what is the molarity of a salt solution that is made from 31.0 grams of ca3(p04)2 placed in a volumetric flask and filled to the 2 liter line with distilled water?

The rate constant for the decomposition reaction 3[tex]RS_{2}[/tex]→ 3R + 6S can be determined by analyzing the initial rate data provided. By plotting the initial rate as a function of the concentration of RS_{2}and using the rate equation, the rate constant can be calculated.

To determine the rate constant for the decomposition reaction, we can analyze the initial rate data provided. The rate equation for the reaction is given by the expression: Rate = k[RS_{2}], where k is the rate constant and [RS_{2}] represents the concentration of RS_{2} By plotting the initial rate (mol/Ls) on the y-axis and the concentration of RS_{2} (mol/L) on the x-axis, we can observe the relationship between the two variables. Based on the data points provided, we can see that as the concentration of RS2 increases, the initial rate also increases.

To calculate the rate constant, we can choose any data point and substitute the corresponding concentration of RS_{2} and the initial rate into the rate equation. Let's use the data point [RS_{2}] = 0.250 mol/L and Rate = 0.109 mol/Ls:

0.109 = k * 0.250

By rearranging the equation and solving for k, we find:

k = 0.109 / 0.250 = 0.436 mol^(-1) L s^(-1)

Therefore, the rate constant for the decomposition reaction is approximately 0.436 mol^(-1) L s^(-1).

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The mass increases, the kinetic energy also increases in a linear fashion, making the graph a straight line.

The relationship between kinetic energy and an object's mass is linear. According to the laws of physics, the kinetic energy of an object is directly proportional to its mass. This means that as the mass of an object increases, its kinetic energy also increases proportionally. Conversely, if the mass decreases, the kinetic energy decreases proportionally.

Mathematically, the relationship between kinetic energy (KE) and mass (m) can be expressed as KE = 0.5 * m * v^2, where v represents the velocity of the object. It is evident from this equation that the mass appears linearly in the formula, without any exponents or other nonlinear terms.

Therefore, when graphed, the relationship between kinetic energy and an object's mass would be represented by a straight line passing through the origin (0,0) with a positive slope.

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If the bus had uniform acceleration, the final velocity of the bus is 14.4 m/s and acceleration is 0.0040 m/s²

According to question

The distance between  Khanikhola and Kathmandu

d = 26 km

= 26000 m

Time,

t = 1 hour

= 3600 seconds

Step-wise explanation:

Consider a is the acceleration of the bus. By using second equation of motion,

d = ut + [tex]\frac{1}{2} at^{2}[/tex]

Where

u is the initial speed of the bus,

u = 0

a = [tex]\frac{2d}{t^2}[/tex]

a = [tex]\frac{2 \times 26000}{3600^2}[/tex]

a = 0.0040 m/s²

By using first equation of motion.

Final velocity, v = u +at

So,

v = 0+0.0040(3600)

v = 14.4 m/s

a = 0.0040 m/s², v = 14.4 m/s.

If the bus had uniform acceleration, the final velocity of the bus is 14.4 m/s and acceleration is 0.0040 m/s².

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The chemical formula ©-CH-CH3 represents a molecule with a carbon atom bonded to two other atoms: one atom of hydrogen (H) and one methyl group (-CH3).

The symbol "©" is not a recognized element symbol in chemistry, so it might be a placeholder or an error. However, based on the given information, we can say that the molecule contains a carbon atom bonded to a hydrogen atom and a methyl group.

A carbon atom is a fundamental building block of matter and is represented by the chemical symbol "C." It is a member of the carbon group on the periodic table and has an atomic number of 6, which means it has six protons in its nucleus. Carbon atoms are particularly unique because they have the ability to form long chains and complex structures due to their versatile bonding properties.

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To calculate the mass of copper that will be plated out, we can use Faraday's law of electrolysis, which states that the mass of a substance deposited or liberated at an electrode is directly proportional to the quantity of electricity passed through the cell.

The formula to calculate the mass of a substance plated out is:

Mass = (Current × Time × Atomic Mass) / (Faraday's Constant × Number of Electrons)

Here we are plating out copper, which has an atomic mass of approximately 63.55 g/mol. The copper (II) sulfate solution contains copper ions with a charge of +2, meaning each copper ion (Cu2+) requires 2 electrons to be reduced to copper metal.

The Faraday's constant is approximately 96,485 C/mol, representing the charge of one mole of electrons.

Calculate the mass of copper plated out:

Mass = (2.3 A × 35 min × 60 s/min × 63.55 g/mol) / (96,485 C/mol × 2)

Mass = 0.0197 g

Therefore,  the correct answer is E) 0.019 g.

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In the context of Q systems, which are also known as Fixed Order Quantity systems, the primary requirement is: C) Perpetual inventory system. This is because Q systems rely on continuous tracking of inventory levels and automatically reordering a fixed quantity of items when the stock reaches a predefined reorder point.

One requirement of Q systems is constant order spacing. This means that orders must be placed at regular intervals, regardless of inventory levels or demand. This helps to maintain a consistent level of inventory and avoid stockouts. While variable lead time and constant demand can impact Q system performance, they are not strict requirements. However, perpetual inventory systems are often used in conjunction with Q systems to ensure accurate tracking of inventory levels and trigger orders at the appropriate time. In summary, the answer to the question is A) Constant order spacing. This is a fundamental requirement for Q systems to function effectively in managing inventory.
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While coefficients of 1 are typically omitted, they can be included for clarity and to satisfy grading requirements.

In balanced chemical equations, coefficients of 1 are typically omitted for simplicity and readability. Here's the balanced chemical equation for the given reaction while including coefficients of 1:

[tex]1 K_2CrO_4 + 1 Na_2SO_3 + 2 HCl -- > 2 KCl + 1 Na_2SO_4 + 1 CrCl_3 + 1 H_2O[/tex]

The purpose of balancing chemical equations is to ensure that the number of atoms of each element is the same on both sides of the equation. By adjusting the coefficients, we can achieve this balance while following the law of conservation of mass. The coefficients represent the relative amounts of each substance involved in the reaction.

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In 4-(1-methylethyl)heptane, the angle between any two substituents or groups connected to the carbon backbone does not have a specific fixed value. The angle can vary depending on the specific conformations and spatial arrangement of the molecule.

The name "4-(1-methylethyl)heptane" provides information about the positions and types of substituents on the heptane carbon backbone. The "4-" indicates that the substituent is attached to the fourth carbon atom of the heptane chain. The "(1-methylethyl)" indicates that the substituent is a 1-methylethyl group. The specific value of the angle between any two substituents or groups in the molecule cannot be determined solely from the name. The actual angle will depend on the three-dimensional conformation of the molecule, which can vary due to rotation around the carbon-carbon single bonds.

The molecule can adopt different conformations, such as eclipsed, staggered, or various degrees of rotation around the carbon-carbon bonds. Each conformation will result in different angles between the substituents or groups. Therefore, without additional information about the conformation or a three-dimensional representation of the molecule, it is not possible to determine a specific angle value between the substituents in 4-(1-methylethyl)heptane.

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In the given reaction, the element that is oxidized is sulfur (S)

In the given reaction, the element that undergoes oxidation can be determined by examining the changes in oxidation states.

The oxidation state of an element is a measure of the number of electrons it has gained or lost in a compound or reaction. An increase in oxidation state indicates oxidation, while a decrease indicates reduction.

Looking at the reaction:

Br2 + H2S + H2O --> H2SO4 + HBr

Before the reaction, bromine (Br2) has an oxidation state of 0, hydrogen sulfide (H2S) has an oxidation state of -2, and water (H2O) has an oxidation state of 0.

After the reaction, sulfur (in H2SO4) has an oxidation state of +6, indicating an increase from -2. This means that sulfur has been oxidized.

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It will take 33 years for a 40-mg sample to decay to a mass of 30.4 mg.

Tο calculate the time it takes fοr a sample οf strοntium-90 tο decay frοm 40 mg tο 30.4 mg, we can use the cοncept οf half-life

Using the half-life formula:

[tex]\rm A=A_02^{-t/h}[/tex], where

A = resulting amount after time t = 39.6 mg

Ao = initial amount = 90 mg

t = decay time

h = half-life of substance= 28 yrs

Now putting the values into the formula, we get

[tex]$ \rm 39.6=90\times2^{-t/28}[/tex]

[tex]$ \rm 2^{-t/28}=\frac{39.6}{90}=\frac{2.2}{5}[/tex]

Taking logarithm both sides

[tex]$ \rm ln(2^{-t/28})=ln(\frac{2.2}{5})[/tex]

[tex]$ \rm \frac{-t}{28}ln(2)=ln(0.44)[/tex]

[tex]$ \rm t=\frac{-28ln(0.44)}{ln(2)}[/tex]

t = 33.16389

t ≈ 33years

Thus, it will take 33 years for a 40-mg sample to decay to a mass of 30.4 mg.

