answer the following 3 questions Please. TIA

The density of pure propionic acid is 0.9930 g.cm-3 and its molecular mass is 74.08g.mol-1.  

a. The mass of propionic acid required to make 250ml of 0.50m propionic acid solution is 9.26 grams.

To calculate the mass of propionic acid required to make 250ml of 0.50m propionic acid solution, we need to use the formula:
m = n x M
where:
m = mass of propionic acid required (in grams)
n = number of moles of propionic acid (in moles)
M = molecular mass of propionic acid (in grams per mole)
First, we need to calculate the number of moles of propionic acid required for a 250ml solution of 0.50m concentration:
Molarity = moles of solute/litres of solution
0.50m = n / 0.250 L
n = 0.50m x 0.250 L
n = 0.125 moles
Now we can substitute the values in the formula:
m = n x M
m = 0.125 moles x 74.08 g/mol
m = 9.26 g
Therefore, the mass of propionic acid required to make 250ml of 0.50m propionic acid solution is 9.26 grams.

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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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Option b. The breaking of the chemical bond causes the release of energy from a chemical bond.

The arrival of energy from a substance bond happens when the bond is broken, either through synthetic responses or actual cycles. Compound bonds result from the sharing or move of electrons among particles, and the energy expected to frame a bond is put away inside the actual bond. At the point when the bond is broken, this put away energy is delivered as dynamic energy, intensity, or light. How much energy delivered relies upon the strength of the bond and the particular synthetic responses included. In this way, the breaking of the bond is the reason for energy discharge, while different choices - iotas having a lopsided number of electrons, harm from free revolutionaries, and the sharing of electrons between molecules - don't straightforwardly connect with the arrival of energy from a bond.

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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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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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In the context of building molecules using model kits such as AXNEM, A, X, and E are abbreviations used to represent the different parts of a molecule.

1) A stands for "central atom," which is usually the atom that has the lowest electronegativity in the molecule and is located at the center of the molecular structure.

2) X stands for "terminal atoms," which are the atoms that are bonded to the central atom. They can be identical or different from one another.

3) E stands for "lone pairs," which are pairs of electrons that are not involved in any bonding and are located on the outer shell of the central atom.

By using these abbreviations, it becomes easier to represent the molecular structure and to understand how the atoms are arranged and bonded to each other.

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The silicon crystal becomes an n-type semiconductor at normal temperature when the phosphorous atoms contribute an extra electron, producing an overabundance of negative charge carriers.

The conductivity of the crystal will rise as the temperature is raised from 300°C to 350°C. This is because a greater temperature results in a higher concentration of free charge carriers since there is more thermal energy available to promote electrons from the valence band to the conduction band.

We can use the following equation to calculate the conductivity change:

σ = nqμ

When the charge of an electron is q, the number of charge carriers is n, the conductivity is, and the mobility of the charge carriers. If the number of charge carriers increases by 10% as a result of the temperature increase.

As a result, we can see that raising the temperature from 300°C to 350°C causes the conductivity to increase by about 14%.

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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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Answer:

Propyl methanoate

Explanation:

The ester that can be synthesized from propanol and methanoic acid is propyl methanoate (also known as methyl propanoate or propyl formate). The reaction between propanol and methanoic acid, which is a carboxylic acid, is a classic example of an esterification reaction, which results in the formation of an ester and water.

Answer:

condensation nuclei

Explanation:

Answer: Because its dissolution is exothermic

Explanation:

The value of Kp at 90°C is zero. This indicates that the decomposition of baking soda at this temperature is essentially complete, and the equilibrium lies far to the right.

We can use the expression for the equilibrium constant Kp, which is given by:

Kp = (P([tex]CO_{2}[/tex] ) × P([tex]H_{2} O[/tex])) / (P([tex]Na_{2} CO_{3}[/tex] ))

where P([tex]CO_{2}[/tex]), P([tex]H_{2} O[/tex]), and P([tex]Na_{2} CO_{3}[/tex]) are the partial pressures of carbon dioxide, water vapor, and sodium carbonate, respectively, at equilibrium.

From the balanced equation, we know that for every 2 moles of [tex]NaHCO_{3}[/tex]that decompose, 1 mole of [tex]CO_{2}[/tex] is produced. Therefore, the partial pressure of [tex]CO_{2}[/tex] can be calculated as:

P([tex]CO_{2}[/tex] ) = (1/2) × (total pressure) = 0.2726 atm

Similarly, for every 2 moles of [tex]NaHCO_{3}[/tex] that decompose, 1 mole of Na2CO3 is produced. Therefore, the partial pressure of [tex]Na_{2} CO_{3}[/tex]can be calculated as:

P([tex]Na_{2} CO_{3}[/tex]) = (1/2) × (total pressure) = 0.2726 atm

Finally, the partial pressure of water vapor can be calculated as the difference between the total pressure and the partial pressures of CO2 and [tex]Na_{2} CO_{3}[/tex]:

P([tex]H_{2} O[/tex]) = (total pressure) - P([tex]CO_{2}[/tex]) - P([tex]Na_{2} CO_{3}[/tex]) = 0.5451 - 0.2726 - 0.2726 = 0.0 atm

This means that there is no water vapor present at equilibrium, and we can assume that its partial pressure is zero. Substituting these values into the expression for Kp, we get:

Kp = (P([tex]CO_{2}[/tex]) × P([tex]H_{2} O[/tex])) / (P([tex]Na_{2} CO_{3}[/tex]))

= (0.2726 × 0.0) / 0.2726

= 0.0

Therefore, the value of Kp at 90°C is zero. This indicates that the decomposition of baking soda at this temperature is essentially complete, and the equilibrium lies far to the right.

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The atmospheric pressure on top of Mt. Everest is 250 mmHg and 0.328 atm, when rounded to 3 significant digits.

Pressure is a force that is exerted over a surface area. It is the amount of force applied to an object per unit area. Pressure is typically expressed in units of force per unit of area, such as pounds per square inch (psi) or pascals (Pa). Pressure is an important factor in many areas of engineering, physics, chemistry, and biology.

Atmospheric pressure can be measured in torr (1 Torr = 1mmHg), atm (1 atm = 760mmHg) or in kPa (1 atm = 101.3kPa).
250 torr = 250 mmHg
250 mmHg / 760 mmHg = 0.328 atm

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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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The decrease in the second ionization energy of alkali metals going down the group is due to the increase in atomic radius.

As the atomic radius increases, the distance between the nucleus and the outermost electron increases, which reduces the coulombic force of attraction between the nucleus and the electron.

This reduced coulombic force of attraction reduces the energy required to remove the electron, thus resulting in a decrease in the ionization energy. Additionally, due to the increased number of electrons, the effective nuclear charge decreases, which further reduces the force of attraction between the nucleus and the electron, thus resulting in a further decrease in the ionization energy.

Therefore, the decrease in the second ionization energy of alkali metals going down the group can be attributed to a decrease in the coulombic force of attraction due to the increase in atomic radius and the decrease in the effective nuclear charge.

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The partial pressure of helium in the flask is 1.12 atm and the total pressure in the flask is 1.99 atm.

To find the partial pressure of helium, we need to first find the moles of each gas present in the mixture.

Moles of methane:

n(CH4) = mass / molar mass = 2.68 g / 16.04 g/mol = 0.167 mol

Moles of helium:

n(He) = mass / molar mass = 0.864 g / 4.00 g/mol = 0.216 mol

Total moles of gas:

n(total) = n(CH4) + n(He) = 0.167 mol + 0.216 mol = 0.383 mol

To find the total pressure in the flask, we can use the ideal gas law:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. Rearranging this equation to solve for P:

P = nRT / V

where R = 0.0821 L·atm/mol·K is the gas constant.

Converting temperature to Kelvin:

T = 65°C + 273.15 = 338.15 K

Plugging in the values:

P = (0.383 mol) x (0.0821 L·atm/mol·K) x (338.15 K) / (5.93 L) = 1.99 atm

To find the partial pressure of helium, we can use the mole fraction of helium:

X(He) = n(He) / n(total) = 0.216 mol / 0.383 mol = 0.563

The partial pressure of helium is then:

P(He) = X(He) x P = 0.563 x 1.99 atm = 1.12 atm

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If a glass manufacturer has only a few costly ways of reducing pollutants, it will end up paying the pollution tax, option A.

A chemical or energy that is introduced into the environment and has negative consequences or reduces the usability of a resource is referred to as a pollutant or new entity. These can be either anthropogenic in origin (i.e., produced materials or results of biodegradation) or naturally formed (i.e., minerals or extracted chemicals like oil). When pollutants are present in sufficient quantities to have noticeable detrimental effects on the environment or public health, pollution results.

By altering the development rate of plant or animal species, or by affecting human amenities, comfort, health, or property values, a pollution may inflict long- or short-term damage.

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Complete question:

If a glass manufacturer has only a few ________________ of reducing pollutants, it will ____________________ .

A. costly ways; end up paying the pollution tax.

B. inexpensive ways; incur the pollution tax instead.

C. costly ways; do so to minimize its pollution taxes.

D. inexpensive ways; buy the most expensive technology.

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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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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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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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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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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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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If 120 cm³ of oxygen gas is collected at 713.3 mm Hg pressure, the volume of the dry gas at STP is 0.102 cm³.

To solve this problem, we will use the ideal gas law, which relates the pressure, volume, temperature, and number of moles of a gas:

PV = nRT

First, we need to convert the given conditions to the correct units. The temperature is already in Celsius, so we need to convert it to kelvins by adding 273.15:

T = 27 + 273.15 = 300.15 K

The pressure is given in millimeters of mercury (mm Hg), so we need to convert it to atmospheres (atm) to use in the ideal gas law. There are 760 mm Hg in 1 atm, so:

P = 713.3 mm Hg / 760 mm Hg/atm = 0.938 atm

Next, we can use the ideal gas law to find the number of moles of oxygen gas:

n = PV/RT = (0.938 atm)(120 cm³)/(0.08206 L·atm/(mol·K))(300.15 K) = 0.00454 mol

Finally, we can use the molar volume of a gas at STP (standard temperature and pressure) to find the volume of the dry gas at STP. At STP, the temperature is 273.15 K and the pressure is 1 atm. The molar volume of a gas at STP is 22.4 L/mol, so:

V = n(22.4 L/mol) = (0.00454 mol)(22.4 L/mol) = 0.102 cm³

Therefore, the volume of the dry gas at STP is 0.102 cm³.

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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:
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."

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

1. Cotton is charged negatively while steel doesn't charge by rubbing. 2. cotton acquires negative while silk acquires positive charge. 3. human hair is negative charge while human hand is positively charged. 4. teflon gets negative charge while wood doesn't acquire charge. 5. glass acquires positive charge when rubbed with plastic wrap.

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