Ionic Equilibrium

At 300 K, the molar conductivities of the aqueous solutions of three salts at two different concentrations are given below:

Salt	Concentration (M)	Molar conductivity (S cm$^2$ mol$^{-1}$)
$\ce{NaNO3}$	0.01	111
	0.04	101
$\ce{NaCl}$	0.01	117
	0.04	107
$\ce{AgNO3}$	0.01	125
	0.04	116

The conductivity of a saturated aqueous solution of AgCl is $1.40\times10^{-6}$ S cm$^{-1}$ at 300 K. If the solubility of AgCl in water at 300 K is X mol L$^{-1}$, then $\log_{10}(X^{-1})$ is

(Assume that AgCl dissolved in water ionizes completely and that the molar conductivity of saturated AgCl solution is equal to its limiting molar conductivity.)

At a given temperature, 0.45 g of acetic acid in 50 mL of water is shaken with 1.0 g of charcoal and the pH of the resulting solution is 3.0. Assume the adsorption of acetic acid from the aqueous solution by charcoal follows Freundlich isotherm,
$$\frac xm=kC^{1/n}$$
If the plot of $\log_{10}(x/m)$ against $\log_{10}C$ gives a straight line with slope 1, the value of $k$ in L mol$^{-1}$ is ____.

Given: The molar mass of acetic acid is 60 g mol$^{-1}$.
The acid dissociation constant of acetic acid is $1.0\times10^{-5}$ at the given temperature.
$x$ is the mass (in grams) of acetic acid adsorbed.
$m$ is the mass (in grams) of charcoal.
$C$ is the equilibrium concentration of acetic acid in the solution after the adsorption is complete.
$k$ and $n$ are constants for acetic acid-charcoal system at the given temperature.

19.5 g of fluoro acetic acid (molar mass = 78 g mol$^{-1}$) is dissolved in 500 g of water at 298 K. The depression in the freezing point of water was 1 °C. What is $K_a$ of fluoro acetic acid ? (For water, $K_f=1.86$ K kg mol$^{-1}$). Assume molarity and molality to have same values.

The solubility product constants of $\ce{Ag2CrO4}$ and AgBr are $32x$ and $4y$ respectively at 298 K. The value of $\left(\dfrac{\text{molarity of }\ce{Ag2CrO4}}{\text{molarity of AgBr}}\right)$ can be expressed as :

The first and second ionization constants of a weak dibasic acid $\ce{H2A}$ are $8.1\times10^{-8}$ and $1.0\times10^{-13}$ respectively. 0.1 mol of $\ce{H2A}$ was dissolved in 1 L of 0.1 M HCl solution. The concentration of $\ce{HA-}$ in the resultant solution is :

At 25 °C, 20.0 mL of 0.2 M weak monoprotic acid HX is titrated against 0.2 M NaOH. The pH of the solution (a) at the start of the titration (when NaOH has not been added) and (b) when 10 mL of NaOH is added respectively, are :
Given : $K_a=5\times10^{-4}$, $pK_a=3.3$, $\alpha\ll1$

Identify the colour of compound 'X' in the sequence of the reaction.

The pH of a solution obtained by mixing 5 mL of 0.1 M $\ce{NH4OH}$ solution with 250 mL of 0.1 M $\ce{NH4Cl}$ solution is ________ $\times10^{-2}$. (Nearest integer)
Given: $pK_b(\ce{NH4OH})=4.74$, $\log2=0.30$, $\log3=0.48$, $\log5=0.70$

20 mL of a solution of acetic acid required 28.4 mL of 0.1 M NaOH for its neutralization. A solution (X) was prepared by mixing 20 mL of the above acetic acid and 14.2 mL of 0.1 M NaOH solution. What is the pH of the solution (X)?
($pK_a$ value of acetic acid is 4.75).

$\ce{M3A2}$ is a sparingly soluble salt of molar mass $y$ g mol$^{-1}$ and solubility $x$ g L$^{-1}$. The ratio of the molar concentration of the anion ($\ce{A^{3-}}$) to the solubility product of the salt is

Arrange the following resultant mixtures in increasing order of their pH values

A. 10 mL 0.2 M $\ce{Ca(OH)2}$ + 25 mL 0.1 M HCl

B. 10 mL 0.01 M $\ce{H2SO4}$ + 10 mL 0.01 M $\ce{Ca(OH)2}$

C. 10 mL 0.1 M $\ce{H2SO4}$ + 10 mL 0.1 M KOH

Choose the correct answer from the options given below:

Given below are two statements:

Statement I: Sodium dichromate and potassium dichromate are classified as primary standards in titrimetric analysis.

Statement II: Phenolphthalein is a weak base, therefore it dissociates in acidic medium.

In the light of the above statements, choose the correct answer from the options given below

Consider the following data.

Electrolyte	$\Lambda^\circ_m$ (S cm² mol$^{-1}$)
$\ce{BaCl2}$	$x_1$
$\ce{H2SO4}$	$x_2$
HCl	$x_3$

$\ce{BaSO4}$ is sparingly soluble in water. If the conductivity of the saturated $\ce{BaSO4}$ solution is $x$ S cm$^{-1}$ then the solubility product of $\ce{BaSO4}$ can be given as

(Here $\Lambda_m=\Lambda^\circ_m$)

Given is a concentrated solution of a weak electrolyte $A_xB_y$ of concentration '$c$' and dissociation constant '$K$'. The degree of dissociation is given by :

At 25 °C, the concentration of $\ce{H+}$ ions in $1.00\times10^{-3}$ M aqueous solution of a weak monobasic acid having acid dissociation constant ($K_a$) of $4.00\times10^{-11}$ is $\boldsymbol{X}\times10^{-7}$ M. The value of $\boldsymbol{X}$ is _____.

Use: Ionic product of water $(K_w) = 1.00\times10^{-14}$ at 25 °C

The solubility of barium iodate in an aqueous solution prepared by mixing 200 mL of 0.010 M barium nitrate with 100 mL of 0.10 M sodium iodate is $\boldsymbol{X}\times10^{-6}\ \mathrm{mol\,dm^{-3}}$. The value of $\boldsymbol{X}$ is _____.

Use: Solubility product constant ($K_{sp}$) of barium iodate $= 1.58\times10^{-9}$

In a conductometric titration, small volume of titrant of higher concentration is added stepwise to a larger volume of titrate of much lower concentration, and the conductance is measured after each addition.

The limiting ionic conductivity ($\Lambda_0$) values (in $\mathrm{mS\,m^2\,mol^{-1}}$) for different ions in aqueous solutions are given below:

Ions	$\ce{Ag+}$	$\ce{K+}$	$\ce{Na+}$	$\ce{H+}$	$\ce{NO3-}$	$\ce{Cl-}$	$\ce{SO4^2-}$	$\ce{OH-}$	$\ce{CH3COO-}$
$\Lambda_0$	6.2	7.4	5.0	35.0	7.2	7.6	16.0	19.9	4.1

For different combinations of titrates and titrants given in List-I, the graphs of 'conductance' versus 'volume of titrant' are given in List-II.

Match each entry in List-I with the appropriate entry in List-II and choose the correct option.

To form a complete monolayer of acetic acid on 1 g of charcoal, 100 mL of 0.5 M acetic acid was used. Some of the acetic acid remained unadsorbed. To neutralize the unadsorbed acetic acid, 40 mL of 1 M NaOH solution was required. If each molecule of acetic acid occupies $\mathbf{P}\times10^{-23}\,\mathrm{m^2}$ surface area on charcoal, the value of P is _____.

[Use given data: Surface area of charcoal $= 1.5\times10^2\,\mathrm{m^2\,g^{-1}}$; