For each of the processes, determine whether the entropy of the system is increasing or decreasing.

a. A snowman melts on a spring day.
b. A document goes through a paper shredder.
c. A water bottle cools down in a refrigerator.
d. Silver tarnishes
e. Dissolved sugar precipitates out of water to form rock candy.

Answer:

- Aluminium sulfate Al2(SO4)3 dissociates in two aluminium ions and three sulfate ions, therefore, van't Hoff factor is 5 (incorrect).

Explanation:

Hello,

In this case, since the van't Hoff factor is related with the species that result from the ionization of a chemical compound, we can see that that

- Aluminium sulfate Al2(SO4)3 dissociates in two aluminium ions and three sulfate ions, therefore, van't Hoff factor is 5 (incorrect).

- Ammonium nitrate NH4NO3 dissociates in one ammonium ions and one nitrate ion, therefore, van't Hoff factor is 2 (correct).

- Sodium sulfate Na2SO4 dissociates in two sodium ions and one sulfate, therefore, van't Hoff factor is 3 (correct).

- Sucrose is not ionized, therefore, van't Hoff factor is 1 (correct).

Best regards.

Answer:

Explanation:

Answer in attached file .

Answer: [tex]Rate=k[A][B][/tex]

Explanation:

Rate law says that rate of a reaction is directly proportional to the concentration of the reactants each raised to a stoichiometric coefficient determined experimentally called as order.

Order of the reaction is defined as the sum of the concentration of terms on which the rate of the reaction actually depends. It is the sum of the exponents of the molar concentration in the rate law expression.

For reactions which takes place in multiple steps are complex reactions and the order is given by the slowest step which is the rate limiting step.

For the given reaction, the rate limiting step is

[tex]A+B\rightarrow D[/tex]

Rate law will be , [tex]Rate=k[A][B][/tex]

Answer:

Chemistry is one of the causes for global warming, and in some cases it can even cause certain illnesses.

Answer:

Chemists have both hurt the environment and helped the environment by their actions.

Explanation:

<3

Answer:

THE VOLUME OF THE OXYGEN GAS AFTER DEFLATION TILL A PRESSURE OF 735 TORR IS ATTAINED IS 7836.99 L

Explanation:

Using Boyle's law,

P1V1 = P2V2

P1 = 150 atm

V1 = 50 L

P2 = 735 Torr

V2 = unknown

We must first convert the pressures into the same SI unit for easy calculation

1torr = 1/760 atm

So converting 735 torr to atm; we have:

1 torr = 1/ 760 atm

735 torr = 735 * 1 / 760 atm

= 0.967 atm

In other words, P2 = 0.957 atm

So rearranging the formula by making V2 the subject of the equation, we have:

V2 = P1 V1 / P2

V2 = 150 * 50 / 0.957

V2 = 7836.99 L

The volume of the oxygen cylinder after deflation to a final pressure of 735 torr or 0.967 atm pressure is 7836.99 L.

Answer:

B. 1-amino-2-methylpentan-2-ol

Explanation:

In this case, the first step, we have the attack of the nucleophile cyanide ([tex] CN^-[/tex] produced by sodium cyanide to the carbon on the carbonyl group (C=O) producing a negative charge in the oxygen.

Then HCl protonates the molecule to produce a cyanohydrin. This cyanohydrin can be reduced by the action of hydrogen gas ([tex]H_2[/tex]) in the presence of a catalyst ([tex]Pd[/tex]), producing an amino group. With this in mind, the final molecule is: 1-amino-2-methylpentan-2-ol.

See figure 1 to further explanations

I hope it helps!

Answer:

Yes, same piece can be used.

Explanation:

The same piece can be used for two different atoms are acceptable because both atoms has 7 electrons in their outermost valance shell. Both atoms belong to same group i. e. halogens so same piece can be used for both atoms. If the atoms belong to different groups and they have different number of electrons in their outermost shell so using same piece will be a problem so it is recommended to use different pieces for different atoms.

The use of the same modeling piece for chlorine and fluorine has been accepted as it has consisted of the same properties and belongs to the same group.

Chlorine and fluorine have been the elements of group 17. The elements are halogens with the presence of 7 valence electrons.

The elements have been belonging to the same group and have the same number of valence electrons thus resembling each other in the chemical properties.

Since both the elements are similar to each other, the use of the same piece for two different atoms has been acceptable.

For more information about the modeling piece, refer to the link:

https://brainly.com/question/701369

The given question is incomplete.

The complete question is:

When methane is burned with oxygen, the products are carbon dioxide and water. If you produce 9 grams of water and 11 grams of carbon dioxide from 16 grams of oxygen, how many grams of methane were needed for the reaction?

Answer: 4 grams of methane were needed for the reaction

Explanation:

According to the law of conservation of mass, mass can neither be created nor be destroyed. Thus the mass of products has to be equal to the mass of reactants. The number of atoms of each element has to be same on reactant and product side. Thus chemical equations are balanced.

{tex]CH_4+2O_2\rightarrow CO_2+H_2O[/tex]

Given:  mass of oxygen = 16 g

Mass of carbon dioxide = 11 g

Mass of water = 9 g

Mass of products = Mass of carbon dioxide + mass of water = 11 g  +9 g = 20 g

Mass or reactant = mass of methane + mass of oxygen = mass of methane + 16 g

As mass of reactants = mass of products

mass of methane + 16 g= 20 g

mass of methane  = 4 g

Thus 4 grams of methane were needed for the reaction

Answer:

[tex]E=2.06\times 10^{-19}\ J[/tex]

Explanation:

Given that,

The wavelength of electromagnetic radiation is 963.5 nm.

We need to find the energy of a photon with this wavelength.

The formula used to find the energy of a photon is given by :

[tex]E=\dfrac{hc}{\lambda}\\\\E=\dfrac{6.63\times 10^{-34}\times 3\times 10^8}{963.5\times 10^{-9}}\\\\E=2.06\times 10^{-19}\ J[/tex]

So, the energy of a photon is [tex]2.06\times 10^{-19}\ J[/tex].

Answer:

When balancing redox reactions under basic conditions in aqueous solution, the first step is to balance oxygen.

Explanation:

Oxidation-reduction reactions or redox reactions are those in which an electron transfer occurs between the reagents. An electron transfer implies that there is a change in the number of oxidation between the reagents and the products.

The gain of electrons is called reduction and the loss of electrons oxidation. That is to say, there is oxidation whenever an atom or group of atoms loses electrons (or increases its positive charges) and in the reduction an atom or group of atoms gains electrons, increasing its negative charges or decreasing the positive ones.

The oxidation and reduction half-reactions, in a basic medium, adjust the oxygens and hydrogens as follows:

In the member of the half-reaction that presents excess oxygen, you add as many water molecules as there are too many oxygen. Then, in the opposite member, the necessary hydroxyl ions are added to fully adjust the half-reaction. Normally, twice as many hydroxyl ions, OH-, are required as water molecules have previously been added.

In short, you first adjust the oxygens with OH-, then you adjust the H with H₂O, and finally you adjust the charge with e-

So, when balancing redox reactions under basic conditions in aqueous solution, the first step is to balance oxygen.

Answer:

c. balance the reaction as though under acidic conditions

Explanation:

When balancing redox reactions under basic conditions, a good technique is to first balance the reaction as though under acidic conditions. We then adjust the result to reflect the basic conditions.

Answer:

Bronsted lowry base = Proton acceptor = H2O

Bronsted lowry acid = Proton donor = HF-

Explanation:

The equation is given as;

HF-(aq) + H2O(l) --> F-(aq) + H3O(aq)

A bronsted lowry base is any specie that can accept hydrogen ion (proton) from another molecule.

Basically a bronsted lowry base is  a proton acceptor while a bronsted lowry acid is a proton donor.

In the reaction above, upon comparing both the reactants and products;

Bronsted lowry base = Proton acceptor = H2O

Bronsted lowry acid = Proton donor = HF-

Answer:

measure the parallax and use it in calculations

Explanation:

got it right on test

There are many more stars at different distances from the earth. The distance to the stars calculated in light years and it is measured using parallax method.Thus option a is correct.

Parallax method is used to measure the approximate distance of stars from earth. It uses the position of nearby star from two points opposite to earth and the small angular displacement observed from the remote stars are noted.

The orbit radius of earth and distance to the stars can be calculated from the parallactic angle p, that is one second of arc. Thus the distance is described in the units parsec.

The distance to the stars are usually calculated in light years. One parsec equals 3.26 light years. The nearest star to earth is named as proxima century having the distance parallax 0.76813'' which equals 4.24 light years. Thus, parallax is inversely proportional to the distance.

To find more on parallax method, refer here:

https://brainly.com/question/13046118

#SPJ2

Answer: C. the same amount of energy as

Explanation:

A reversible reaction is a chemical reaction where the reactants form products that, in turn, react together to give the reactants back.

Reversible reactions will reach an equilibrium point where the concentrations of the reactants and products will no longer change.

[tex]A+B\rightleftharpoons C+D[/tex]

Thus if forward reaction is exothermic i.e. the heat is released , the backward reaction will be endothermic i.e. the heat is absorbed and in same amount.

The amount of energy released will be equal and opposite in sign to the energy absorbed in that reaction.

Answer:

C.) the same amount of energy as

Explanation:

I got it correct on founders edtell

Answer:

Entropy change of ice changing to water at 0°C is equal to 57.1 J/K

Explanation:

When a substance undergoes a phase change, it occurs at constant temperature.

The entropy change Δs, is given by the formula below;

Δs = q/T

where q is the quantity of heat absorbed or evolved in Joules and T is temperature in Kelvin at which the phase change occur

From the given data, T = 0°C = 273.15 K, q = 15.6 KJ = 15600 J

Δs = 15600 J / 273.15 K

Δs = 57.111 J/K

Therefore, entropy change of ice changing to water at 0°C is equal to 57.1 J/K

The entropy change of ice changing to water will be "57.1 J/K".

The shift in what seems like a thermodynamic system's condition of confusion is caused by the transformation of heat as well as enthalpy towards activity. Entropy seems to be greater mostly in a network with a high quantity or measure of chaos.

According to the question,

Temperature, T = 0°C or,

                          = 273.15 K

Heat, q = 15.6 KJ or,

            = 15600 J

We know the formula,

Entropy change, Δs = [tex]\frac{q}{T}[/tex]

By substituting the values, we get

                                 = [tex]\frac{15600}{273.15}[/tex]

                                 = 57.11 J/K

Thus the above answer is correct.    

Find out more information about Entropy change here:

https://brainly.com/question/6364271

Answer:

1.84 × 10⁻³

Explanation:

Step 1: Write the balanced equation

2 NOBr(g) ⇄ 2 NO(g) + Br₂(g)

Step 2: Calculate the initial concentration of NOBr

0.143 moles of NOBr(g) are introduced into a 1.00 liter container. The molarity is:

M = 0.143 mol / 1.00 L = 0.143 M

Step 3: Make an ICE chart

         2 NOBr(g) ⇄ 2 NO(g) + Br₂(g)

I             0.143               0           0

C              -2x               +2x        +x

E          0.143-2x            2x          x

Step 4: Find the value of x

The equilibrium concentration of NOBr(g) was 0.108 M. Then,

0.143-2x = 0.108

x = 0.0175

Step 5: Calculate the concentrations at equilibrium

[NOBr] = 0.108 M

[NO] = 2x = 0.0350 M

[Br₂] = x = 0.0175 M

Step 6: Calculate the equilibrium constant (Kc)

Kc = [0.0350]² × [0.0175] / [0.108]²

Kc = 1.84 × 10⁻³

Answer:

Explanation:

[tex]H_3O^+[/tex] also known as hydronium ion is formed as a result of the reaction between an hydrogen proton and a water molecules.

i.e [tex]\mathtt{H^+ + H_2O \to H_3O^+}[/tex]

(molecular geometry for the hydronium ion shows that the lewis structure of hydronium ion possess a three hydrogen ion bonded to a central atom known as oxygen. The oxygen possess a lone pair with a positive ion. So we have three hydrogen atoms and a lone pair attached to the oxygen. We can now say that there are four groups as the steric number in which one of them is a lone pair. This give rise to the trigonal pyramidal shape of the [tex]H_3O^+[/tex] (hydronium ion) with a bond angle of about 109,5°

Similarly, [tex]NH_3[/tex] on the other hand also known as ammonia has a shape that can be also determined by the Lewis structure.

IN ammonia,  there are three hydrogen  and a lone pairs of electron spreading out as far away from each other  from the centre nitrogen. In essence, the valence shell electron pair around hydrogens tend to repel each other. Hence, giving it a trigonal pyramidal shape.

From above the similarities between H3O and NH3 is in their molecular geometry in which both  H3O and NH3 have the same shape.

These molecules are called isoelectronic. Why?

Isoelectronic molecules are molecules having the same number of electrons and same electronic configuration  structure. As a result H3O and NH3 possess the same  number of electrons in the same orbitals and they also posses the same structure.

Answer:

The answer is noble gases

Explanation:

Here is your explanation The vertical columns are called groups. There are eighteen groups. The last group on the far right is called the noble, or inert gases. Elements in a group have similar chemical properties. For example, elements in the noble gas group are all gases under. This is the thing from the passege bye god bless you

The last group of elements on the periodic table are called "noble gases."

The noble gases are a group of elements located in Group 18 of the periodic table. They are also known as Group 0 or the "inert gases." The noble gases include helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and radon (Rn).

The noble gases are unique because they have a full complement of valence electrons in their outermost energy level. This full electron configuration gives them exceptional stability, making them chemically unreactive or inert under normal conditions. In other words, noble gases are less likely to form chemical bonds with other elements.

Learn more about noble gases from the link given below.

https://brainly.com/question/19024000

#SPJ2

Answer:

False

Explanation:

Reaction rates is a field under chemical kinetics that deals with the measure of speed of a chemical reaction. It is the change in the concentration of a reactant or product per unit time.

Activation Energy is a theory been  put forward to explain why different chemical reactions proceed at different rates.

Activation Energy theory postulates that for a reactant to transform into a product , the colliding particles or molecules of the reactant must possess a certain amount of energy so as to overcome the reaction barrier.

An important factor which may influence the attainment of activation energy by colliding particles of reactants is the temperature at which the reaction is carried out. The higher the temperature, the  greater is the fraction of the reactant particles which possess the activation energy and thus the faster the reaction becomes. SO , in essence increasing the temperature of a reaction system do not decreases the activation energy of the reaction but rather also increases  the activation energy of the reaction.

Answer:

(R)-but-3-en-2-ylbenzene

Explanation:

In this reaction, we have a very strong base (sodium ethoxide). This base, will remove a hydrogen producing a double bond. We know that the reaction occurs through an E2 mechanism, therefore, the hydrogen that is removed must have an angle of 180º with respect to the leaving group (the "OH"). This is known as the anti-periplanar configuration.

The hydrogen that has this configuration is the one that placed with the dashed bond (red hydrogen). In such a way, that the base will remove this hydrogen, the "OH" will leave the molecule and a double bond will be formed between the methyl and the carbon that was previously attached to the "OH", producing the molecule (R) -but-3- en-2-ylbenzene.

See figure 1

I hope it helps!

Answer:

The correct answer is 206 ml.

Explanation:

Based on the given information, the molarity or M₁ of MgF₂ solution is 0.0887 M, the molarity or M₂ of the final solution given is 0.0224 M. The initial volume of V₁ of the solution is 69.6 ml, for finding the final volume of V₂ of the solution, the formula to be used is,  

M₁V₁ = M₂V₂

Now putting the values in the formula we get,  

0.0887 × 69.6 = 0.0224 M × V₂

V₂ = 0.0887 × 69.6 / 0.0224

V₂ = 275.6 ml

Therefore, the volume in ml added to the initial volume of 69.6 ml to make the molarity of the solution 0.0224 will be,  

= 275.6 ml - 69.6 ml = 206 ml

Answer:

Jesseca Kusher, an 18-year-old researcher from Spartansburg, S.C., invented a paint-on coating for roofing shingles. Her formula could reduce a home's cooling costs and possibly cut ozone pollution in urban areas...

SUPPORT ME ...........

Answer:

Jesseca created mixtures containing graphite, gypsum, and mica that could be painted on roof shingles.

Explanation:

Hope this helped!!

Answer:

The two elements with atomic number 9 and 12 are represented by letter Q and R respectively, where Q represents fluorine atom and R represents magnesium atom.

1. Electronic configuration of R that is magnesium (atomic number 12) is:

1s2 2s2 2p6 3s2

2. Q represents fluorine atom, which belongs to group 17 in periodic table that is the most reactive and lightest member of the group.

3. Q and R that is fluorine and magnesium combinely form magnesium fluoride or MgF2.

Answer:

Electrons "surround"

Explanation:

Protons and neutrons "make up" the nucleus so they are contained "within" the nucleus meaning that electrons would "surround" the nucleus as they orbit around the nucleus

Answer:

Electrons

Explanation:

Protons and nuetrons are present inside the nucleus of an atom while the electron revolve around the nucleus in different energy levels.

Answer:

a. Ca₃(PO₄)₂.

b. 0.010 moles of Ca₃(PO₄)₂ can we expect to be produced

c. 3.1g of Ca₃(PO₄)₂

d. Percent yield = 93.5%

Explanation:

a. Based on the reaction:

3Ca(NO₃)₂(aq) + 2Na₃PO₄(aq) → Ca₃(PO₄)₂(s) + 6NaNO₃(aq)

3 moles of calcium nitrate reacts with 2 moles of sodium phosphate producieng 1 mole of calcium phosphate.

As you can see, Ca₃(PO₄)₂ is a solid product -(s)-, that means when the reaction occurs the precipitate produced is the solid,

b. As 3 moles of calcium nitrate produce 1 mole of calcium phosphate and there are 0.030 moles of calcium nitrate

0.030 moles Ca(NO₃)₂ × (1 mol Ca₃(PO₄)₂ / 3 moles Ca(NO₃)₂) =

c. As molar mass of Ca₃(PO₄)₂ is 310.18g/mol, the mass of 0.010 moles (The expected mass) is;

0.010 moles Ca₃(PO₄)₂ × (310.18g / mol) =

d. The percent yield is defined as 100 times the ratio between the obtained yield (That is 2.9g of precipitate, Ca₃(PO₄)₂) and the expected yield, 3.1g of Ca₃(PO₄)₂:

[tex]\frac{2.9g}{3.1g} *100[/tex]

(a) The product in solid state would be the precipitate. Hence, the precipitate would be Ca3(PO4)2

(b) From the balanced equation of the reaction: 3 moles of Ca(NO3)2 is required for 1 mole of Ca3(PO4)2

If there are just 0.030 moles of Ca(NO3)2, then"

3 moles = 1

0.030 moles =    1 x 0.030/3

                         = 0.01 moles of Ca3(PO4)2

In other words, 0.01 moles of the precipitate would be expected to be produced from 0.030 moles of calcium nitrate.

(c) 0.01 moles solid (Ca3(PO4)2) is expected. Mass of Ca3(PO4)2 expected:

      mass   = mole x molar mass

molar mass of Ca3(PO4)2 = 310.18 g/mol

mass of Ca3(PO4)2 expected to be produced = 0.01 x 310.18

                                                                       = 3.1018 g

Hence, 3.1018g of solid is expected to be produced.

(d) Percentage yield = actual yield/theoretical yield x 100

                          = 2.9/3.1018 x 100

                               = 93.5%

More on precipitation reaction can be found here:  https://brainly.com/question/24158764

Answer:2.62 L

Explanation:

A sample of gas occupies a volume of 2.62 liters at 25° C and 1.00 atm. and the volume at 50° C and 2 atm then volume is 2.62 liters.

The equation of state for a fictitious perfect gas is known as the ideal gas law, sometimes known as the generic gas equation. Although it has significant drawbacks, it is a decent approximation of the behavior of many gases under various situations.

An ideal gas is one in which there are no intermolecular attraction forces and all collisions between atoms or molecules are entirely elastic. It may be seen as a group of perfectly hard spheres that collide but do not else interact with one another.

By using ideal gas equation,

P₁ V ₁ ÷ T = P₂V₂ ÷ T

1 × 2.62 ÷ 25 = 2 × V₂ ÷ 50

V₂ = 1 × 2.62 × 50 ÷ 25 × 2

V₂ = 2.62 liters.

Thus, a sample of gas occupies a volume of 2.62 liters at 25° C and 1.00 atm. and the volume at 50° C and 2 atm then volume is 2.62 liters.

To learn more about ideal gas law follow the link below;

https://brainly.com/question/6534096

#SPJ5

Answer:

All of the above processes have a ΔS < 0.

Explanation:

ΔS represents change in entropy of a system. Entropy refers to the degree of disorderliness of a system.

The question requests us to identify the process that has a negative change of entropy.

carbon dioxide(g) → carbon dioxide(s)

There is  a change in state from gas to solid. Solid particles are more ordered than gas particles so this is a negative change in entropy.

water freezes

There is  a change in state from liquid to solid. Solid particles are more ordered than liquid particles so this is a negative change in entropy.

propanol (g, at 555 K) → propanol (g, at 400 K)

Temperature is directly proportional to entropy, this means higher temperature leads t higher entropy.

This reaction highlights a drop in temperature which means a negative change in entropy.

methyl alcohol condenses

Condensation is the change in state from gas to liquid. Liquid particles are more ordered than gas particles so this is a negative change in entropy.

Answer:1 )T2=134°C   2) T2=339.48°C. 3)

P=817.59 mmHg.

Explanation:

1.Given ;

pressure, P1 of neon gas = 0.646 atm

temperature, T1 =242oC + 273=515oC

Volume, V1 =515ml

Volume V2= 407ml

temperature , T 2= ?

Solution;

And at constant pressure, the volume cools at V2=407 mL at T2=?

From ideal gas equation, PV=nRT

V/T=constant

therefore

V1/V2=T1/T2 = T2=(V2 xT1)/V1

T2=(407 mL x 515 K)/515 mL= 407K.

T2= 407K -273= 134°C.   recall 0°C=273 K)

2..Given ;

pressure, P1 of neon gas = 0.633 atm

temperature, T1 =261oC + 273=534oC

Volume, V1 =694ml

Volume V2= 796ml

temperature , T 2= ?

Solution;

And at constant pressure, the volume expands  at V2=796mL at T2=?

From ideal gas equation, PV=nRT

V/T=constant

therefore

V1/V2=T1/T2 = T2=(V2 xT1)/V1

T2=(796 mL x 534 K)/694mL= 612.48K.

T2= 612.48K -273= 339.48°C. recall 0°C=273 K

3

Given;

moles of CO2= n=0.962 mol,

temperature T=20°C=20+273 K =293 K,

volume V=21.5 L,

gas constant R at L·mmHg/mol·K= 62.3637 L mmHg mol^-1 K^-1

Using  ideal gas equation PV=nRT

P=nRT/V

P=(0.962 mol)x(62.3637mmHg mol^-1 K^-1)x(293 K)/(21.5L)

P=817.59 mmHg.

Answer:

37.8 L OF CARBON MONOXIDE IS REQUIRED TO PRODUCE 18.9 L OF NITROGEN.

Explanation:

Equation for the reaction:

2 CO + 2 NO ------> N2 + 2 CO2

2 moles of carbon monoxide reacts with 2 moles of NO to form 1 mole of nitrogen

At standard temperature and pressure, 1 mole of a gas contains 22.4 dm3 volume.

So therefore, we can say:

2 * 22.4 L of CO produces  22.4 L of N2

44.8 L of CO produces 22.4 L of N2

Since, 18.9 L of Nitrogen is produced, the volume of CO needed is:

44.8 L of CO = 22.4 L of N

x L = 18.9 L

x L = 18.9 * 44.8 / 22.4

x L = 18.9 * 2

x = 37.8 L

The volume of Carbon monoxide required to produce 18.9 L of N2 is 37.8 L

Answer:

37.8

Explanation:

Answer:

804 J

Explanation:

Step 1: Given data

Step 2: Calculate the energy required (Q)

We will use the following expression.

Q = c × m × ΔT

Q = 0.0235J·g⁻¹K⁻¹ × (1.50 × 10³g) × [15.0°C-(-7.8°C)]

Q = 804 J

Answer:

The length the divider is to  equilibrium from Part A = 1.30 m and from Part B = 3.70 m

Explanation:

Given that:

A rectangular cube with 3.2 m breadth, 1.2 m height and 5 m in length is splitted into two parts.

The diagrammatic expression for the above statement can be found in the attached diagram below.

The container has a movable airtight divider that divides its length as necessary.

Part A has 58 moles of gas

Part B has 165 moles of a gas.

Thus, the movable airtight divider will stop at a length where the pressure on it is equal on both sides.

i.e

[tex]\mathtt{P = P_A = P_B}[/tex]

Using the ideal gas equation,

PV = nRT

where, P,R,and  T are constant.

Then :

[tex]\mathsf{\dfrac{V_A}{n_A}= \dfrac{V_B}{n_B}}[/tex]

[tex]\mathsf{\dfrac{L_A \times B \times H}{n_A}= \dfrac{L_B \times B \times H}{n_B}}[/tex] --- (1)

since Volume of a cube = L × B × H

From the question; the L = 5m

i,e

[tex]\mathsf{L_A +L_B}[/tex] = 5

[tex]\mathsf{L_A = 5 - L_B}[/tex]

From equation (1) , we divide both sides by (B × H)

Then :

[tex]\mathsf{\dfrac{L_A }{n_A}= \dfrac{L_B }{n_B}}[/tex]

[tex]\mathsf{\dfrac{5-L_B}{58}= \dfrac{L_B }{165}}[/tex]

By cross multiplying; we have:

165 ( 5 - [tex]\mathsf{L_B}[/tex] )  = 58 (

825 - 165[tex]\mathsf{L_B}[/tex]  = 58

825 = 165[tex]\mathsf{L_B}[/tex] +58

825 = 223[tex]\mathsf{L_B}[/tex]

[tex]\mathsf{L_B}[/tex] = 825/223

[tex]\mathsf{L_B}[/tex]  = 3.70 m

[tex]\mathsf{L_A = 5 - L_B}[/tex]

[tex]\mathsf{L_A = 5 - 3.70}[/tex]

[tex]\mathsf{ L_A}[/tex] = 1.30 m

The length the divider is to  equilibrium from Part A = 1.30 m and from Part B = 3.70 m