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a) To calculate the grams of stearic acid per drop, we need to use the concentration of the stearic acid solution. The concentration is given as 0.11 g/L. Since 1 mL is equivalent to the average number of drops in 1 mL, we can calculate the grams of stearic acid per drop as follows:

Grams of stearic acid per drop = (Concentration of stearic acid solution in g/L) / (Average number of drops in 1 mL)

b) To calculate the grams of stearic acid needed to make a monolayer, we can multiply the number of drops of solution delivered to the water surface (provided in the question) by the grams of stearic acid per drop calculated in part (a).

c) Using the density of stearic acid (0.85 g/mL) and the mass of stearic acid calculated in part (b), we can calculate the volume of stearic acid in cm³ in the monolayer. Since the density is given in g/mL, the volume can be determined using the formula:

Volume of stearic acid = Mass of stearic acid / Density of stearic acid

d) To calculate the thickness (L) of the monolayer, we can divide the volume of stearic acid in cm³ by the area of the water surface. The area of the water surface is not provided in the question, so it would need to be obtained from additional information.

e) To convert the thickness in cm to Angstroms, we can multiply the thickness in cm by a conversion factor. 1 cm is equivalent to 10,000 Angstroms, so the thickness in Angstroms can be calculated by multiplying the thickness in cm by 10,000.

a) The concentration of the stearic acid solution is provided as 0.11 g/L. To find the grams of stearic acid per drop, we divide this concentration by the average number of drops in 1 mL.

b) The number of drops of solution delivered to the water surface is given in the question. To calculate the grams of stearic acid needed to make a monolayer, we multiply this number by the grams of stearic acid per drop calculated in part (a).

c) The density of stearic acid is given as 0.85 g/mL. Using this density and the mass of stearic acid calculated in part (b), we can determine the volume of stearic acid in cm³ in the monolayer.

d) To calculate the thickness of the monolayer, we divide the volume of stearic acid in cm³ by the area of the water surface. The area of the water surface is not provided in the question, so additional information is needed to perform this calculation accurately.

e) To convert the thickness from cm to Angstroms, we multiply the thickness in cm by the conversion factor of 10,000 since 1 cm is equivalent to 10,000 Angstroms.

By following the steps outlined above, you can determine the grams of stearic acid per drop, the grams of stearic acid needed to make a monolayer, the volume of stearic acid in cm³ in the monolayer, the thickness of the monolayer in cm, and finally, the conversion of the thickness to Angstroms. However, please note that the calculations depend on additional information such as the area of the water surface, which is not provided in the given question.

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The molality of the solution containing 30.0 g of naphthalene dissolved in 500.0 g of toluene is 0.468 mol/kg.

The molality of the solution can be calculated by dividing the moles of solute (naphthalene) by the mass of the solvent (toluene) in kilograms. In this case, 30.0 g of naphthalene is dissolved in 500.0 g of toluene.

To find the molality (m) of the solution, we need to calculate the moles of naphthalene and convert the mass of toluene to kilograms.

The molar mass of naphthalene (C10H8) is 128.18 g/mol. To find the moles of naphthalene, we divide the mass by the molar mass:

moles of naphthalene = \frac{30.0 g }{128.18 g/mol }= 0.234 mol.

Next, we convert the mass of toluene to kilograms:

mass of toluene = 500.0 g = \frac{500.0 g }{ 1000} = 0.500 kg.

Finally, we calculate the molality:

molality (m) = \frac{moles of solute }{ mass of solvent in kg}

molality =\frac{ 0.234 mol }{ 0.500 kg} = 0.468 mol/kg.

Therefore, the molality of the solution containing 30.0 g of naphthalene dissolved in 500.0 g of toluene is 0.468 mol/kg.

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Answer :

Empirical formula : CH3

Molecular Formula : C6H18

Explanation :

C : H

80/ 12 : 20/ 1

6.67/ 6.67 : 20/ 6.67

1 : 3

Therefore : CH3

Molecular formula :

First calculate n

n = Relative molecular mass / Empirical formula mass

= 90/15

= 6

Therefore : ( CH3) subscript 6

= C6H18

The amino acid arginine can be synthesized by an anabolic pathway that requires seven enzymes. Wild type bacteria should repress production of these enzymes if arginine is present in the environment. Your answer: a. an anabolic; repress

The amino acid arginine can be synthesized by a pathway that requires seven enzymes.Wild type bacteria should induce production of these enzymes if arginine is present in the environment. This is because the presence of arginine signals to the bacteria that it is available as a nutrient source, and the bacteria will need to produce the necessary enzymes to synthesize it. The pathway for arginine synthesis is an anabolic process, meaning it requires energy and building blocks to create larger molecules from smaller ones. Therefore, the bacteria need to increase enzyme production to facilitate this process. Repression would not make sense in this context, as it would inhibit the synthesis of a necessary nutrient.
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An exothermic reaction with a positive value for ΔSsys generally favors the reactants.

In chemical reactions, the change in entropy (ΔS) is an important factor in determining the direction of the reaction. ΔSsys represents the change in entropy of the system, which is the reactants and products involved in the reaction. A positive value for ΔSsys indicates an increase in entropy, meaning that the products have a higher level of disorder or randomness compared to the reactants.

For an exothermic reaction, the heat is released to the surroundings, resulting in a decrease in the entropy of the surroundings (ΔSsurr). If ΔSsys is positive, it means that the increase in disorder within the system is greater than the decrease in disorder in the surroundings.

Since an exothermic reaction with a positive value for ΔSsys indicates an increase in disorder, it suggests that the reaction favors the reactants. This is because the reactants have a lower level of disorder compared to the products, and the reaction proceeds in the direction that increases the disorder or entropy of the system.

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The total radioactivity emitted by 300 students in a lecture hall is approximately [tex]2.2 \times 10^6 decay/s.[/tex]

To calculate the total radioactivity emitted, we need to multiply the radioactivity generated by each student by the number of students. Given that each person's body generates about 0.2 μCi of radioactivity, we first convert this value to Becquerels (Bq) using the conversion factor: [tex]1 Ci = 3.7 \times10^{10} Bq.[/tex]

Converting 0.2 μCi to Bq:

[tex]0.2 \mu Ci = 0.2 \times 10^{-6} Ci = 0.2 \times 10^{-6} \times 3.7 \times 10^{10} Bq = 7.4 \times 10^{-6} Bq[/tex]

Now, we can calculate the total radioactivity emitted by the 300 students:

Total radioactivity emitted[tex]= 7.4 \times 10^{-6} Bq/student \times 300 students[/tex]= [tex]2.2 x 10^{-3} Bq \times 300 = 2.2 \times 10^6 Bq[/tex]

Therefore, the total radioactivity emitted by 300 students in the lecture hall is approximately 2.2 x 10^6 decay/s, which corresponds to option A.

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Wrapping a hot potato in aluminum foil significantly reduces the rate at which it cools primarily by reducing heat loss through conduction. The aluminum foil acts as a barrier that slows down the transfer of heat from the potato to its surroundings, keeping it warm for a longer period.

Wrapping a hot potato in aluminum foil significantly reduces the rate at which it cools by reducing the process of conduction. Conduction is the transfer of heat between two objects that are in contact with each other. When a hot potato is left in open air, it transfers heat to the surrounding air molecules through conduction, resulting in a rapid decrease in temperature. However, wrapping the potato in aluminum foil prevents direct contact with the air, which decreases the rate of conduction and keeps the potato hotter for a longer period. Therefore, the correct answer is D. conduction.
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Radioactive decay refers to the spontaneous process by which unstable atomic nuclei transform or "decay" into more stable configurations by emitting radiation. α, β, and γ rays are types of ionizing radiation emitted during radioactive decay processes. The characteristics of α, β, and γ rays can be identified as follows:

α rays:

It is symbolized as 4/2 He.

It possesses neither mass nor charge.

It is the most massive of all the components.

β rays:

It is a high-speed electron.

It is symbolized as 0/-1e.

γ rays:

It has the weakest ionization power.

It has the strongest penetrating power.

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We must take into account the sodium acetate's hydrolysis reaction, which involves the dissolution of the sodium acetate into sodium ions (Na+) and acetate ions (C2H3O2-), in order to get the theoretical percent hydrolysis for a 1M solution of NaC2H3O2 (sodium acetate).

The following is a representation of the hydrolysis reaction:

Na+ + C2H3O2- NaC2H3O2 + H2O

The initial concentration of NaC2H3O2 in a 1M solution is 1M. Some of the sodium acetate molecules split apart into sodium and acetate ions during hydrolysis. By dividing the concentration of the hydrolyzed ions by the initial concentration of the sodium acetate and multiplying by 100, the theoretical percent hydrolysis can be computed. The concentration of hydrolyzed ions is equivalent because 1 mole of NaC2H3O2 dissociates into 1 mole of Na+ and 1 mole of C2H3O2-.

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There are four non-equivalent protons present in CH3CH═CH2. The molecule has two different types of carbons, one is a sp2 hybridized carbon and the other two are sp3 hybridized carbons.

The sp2 hybridized carbon is attached to two different types of hydrogen atoms, one is attached to two methyl groups and the other is attached to a hydrogen atom. These two hydrogen atoms are non-equivalent because they are attached to different types of carbons. Similarly, the two sp3 hybridized carbons are attached to different types of hydrogen atoms, one is attached to three methyl groups and the other is attached to a hydrogen atom. Therefore, there are four non-equivalent protons in CH3CH═CH2.

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One molecule that could show two signals with an integration ratio of 2:3 in its 1H NMR spectrum is propanal ([tex]CH_3CH_2CHO[/tex]).

This molecule has two distinct types of protons: the two methyl ([tex]CH_3[/tex]) groups and the aldehyde (CHO) proton. The methyl protons will appear as a triplet due to coupling to the neighboring protons, while the aldehyde proton will appear as a singlet. The integration ratio of the methyl protons to the aldehyde proton is 2:1, which is equivalent to 2:3 when simplified. Therefore, propanal is a good example of a molecule that could show two signals with an integration ratio of 2:3 in its 1H NMR spectrum.

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To identify an aromatic aldehyde, you can follow the following identification scheme Test for Carbonyl Group and Chromic Acid Test

Test for Carbonyl Group: Perform a test to confirm the presence of a carbonyl group, which is a characteristic functional group of aldehydes. This can be done using Tollens' test or Fehling's test, which give positive results for aldehydes.

Test for Carbonyl Group: Aromatic aldehydes often have distinct odors. Conduct a smell test to check for the presence of a strong, sweet, or floral odor, which is typical of many aromatic aldehydes.

Chromic Acid Test: Perform the chromic acid test by adding a small amount of chromic acid reagent to the sample. A positive result indicated by a color change indicates the presence of an aldehyde, including aromatic aldehydes.

NMR Spectroscopy: Utilize Nuclear Magnetic Resonance (NMR) spectroscopy to analyze the compound's structure and identify the presence of an aldehyde group. The aldehyde proton signal typically appears in the region of 9-10 ppm.

Other Tests: Additional tests can be performed to confirm the presence of an aromatic aldehyde. These include Schiff's test, which gives a positive result for aldehydes, and silver mirror test, which forms a silver mirror on the inner surface of the test tube for aldehydes.

Challenges in making a unique, positive identification of an aromatic aldehyde and differentiating it from other molecules include:

Similar Functional Groups: Some other functional groups, such as ketones, may also give positive results in certain tests, making it necessary to perform additional tests to confirm the presence of an aldehyde.

Isomeric Structures: Aromatic aldehydes can have isomeric structures, making it important to analyze the compound's structure accurately using techniques like NMR spectroscopy to distinguish between different isomers.

Impurities or Mixtures: Presence of impurities or mixtures can complicate the identification process, as they may interfere with the test results or provide additional signals in spectroscopic analysis.

To overcome these challenges, it is important to perform a combination of tests and use multiple analytical techniques to make a reliable and conclusive identification of an aromatic aldehyde.

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Approximately 13.9 milliliters of 0.36 M [tex]H_2SO_4[/tex]are required to neutralize 25.00 mL of 0.10 M [tex]Ba(OH)_2[/tex]

To determine the volume of 0.36 M [tex]H_2SO_4[/tex]required to neutralize 25.00 mL of 0.10 M [tex]Ba(OH)_2[/tex], we need to use the stoichiometry and balanced chemical equation between sulfuric acid ([tex]H_2SO_4[/tex]) and barium hydroxide [tex]Ba(OH)_2[/tex]

The balanced chemical equation for the reaction between [tex]H_2SO_4[/tex] and [tex]Ba(OH)_2[/tex]is:

[tex]H_2SO_4[/tex]+ 2[tex]Ba(OH)_2[/tex] ->[tex]BaSO_4 + 2H_2O[/tex]

From the equation, we can see that the molar ratio between [tex]H_2SO_4[/tex] and [tex]Ba(OH)_2[/tex]is 1:2.

First, let's calculate the number of moles of[tex]Ba(OH)_2[/tex]in the given 25.00 mL solution. We can use the formula:

Moles = Concentration (M) x Volume (L)

Moles of [tex]Ba(OH)_2[/tex] = 0.10 M x (25.00 mL / 1000 mL/L) = 0.0025 mol

According to the balanced equation, 1 mole of [tex]H_2SO_4[/tex] reacts with 2 moles of [tex]Ba(OH)_2[/tex]. Therefore, we need twice as many moles of [tex]H_2SO_4[/tex] to neutralize the [tex]Ba(OH)_2[/tex]

Moles of [tex]H_2SO_4[/tex] required = 2 x Moles of [tex]Ba(OH)_2[/tex] = 2 x 0.0025 mol = 0.0050 mol

Now, let's calculate the volume of 0.36 M [tex]H_2SO_4[/tex] needed to obtain 0.0050 moles. We can rearrange the formula:

Volume (L) = Moles / Concentration (M)

Volume of [tex]H_2SO_4[/tex] = 0.0050 mol / 0.36 M = 0.0139 L

Finally, to convert the volume to milliliters:

Volume of[tex]H_2SO_4[/tex] = 0.0139 L x (1000 mL/L) = 13.9 mL

Therefore, approximately 13.9 milliliters of 0.36 M [tex]H_2SO_4[/tex]are required to neutralize 25.00 mL of 0.10 M [tex]Ba(OH)_2[/tex].

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Answer:

19.6 mole

Explanation:

because Fe molar mass is 56

The correct answer is d. It will take 20.0 minutes or the reaction to be 75.0% complete.

In a zero-order reaction, the half-life remains constant regardless of the initial concentration. In this case, we are given that the half-life is 10.0 minutes when the reactant concentration is 0.250 M.

To determine the time it takes for the reaction to be 75.0% complete, we can use the concept that in a zero-order reaction, the concentration decreases linearly with time. Since the half-life is 10.0 minutes, it means that after 10.0 minutes, the concentration is reduced by half (50%). Therefore, after 20.0 minutes (2 times the half-life), the concentration will be reduced to 25% of the initial concentration.

Since we want to find the time it takes for the reaction to be 75.0% complete, which is 25% remaining, it will take 20.0 minutes.

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In a cyclohexane (C6H12) molecule, a cyclic compound used in the manufacture of nylon and found in the distillation of petroleum, the molecular geometry around each carbon atom is tetrahedral. This 3D representation allows for optimal spatial arrangement and minimal steric strain between the carbon and hydrogen atoms in the molecule.

The molecular geometry around each carbon atom in a cyclohexane molecule is considered to be a tetrahedral shape. This means that each carbon atom is bonded to four other atoms in a tetrahedral arrangement, resulting in a three-dimensional shape with bond angles of approximately 109.5 degrees. The cyclohexane molecule is a cyclic compound that is commonly used in the manufacture of nylon and can be found in the distillation of petroleum. The unique molecular geometry of cyclohexane allows it to form stable structures that contribute to its usefulness in industrial applications.
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The increase in energy of particles increases the movement and kinetic energy of the particles changing their state of matter.

Particles or matter change their state either by absorbing or releasing energy usually in the form of heat or thermal energy. When a particle is given this thermal energy and absorbs it, the kinetic energy of these particles increases. Thereby increasing their movement across the medium.

This results in rapid movement and the force of attraction between the particles decrease. They spread out changing their state of matter. In the case of water, when ice is heated, the water molecules absorb heat and move around turning ice into water.

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The shape of [Cr(NH3)3Cl3]-3 is octahedral.

This means that the complex ion has six ligands attached to the central chromium atom, arranged at the vertices of an octahedron. The three ammonia ligands are arranged in an equatorial plane, while the three chloride ligands are arranged in an axial plane perpendicular to the equatorial plane. The octahedral shape is a common geometry for six-coordinate transition metal complexes, and it allows for efficient bonding with a wide variety of ligands. The complex ion is also overall negatively charged, due to the presence of three chloride ions, which act as counterions to the positively charged central chromium atom. The shape of the complex ion [Cr(NH3)3Cl3]-3 is octahedral. In this complex, the central metal ion (Cr) is surrounded by six ligands - three ammonia (NH3) molecules and three chloride (Cl-) ions. These ligands are arranged at the vertices of an octahedron, with each ligand equidistant from the central ion, resulting in an octahedral geometry. This shape is common in coordination compounds, providing stability and symmetry for the complex ion.

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Among the compounds listed, [tex]Ca(ClO_4)_2[/tex] will be more soluble in acidic solution than in pure water.

The solubility of a compound depends on its interaction with the solvent molecules. In the case of acidic solutions, the presence of excess hydrogen ions (H+) affects the solubility of certain compounds.

a) [tex]PbCl_2[/tex]: Lead(II) chloride ( [tex]PbCl_2[/tex]) is a sparingly soluble salt in pure water. In acidic solutions, the solubility of  [tex]PbCl_2[/tex]is not significantly affected because there are no specific interactions between lead ions and hydrogen ions.

b) FeS: Iron(II) sulfide (FeS) is insoluble in both pure water and acidic solutions. Its solubility is not influenced by the presence of acid.

c)  [tex]Ca(ClO_4)_2[/tex] : Calcium perchlorate  [tex]Ca(ClO_4)_2[/tex]  is more soluble in acidic solutions than in pure water. The perchlorate anions (ClO4-) in the compound can undergo acid-base reactions with the excess hydrogen ions in the acidic solution, increasing its solubility.

d) CuI: Copper(I) iodide (CuI) is insoluble in both pure water and acidic solutions. It does not exhibit significant solubility changes in the presence of acid.

Therefore, among the given options,  [tex]Ca(ClO_4)_2[/tex]  is the compound that will be more soluble in an acidic solution compared to pure water due to acid-base interactions between the perchlorate anions and hydrogen ions in the solution.

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415.25 grams of sulfur ([tex]S_{8}[/tex]) are needed to produce 200 grams of boron sulfide ([tex]B_{2}S_{3}[/tex]).

The balanced chemical equation for the reaction between sulfur and boron sulfide is:

[tex]3S_{8}+4B[/tex] → [tex]4B_{2}S_{3}[/tex]

From the equation, we can see that 3 moles of sulfur react to form 4 moles of boron sulfide.

Molar mass of [tex]B_{2}S_{3}[/tex] - 2(10.81 g/mol) + 3(32.06 g/mol) = 55.98 g/mol

Molar mass of [tex]S_{8}[/tex]- 8(32.06 g/mol) = 256.48 g/mol

Now, we can set up a ratio using the molar masses and molar ratios:

(256.48 g [tex]S_{8}[/tex]) / (1 mol [tex]S_{8}[/tex]) = (200 g [tex]B_{2}S_{3}[/tex]) / (55.98 g [tex]B_{2}S_{3}[/tex]) * (3 mol [tex]S_{8}[/tex]) / (4 mol [tex]B_{2}S_{3}[/tex])

Simplifying:

256.48 g [tex]S_{8}[/tex] ={ (200 g [tex]B_{2}S_{3}[/tex]) * (3 mol [tex]S_{8}[/tex]) / (4 mol [tex]B_{2}S_{3}[/tex]) * (55.98 g [tex]B_{2}S_{3}[/tex]) ]*(1 mol [tex]S_{8}[/tex])

256.48 g  [tex]S_{8}[/tex] = 415.25 g [tex]S_{8}[/tex]

Therefore,  415.25 grams of sulfur ([tex]S_{8}[/tex]) are needed .

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