what happens to the hydrogen gas that is bubbled in SHE

 

electronegativity vs reduction potential

 

Periodic trends in electronegativity

 

Periodic trends in reduction potentials

 

Relation between kp and kc for gaseous reactions

 

why does the voltage of a galvanic cell becomes zero at equilibrium?

 A galvanic cell's voltage drops to zero at equilibrium because the electrical potential of the two half-cells becomes perfectly equal. The cell produces voltage by allowing a spontaneous redox reaction to occur. At equilibrium, the forward and reverse reactions proceed at the exact same rate, meaning no net work can be done and no electrons can flow through the external circuit.  As the cell operates, products are formed and reactants are consumed, driving the reaction quotient Q toward the equilibrium constant K. At chemical equilibrium, Q = K.

Because there is no longer a driving force for the reaction, the Gibbs free energy change Delta G equals zero. Consequently, the cell potential Ecell drops to exactly '0'volts.

Mathematicaly we know that

Delta G = -nFEcell = -(nF)V = - (total charge transfered) x Voltage = work done by the cell = loss in its potential energy.

so Delta G = 0 is possible only when Ecell = 0

Helpful Videos:

Nernst equation and cell emf

Galvanic cells

As the reaction approaches equilibrium, the anode and cathode half-cells alter their concentrations:

At the anode: The concentration of oxidized species (products) increases, making it less negative.

At the cathode: The concentration of reduced species (reactants) decreases, making it less positive.

At equilibrium, the reduction potentials of both electrodes become completely equal, making the potential difference (voltage) between them zero.

As the cell runs, reactants are consumed and products are formed, which causes Q to increase. This causes the subtracting term to grow , steadily decreasing the voltage. At equilibrium, the reaction quotient equals the equilibrium constant Q = K, and the equation becomes E cell = 0. 

Because as Q approaches K , (RT/nF)ln(Q) becomes = Ecell_standard. Hence Ecell = 0.

4 major effects of inserting a dielectric slab inside a parallel plate capacitor

 

(i) Electric filed DECREASES by a factor K

Enew = Eold/K 

(ii) Capacitance INCREASES by a factor K

Cnew = KCold

(iii)

Voltage DECREASES by a factor K

Vnew = Vold/K

(iv) 

PERMITIVITY of capacitor INCREASES by a factor K

ε = Kε₀

Is the number of all INTO functions from the set {1, 2, 3, ..... n} to itself equal to all number of MANY to ONE fuctions?

Yes,  the number of all into functions from the set {1, 2, 3, .... n} to itself is exactly equal to the number of many-to-one functions for all positive integers n, as both are quantified by the formula n^n - n!

Find the number of all INTO functions from the set {1, 2, 3, ..... n} to itself

 

Is a ONE to MANY relation a function?

 

Is a MANY to MANY relation a function?

 

find the number of all BIJECTIVE functions from the set {1, 2, 3, ..... n} to itself

 

find the number of all ONE - ONE functions from the set {1, 2, 3, ..... n} to itself

 It is same as number of all ONTO functions, because if a set of FINITE number of elements is ONTO then it is ONE - ONE too.

find the number of all MANY - ONE functions from the set {1, 2, 3, ..... n} to itself

 

Find the number of all ONTO functions from the set {1, 2, 3, ..... n} to itself

 

If a function f in set A = {1,2,3,.......n} is ONTO then , it is ONE - ONE too?

 

Correct solution of class 12 NCERT physics book

 

The given solution is wrong. 

My google query: work is done on the dipole, therefore there should be gain in its potential energy?

Following is the correct solution by google AI search:

What is a Redox Couple

 

why we take the electrolyte of the same substance?

Potential energy of a dipole in a uniform electric field

 

Function of Salt Bridge in a Voltaic cell

 Salt Bridge video

The depression in freezing point of water observed for the same amount of acetic acid, trichloroacetic acid and trifluoroacetic acid increases in the order given above. Explain briefly.

 Depression in freezing point is a colligative property that depends on the number of solute particles in a solution. Since the order of depression is 

Acetic acid < Trichloroacetic acid < Trifluoroacetic acid

It means the number of ions produced in the solution increases in the same order. 

