 x 30.97 g/mol) + (8 x 16.00 g/mol)

= 120.24 g/mol + 61.94 g/mol + 128.00 g/mol

= 310.18 g/mol.

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A proflavine molecule absorbs one mole of blue light at 470 nm, which has an energy content of about 25.4 kJ.

A photon is a microscopic particle made up of electromagnetic radiation waves. Maxwell demonstrated that photons are merely electric fields moving through space. Photons move at the speed of light and have no charge or rest mass.

We can calculate by using the following formula:

E = hc/λ

E = energy of the photon

h = Planck's constant (6.626 × 10^-34 J·s)

c = speed of light (2.998 × 10^8 m/s)

λ = wavelength of the light

We have to multiply the energy per photon by Avogadro's number (6.022 × 10^23 photons/mol).

we have to convert the 470 nm to meters:

λ = 470 nm × (1 m/10^9 nm) = 4.70 × 10^-7 m

We calculate the energy per photon,

E = hc/λ

E = (6.626 × 10^-34 J·s) × (2.998 × 10^8 m/s) / (4.70 × 10^-7 m)

E = 4.21 × 10^-19 J

Now:

E = (4.21 × 10^-19 J/photon) × (6.022 × 10^23 photons/mol) / 1000 J/kJ = 25.4 kJ/mol

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The fraction of the cofactors in the NAD form would be:

[NADH]/([NADH] + [NAD+]) = 1/237.8 = 0.0042 or approximately 0.4%.

To determine the fraction of a population of cofactors that would be in the NAD form at a given pH and potential, the Nernst equation can be used. For the reduction reaction of NAD+ to NADH, the standard reduction potential (E°) is -0.32 V. At a pH of 7.0, the Nernst equation can be written as:

E = E° - (RT/nF)ln([NADH]/[NAD+]

Where:

E = potential of the half-reaction

R = gas constant

T = temperature in Kelvin

n = number of electrons transferred

F = Faraday constant

[NADH]/[NAD+] = ratio of reduced to oxidized forms of the cofactor

Substituting the given values, we get:

-300 mV = -0.32 V - (RT/2F)ln([NADH]/[NAD+])

Solving for ln([NADH]/[NAD+]), we get:

ln([NADH]/[NAD+]) = -(2F/RT)(-300 mV + 0.32 V)

ln([NADH]/[NAD+]) = 5.47

Taking the exponential of both sides, we get:

[[tex]NADH]/[NAD+] = e^(5.47) = 236.8[/tex]

Therefore, the fraction of the cofactors in the NAD form would be:

[NADH]/([NADH] + [NAD+]) = 1/237.8 = 0.0042 or approximately 0.4%.

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Answer:

condensation nuclei

Explanation:

The sour mash used to make distilled spirits is blank is the liquid fermented grain that is collected from the previous batch.

The Sour mash or we can say that the  sourmash is the process that is used in the industry of the distilling which uses the material from the older batch of the mash and to start the fermentation for the new batch, the analogous to the make of the sourdough bread with the starter.

Therefore, the liquid fermented grain that is collected from the previous batch is the sour mash used to make the distilled spirits is blank.

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Answer:

the answer is D. the molecules of a gas are small compared to the distance between them

Explanation:

The postulates of Kinetic-Molecular Theory are as follows:

The molecules of a gas move rapidly, constantly, and in straight lines.

The average kinetic energy of the molecules of a gas is directly proportional to the Kelvin temperature.

A gas exerts pressure because the gas molecules repel each other.

The molecules of a gas are small compared to the distance between them1.

Therefore, “the molecules of a gas are small compared to the distance between them” is not a postulate of Kinetic-Molecular Theory

E'a (also known as reverse activation energy) is the (Ea = +7 kJ/mol)  energy barrier for the reverse reaction, which is the energy difference between the products and the transition state in the reverse direction.

What is Energy?

Energy is a fundamental concept in physics and refers to the ability or capacity to do work or cause change. It is a scalar quantity, typically measured in joules (J) or other units such as kilocalories (kcal) or electron volts (eV).

In general, the activation energy (Ea) is the energy barrier that must be overcome for a chemical reaction to occur. It is the energy difference between the reactants and the transition state or activated complex of the reaction. The activation energy can be determined from the energy diagram by subtracting the energy of the reactants from the peak energy of the transition state.

∆Eforward = -36 kJ/mol

∆Ereverse = +48 kJ/mol

Ea = +7 kJ/mol

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Answer:

Their ability to act as a source of energy.

Explanation:

One characteristic of carbohydrates that are not commonly found in previously studied classes of compounds is their ability to act as a source of energy. Carbohydrates are considered the primary source of energy for living organisms and are broken down through cellular respiration to release energy for use in metabolic processes. In contrast, lipids, proteins, and nucleic acids have other primary functions in living organisms such as membrane structure, enzyme activity, and genetic information storage and expression.

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The base name for an ester with a propyl group attached to the carbonyl carbon atom is "propyl ester." In the context of a simulation, you would need to extend the left chain according to the given parameters within the simulation for the specific compound you are working with.

If we extend the left chain of an ester with a propyl group attached to the carbonyl carbon atom as far as the simulation allows, we would have the following structure:

CH3-(CH2)2-C(=O)-OR

Where R represents the rest of the ester molecule.The base name for an ester with a propyl group attached to the carbonyl carbon atom is propyl propanoate. This name is derived from the parent carboxylic acid, which is propanoic acid (also known as propionic acid), and the alcohol used to form the ester, which is propanol (also known as 1-propanol or n-propanol).The esterification reaction between propanoic acid and propanol yields propyl propanoate as the ester product, with the elimination of a molecule of water. The ester is commonly used as a flavor and fragrance ingredient in various food and cosmetic products.

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If the mass of H₂o is 102. 3g and the initial temp is 23. 1c and the final temp is 26. 0c . The final initial temp is 296.67 K or 23.52 °C.

The amount of heat required to raise the temperature of a substance by 1°C is known as specific heat capacity of that substance.

Given that,

The mass of water (H₂O ), m = 102.3 g.

The initial temperature is given by T₁ = 23.1°C = 296.1 K

The finial temperature is T₂= 26°C =299 K

Therefore, change in temperature,ΔT = T₂- T₁= 299k - 296.1k=2.9

The final initial temperature is given as

= mΔT

=102.3 ×2.9

=296.67 K

=23.52 °C

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The root mean square speed of F2 Gas molecules under the same conditions is approximately 582.19 m/s

Given: Average kinetic energy (E_k) = 6430 J/mol
Molar mass of F2 = 2 * Molar mass of F = 2 * 19 g/mol = 38 g/mol (since F has a molar mass of 19 g/mol)

First, let's convert the molar mass of F2 from grams to kilograms:
Molar mass of F2 = 38 g/mol * (1 kg/1000 g) = 0.038 kg/mol

Now, we can use the equation for the average kinetic energy to determine the root mean square speed (v_rms):

E_k = (3/2) * R * T = (1/2) * m * v_[tex]rms^{2}[/tex]

Where R is the universal gas constant (8.314 J/mol K) and T is the temperature in Kelvin.

Since we want to find v_rms, we can rearrange the equation as follows:

v_[tex]rms^{2}[/tex] = (2 * E_k) / m

Plugging in the given values:

v_[tex]rms^{2}[/tex] = (2 * 6430 J/mol) / 0.038 kg/mol = 338947.37[tex]m^{2}/ s^{2}[/tex]

Finally, we take the square root to find the root mean square speed: a

v_rms = √338947.37[tex]rms^{2}[/tex] = 582.19 m/s

So, the root mean square speed of F2 gas molecules under the same conditions is approximately 582.19 m/s.

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If you had 6 M acetic acid rather than glacial acetic acid in the first step of the Friedel-Crafts reaction, less product would likely have formed.

The Friedel-Crafts reaction requires a strong Lewis acid catalyst, such as aluminum chloride (AlCl3), which reacts with the acylating agent to form a reactive electrophile. In this case, the acylating agent is acetic anhydride, which reacts with AlCl3 to form an acylium ion that can then react with the aromatic ring. However, the reaction is sensitive to the amount of water present, and the presence of excess water (which would be more likely in the case of dilute acetic acid) can lead to hydrolysis of the acylium ion and a decrease in the yield of the desired product.

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Changes in the chemical environment of a basic buffer solution can cause shifts in the equilibrium between ammonia, hydroxide ion, and ammonium ion, leading to changes in their respective concentrations.

When a basic buffer solution of equal concentrations of ammonia and ammonium nitrate is subjected to changes in its chemical environment, the concentrations of ammonia, hydroxide ion, and ammonium ion will be affected as follows:

1) Addition of an acid: The acid reacts with the hydroxide ion present in the buffer solution to form water. This decreases the concentration of hydroxide ion and shifts the equilibrium towards the formation of more ammonia and ammonium ion, thus increasing their concentrations.

2)Addition of a base: The base reacts with the ammonium ion present in the buffer solution to form ammonia and water. This decreases the concentration of ammonium ion and shifts the equilibrium towards the formation of more hydroxide ion, thus increasing its concentration.

3)Dilution: Diluting the buffer solution with water decreases the concentrations of both ammonia and ammonium ion, but does not affect the concentration of hydroxide ion.

4)Addition of ammonium chloride: The ammonium chloride dissociates into ammonium ion and chloride ion in the buffer solution. The increase in ammonium ion concentration causes the equilibrium to shift towards the formation of more ammonia and hydroxide ion, thus increasing their concentrations.

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We separate porridge from cooked rice using a strainer or a sieve.

Porridge and cooked rice are both similar in texture and appearance, making it difficult to separate them. One way to do it is to use a strainer or a colander with small holes. Pour the mixture of porridge and rice into the strainer or colander and let the liquid portion drain out. You can also use a cheesecloth or a muslin cloth to squeeze out the liquid while retaining the rice grains.

Another method is to use a spoon to scoop out the rice from the top, leaving the porridge at the bottom. However, this method may not be as effective as the others. Regardless of the method you choose, it is important to be gentle and patient to avoid breaking the rice grains and mixing them with the porridge.

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The IUPAC name for the compound shown of a 6 carbon ring has two alcohol substituents on carbons 1 and 3 is cyclohexane-1,3-diol.

The compound shown is called cyclohexane-1,3-diol.

It has a place with the group of cyclic alcohols, which are compounds containing both a hydroxyl (- Goodness) bunch and a cyclic construction in their substance structure.

Cyclohexane-1,3-diol is named by the IUPAC classification framework, which relegates an exceptional and precise name to a given compound in view of its sub-atomic construction.

For this situation, the prefix "cyclo" shows the presence of a cycloalkane ring, explicitly a six-membered ring (cyclohexane). The addition "- diol" demonstrates that there are two hydroxyl (- Gracious) bunches connected to the ring, explicitly at positions 1 and 3.

Accordingly, cyclohexane-1,3-diol is the right IUPAC name for this compound.

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In changing the size of the zinc electrode would not impact the voltage of the cell.

If the size of the zinc electrode were doubled, the cell voltage would stay the same. This is because the voltage of a cell is dependent on the difference in potential between the two electrodes, not their size.

Doubling the size of the zinc electrode would not change the potential difference between the zinc and copper electrodes, therefore the cell voltage would remain constant.

The only factor that would affect the cell voltage would be a change in the concentration or temperature of the electrolyte solution or a change in the material or surface area of the copper electrode.

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You would need to pipette 2.6 mL of stock solution to make a 1:5 dilution with a final volume of 13 mL.

To calculate this, first note that a 1:5 dilution means that for every 1 unit of stock solution, you need to add 4 units of solvent to make a total of 5 units. This can be expressed as a ratio of stock solution to solvent as 1:4. To find the amount of stock solution needed, you can use the following equation:

Plugging in the given values, we get:

Solving for the volume of stock solution, we get:

Therefore, you would need to pipette 2.6 mL of stock solution to make a 1:5 dilution with a final volume of 13 mL.

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When lactic acid accumulates, the compensatory mechanism initially triggered to maintain acid-base balance is the respiratory system. It increases the rate and depth of breathing to eliminate more carbon dioxide, which helps reduce acidity and restore pH balance in the body.

As lactic acid accumulates, the compensatory mechanism that is initially triggered to maintain acid-base balance is increased ventilation or hyperventilation. This is because the increased ventilation leads to a decrease in carbon dioxide (CO2) levels in the blood, which helps to offset the acidic effects of lactic acid accumulation. This is a temporary compensatory mechanism, however, as the body will eventually need to eliminate the excess lactic acid through other means such as metabolism and excretion.

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The dipeptide structure with labels a through d represents the different functional groups and atoms present in the molecule.

Label a is located at the end of the molecule with the positively charged NH3 group, indicating the presence of an amino group. The b label is placed by the bond between the carbonyl group and the amine, indicating the presence of a peptide bond.

Label c is next to a carbon with shown single bonds to the carboxylate, a CH2OH, and the rest of the molecule, indicating the presence of a side chain. Finally, the d label is next to the carboxylate at the end of the molecule,

indicating the presence of a carboxylic acid functional group. Understanding the different functional groups and atoms present in the dipeptide structure is important in understanding its properties and behavior in chemical reactions and biological processes.

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The {H⁺} of the solution is 2.238 × 10^(-12) M.

pH is a measure of the acidity or basicity of an aqueous solution. It is defined as the negative logarithm (base 10) of the concentration of hydrogen ions ([H+]) in moles per liter. The pH scale ranges from 0 to 14, where a pH of 7 is neutral. Solutions with a pH less than 7 are acidic, while solutions with a pH greater than 7 are basic (also called alkaline).

The pH of a solution is defined as:

pH = -log[H⁺]

Rearranging the equation, we get:

[H⁺] = 10^(-pH)

Substituting the given value of pH, we get:

[H⁺] = 10^(-11.55)

[H⁺] = 2.238 × 10^(-12) M

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Molarity (M) is a unit of concentration that expresses the amount of solute dissolved in a solution. It is defined as the number of moles of solute present per liter of solution (mol/L).

Molarity is commonly used in chemistry to express the concentration of a solute in a solution and is typically represented as moles of solute per liter of solution (mol/L or mol L^-1). Molarity is used to describe the concentration of a solution and is important in various calculations involving chemical reactions and solutions.

To calculate molarity, follow these steps:
1. Determine the number of moles of solute in the solution.
2. Measure the volume of the solution in liters.
3. Divide the moles of solute by the volume of the solution in liters.

Molarity = moles of solute/liters of solution

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Molarity is a unit of concentration in chemistry. It is defined as the number of moles of solute per liter of solution. In other words, it measures the amount of substance (in moles) dissolved in a given volume of solution (in liters). the left column contains "molarity," "moles," and "liters," and the sentences.

To match the items in the left column to the appropriate blanks in the sentences on the right, we can use the following:
- Molarity: a unit of concentration in chemistry
- Number of moles: the amount of substance dissolved in a solution
- Liter of solution: the volume in which the substance is dissolved
- Solvent: the substance in which the solute is dissolved
- Solute: the substance that is dissolved in a solvent to make a solution

So the sentences could be:
- Molarity is a unit of concentration in chemistry that measures the amount of substance (in moles) dissolved in a given volume of solution (in liters).
- The number of moles of solute per liter of solution is known as molarity.
- A liter of solution is the volume in which the solute is dissolved to make a solution with a certain molarity.
- A solvent is a substance in which a solute is dissolved to make a solution of a certain molarity.
- A solute is a substance that is dissolved in a solvent to make a solution of a certain molarity.
Hello! Molarity is a measure of the concentration of a solute in a solution, expressed as moles of solute per liter of solution. To match items in the left column to the appropriate blanks in the sentences on the right, follow these steps:

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Answer:

data given

mass of NaCl 4.56

dissolved volume 20ml(0.02l)

density of solution 1.03g/ml

Required molality

Explanation:

molarity=m/mr×v

where

m is mass

mr molar mass

v is volume

now,

molarity=4.56/58.5×0.02

molarity =3.9

: .molarity is 3.9mol/dm^3

According to molal concentration, the concentration (in molality) of an aqueous solution of NaCl is 0.0047 mole/kg.

Molal concentration is defined as a measure by which concentration of chemical substances present in a solution are determined. It is defined in particular reference to solute concentration in a solution . Most commonly used unit for molal concentration is moles/kg.

The molal concentration depends on change in volume of the solution which is mainly due to thermal expansion. Molal concentration is calculated by the formula, molal concentration=mass/ molar mass ×1/mass of solvent in kg.

In terms of moles, it's formula is given as molal concentration= number of moles /mass of solvent in kg.

Substitution in formula gives the answer but first mass of solution is determined which  is density×volume= 1.03×20=20.6 g , mass of solvent= 20.6-4.56=16.05, thus molal concentration=4.56/58.5×1/16.05=0.0047 moles/kg.

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Both options (a) and (b) are evidence for a chemical reaction.

In option (a), the yellow flame is an indication that a chemical reaction has occurred between the sodium metal and water, producing hydrogen gas and sodium hydroxide.

In option (b), the gas bubbles produced indicate that a chemical reaction has occurred between the iron metal and the acid, producing hydrogen gas and iron(II) ions. Based on the given options, evidence for a chemical reaction can be observed in both (a) and (b).

In (a), dropping sodium metal into water produces a yellow flame, indicating a chemical reaction as new substances are formed. In (b), dropping iron metal into acid produces gas bubbles, which also signifies a chemical reaction as a new product, in this case gas, is generated.

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When building a bridge in South America, it is important to consider the climate and terrain of the region. The company should research the area and use the most appropriate materials for the task.

Materials are substances or resources that are used to create or make something else. Examples of materials include plastics, metals, fabrics, and paper. Materials are used in the manufacturing of products, such as food, clothing, furniture, and electronics. Materials can also be found in nature, including wood, stone, and minerals. They are also used in the construction of buildings, bridges, and other structures.

For example, they should use steel or reinforced concrete to build the bridge, as these materials are highly durable in wet, humid climates. Additionally, they should make sure to use corrosion-resistant fasteners and coatings to prevent rusting. The company should also consider the seismic activity in the region when designing the bridge, as earthquakes can cause significant structural damage. They should make sure to use seismic-resistant designs and materials, such as flexible joints, to help reduce the risk of damage. Lastly, the company should include guardrails and other safety features on the bridge, as it will be traversed by both pedestrians and vehicles.

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the overlap integral simplifies to:

S = c1c2 + d1d2d1d2.

To calculate the overlap integral between two linear combinations of atomic orbitals on a carbon atom in ethene, we first need to express the orbitals in terms of the hydrogen-like atomic orbitals. Let's assume that the two orbitals are denoted as ψ1 and ψ2, and can be expressed as linear combinations of the hydrogen-like atomic orbitals ϕ1 and ϕ2 as follows:

ψ1 = c1ϕ1 + d1ϕ2
ψ2 = c2ϕ1 + d2ϕ2

where c1, d1, c2, and d2 are constants.

The overlap integral between these two orbitals can be calculated using the following formula:

S = ∫ψ1ψ2*dτ

where dτ represents the infinitesimal volume element.

Substituting for ψ1 and ψ2, we get:

S = ∫(c1ϕ1 + d1ϕ2)(c2ϕ1 + d2ϕ2)*dτ

Expanding the product, we get:

S = c1c2∫ϕ1ϕ1*dτ + c1d2∫ϕ1ϕ2*dτ + d1c2∫ϕ2ϕ1*dτ + d1d2∫ϕ2ϕ2*dτ

Since the hydrogen-like atomic orbitals are orthonormal, the integral of ϕ1ϕ2 and ϕ2ϕ1 will be zero. Therefore, we can simplify the expression as follows:

S = c1c2∫ϕ1ϕ1*dτ + d1d2∫ϕ2ϕ2*dτ

Using the orthonormality of the hydrogen-like atomic orbitals, we know that the integral of ϕ1ϕ1 and ϕ2ϕ2 will both be equal to 1. Therefore, the overlap integral simplifies to:

S = c1c2 + d1d2d1d2.

In order to calculate the value of S, we need to know the values of the constants c1, d1, c2, and d2. These constants will depend on the specific linear combinations of atomic orbitals that we are considering. Without this information, we cannot calculate the value of the overlap integral.

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If two orbitals as linear combinations of two atomic orbitals on carbon atom in ethene, then value of the overlap integral [tex]S_{12} = \int{\phi_{1}}^{*}\phi_{2}d \tau[/tex], is equals to zero. So, option(b) is correct.

Orthonormal atomic orbitals are follow the following property:

Now, we have provide that two orbitals are as a linear combinations of two atomic orbitals on carbon atom in ethene. [tex]\phi_{1 } = \frac{1}{ \sqrt{2} } ( {\psi_{2s }} + {\psi_{2p }}_{2})[/tex]

[tex]\phi_{2 } = \frac{1}{ \sqrt{2} } ( \psi_{2 s} - {\psi_{2p} }_{2})[/tex]

In the ethylene molecule, consists each carbon atom is bonded to two hydrogen atoms. Therefore, for the C-H, σ bond (sp²(C) - 1s(H)) in ethylene, the two sp² hybrid orbitals overlap with the 1s orbitals of the two hydrogen atoms. Let the hydrogen-like atomic orbitals, [tex]\psi_{2 s} and {\psi_{2p} }_{2}[/tex] are orthonormal to each other. So, the overlap integral [tex]S_{12} = \int{ \phi_{1}}^{*}\phi_{2}d \tau[/tex]

[tex] = \int \frac{1}{\sqrt{2}}( \psi_{2s} + {\psi_{2p} }_{2}) \frac{1}{\sqrt{2}}( \psi_{2s} - {\psi_{2p} }_{2})d \tau\\ [/tex]

[tex] = \frac{1}{\sqrt{2}}( \int \psi_{2s}\psi_{2s} d \tau + \int {\psi_{2p} }_{2}\psi_{2s} d \tau - \int \psi_{2s} {\psi_{2p}}_{2} d \tau - \int {\psi_{2p} }_{2} {\psi_{2p} }_{2} d \tau) \\ [/tex].

Using above formula, [tex]\psi_{2 s} [/tex] and [tex]{\psi_{2p} }_{2}[/tex] are orthonormal so, [tex]\int \psi_{2 s} {\psi_{2p} }_{2} d\tau = 0[/tex]. Also [tex]\psi_{2 s} [/tex] and [tex]\psi_{2 s}[/tex] are normalised so [tex]\int \psi_{2 s} \psi_{2 s} d\tau = 1[/tex]. Similarly [tex]\int {\psi_{2p} }_{2} {\psi_{2p} }_{2} d\tau = 1 [/tex].

Substitute all integral values in equation (1),

= 1 + 0 - 0 - 1

= 0

Hence, the required integral value is 0.

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Complete question:

given two orbitals as linear combinations of two atomic orbitals on carbon atom in ethene:

[tex]\phi_{1 } = \frac{1}{ \sqrt{2} } ( {\psi_{2s }} + {\psi_{2p }}_{2})[/tex]

[tex]\phi_{2 } = \frac{1}{ \sqrt{2} } ( \psi_{2 s} - {\psi_{2p} }_{2})[/tex]

where the hydrogen-like atomic orbitals are orthonormal. what is the value of the overlap integral,

[tex] S_{12} = \int \phi_{1} \times \phi_{2}dr[/tex]

a) 1

b) 0

c) 1.5

d) 2