This increase in ionization relates directly to the acidic strength of each acid: 

Trifluoroacetic acid (CF3COOH) has the strongest electron-withdrawing inductive effect due to the highly electronegative fluorine atoms, making it the strongest acid. It ionizes to the largest extent in water, producing the highest number of ions. 
Trichloroacetic acid (CCl3COOH) is weaker than the trifluoro derivative because chlorine is less electronegative than fluorine, resulting in a moderate degree of ionization. 
Acetic acid (CH3COOH) is the weakest acid because the methyl group (CH3) is electron-donating effect, which hinders ionization. It produces the fewest ions.

Because a greater degree of dissociation results in more solute particles, the depression in freezing point is maximum for trifluoroacetic acid and minimum for acetic acid.

Suggest the most important type of intermolecular attractive interaction in the following pairs. (i) n-hexane and n-octane (ii) 12 and CC14 (iii) NaCIO, and water (iv) methanol and acetone (v) acetonitrile (CH3CN) and acetone (C3H6O).

 Here are the most important types of intermolecular attractive interactions for each pair based on their molecular structures and polarities: 

(i) n-hexane and n-octane: Both are nonpolar hydrocarbons. The primary interaction is London dispersion forces.
(ii) (I2) and (CCl4: Both are nonpolar molecules. The primary interaction is London dispersion forces.
(iii) (NaClO4) and water: (NaClO4) is an ionic compound that dissociates into ions, and water is polar. The interaction is an ion-dipole interaction.
(iv) Methanol and acetone: Both are polar molecules, and methanol features a hydroxyl (-OH) group. The most important interaction is hydrogen bonding.
(v) Acetonitrile (CH3CN) and acetone (C3H6O): Both are polar molecules lacking (H) directly attached to highly electronegative atoms. The primary interaction is dipole-dipole interactions

Based on solute-solvent interactions, arrange the following in order of increasing solubility in n-octane and explain. Cyclohexane, KCI, CH3OH, CH3CN.

 The correct arrangement of the given compounds in order of increasing solubility in n-octane is:

KCl < CH3OH< CH3CN < Cyclohexane 

---

Explanation based on Solute-Solvent Interactions

The rule governing solubility is "like dissolves like", which means polar/ionic solutes dissolve in polar solvents, and non-polar solutes dissolve in non-polar solvents.

Nature of Solvent: n-Octane (C8H18) is a long-chain hydrocarbon and is entirely non-polar.
Cyclohexane (Most Soluble): Like n-octane, cyclohexane (C6H12) is a non-polar hydrocarbon. The solute-solvent interactions involved are weak London dispersion forces. Because their natures are identical, they mix completely in all proportions.
(CH3CN) (Acetonitrile): It is a polar molecule due to the cyano (-CN) group, but it lacks the capability to form strong intermolecular hydrogen bonds. Therefore, it is less tightly held to itself than methanol and exhibits relatively better compatibility with the non-polar solvent.
(CH3OH) (Methanol): It is a highly polar molecule capable of strong intermolecular hydrogen bonding. Because breaking these hydrogen bonds to fit into a non-polar hydrocarbon solvent is energetically unfavorable, its solubility in n-octane is lower than that of acetonitrile.
KCl (Least Soluble): Potassium chloride is an ionic compound with high lattice energy. Since a non-polar solvent like n-octane cannot provide ion-dipole interactions to break the ionic lattice, KCl is virtually insoluble in it.

Amongst the following compounds, identify which are insoluble, partially soluble and highly soluble in water? (i) phenol (ii) toluene (iii) formic acid (iv) ethylene glycol (v) chloroform (vi) pentanol.

 

Answer:

Because the following rule of solubility:

*'Like dissolves Like"* i.e. a polar molecule dissolves in other polar molecules and non-polar dissovles in non-polar molecules.

The solubility categorization for each compound in water is as follows:

*Insoluble: (ii) toluene, (v) chloroform* , because Toluene is a non-polar molecule while chloroform is a polar molecule. Here are the specific details for each:

*Toluene (C7H8 ):* Toluene consists of a nonpolar benzene ring and a weakly polar methyl group -CH3). Because carbon and hydrogen have very similar electronegativities (2.55) and (2.20), respectively, the C-H bonds are essentially nonpolar. Although there is a slight asymmetry due to the methyl group, it is negligible, making the molecule as a whole nonpolar overall.

*Chloroform (CHCl3):* Chloroform is a polar molecule with a net dipole moment of roughly (1.04D). It has a tetrahedral molecular geometry, composed of three highly electronegative chlorine atoms (Electronegativity = 3.16) and one hydrogen atom (Electronegativity = (2.20) bonded to the central carbon atom. Because chlorine is significantly more electronegative than carbon, electrons are pulled toward the chlorine atoms, creating a region of partial negative charge on one side and a partial positive charge on the hydrogen side.

*Partially soluble: (i) phenol, (vi) pentanol,* because phenol is highly polar while pentanol is moderately polar molecule. (i) *Phenol (C6H5OH)*

Phenol is a highly polar molecule with a net dipole moment of about (1.5D to 1.7D).

Structure: It consists of a polar hydroxyl group (-OH) directly attached to an aromatic benzene ring (phenyl group).

Resonance Effect: The lone pair of electrons on the oxygen atom overlaps with the pi-electrons of the benzene ring. This delocalization (resonance) enhances the polarity of the O-H bond, making phenol more polar than standard aliphatic alcohols and imparting weakly acidic properties.

*Pentanol (C5H11OH)*

Pentanol is a moderately polar molecule with a net dipole moment similar to small alcohols around (1.6D to 1.7D).

Structure: It features a polar hydroxyl group (-OH) attached to a 5-carbon aliphatic chain (pentyl group).

"Dual" Nature: Pentanol has both a polar end and a nonpolar end. The (-OH) group allows it to engage in hydrogen bonding (making it somewhat soluble in water), while the relatively long 5-carbon nonpolar chain limits its solubility compared to smaller alcohols like methanol or ethanol.

*Highly soluble: (iii) formic acid, (iv) ethylene glycol* , because both are highly polar molecules.

*Formic Acid (HCOOH)*

Polarity: Highly polar.

Reason: It features a strongly polar carboxyl group (–COOH). The highly electronegative oxygen atoms pull electron density away from the carbon and hydrogen atoms.

Dipole Moment: The molecule has an asymmetrical, angular geometry. The uneven distribution of charge yields a distinct net dipole moment (approx 1.4 D).

Solubility: Because of its polarity, it can form strong hydrogen bonds and is infinitely miscible in other polar compunds.

*Ethylene Glycol (HOCH2CH2OH)*

Polarity: Highly polar.

Reason: Ethylene glycol contains two hydroxyl (–OH) groups that are highly polar because oxygen is significantly more electronegative than hydrogen.

Dipole Moment & Geometry: While the two (C–O) bond dipoles can cancel each other out when the molecule is drawn in a straight, fully extended (trans) configuration, this conformation is unstable. Instead, the molecule preferentially adopts a bent or "gauche" configuration due to internal hydrogen bonding. This rotation causes the molecule to have a permanent dipole moment, making it polar.

Why gases always tend to be less soluble in liquids as the temperature is raised?

 Gases are less soluble at higher temperatures because dissolving a gas in a liquid is similar to condensation and heat is evolved during the process. Hence it is an exothermic. 

According to Le Chatelier's Principle, the solubility of a gas or solid in lquid is inversily proportional to temperature for exothermic reactions and directly proportional to endothermic reactions. 

Therefore, as temperature increases gases are less soluble in a liquid. 

What role does the molecular interaction play in a solution of alcohol and water?

 In a solution of alcohol and water, hydrogen bonding is the dominant molecular interaction. The polar hydroxyl group (-OH) in alcohol readily forms hydrogen bonds with water molecules, making them miscible.

The Role of Molecular Interactions

When mixed, the interaction between alcohol and water molecules is inherently weaker than the strong cohesive forces found within pure water and pure alcohol molecules. Because the overall intermolecular attractive forces are reduced upon mixing, molecules can escape into the gas phase much more easily.

This specific behavior drives several key physicochemical outcomes:

Positive Deviation from Raoult's Law: Because the new intermolecular interactions are weaker than the original ones, the solution exhibits a positive deviation from ideal behavior. 
Increased Vapor Pressure: The weaker bonds allow molecules to break free from the liquid surface more readily, significantly increasing the total vapor pressure of the solution compared to what it would be ideally. 
Decreased Boiling Point: Since vapor pressure increases and meets atmospheric pressure at a lower temperature, the boiling point of the resulting alcohol-water mixture becomes lower than that of pure water.

Structural Variations

The strength of these interactions depends heavily on the structure of the alcohol. While smaller alcohols (like ethanol) dissolve perfectly in water due to dominating polar interactions, longer-chain alcohols feature a bulky, non-polar alkyl group that disrupts this hydrogen bonding, drastically decreasing solubility.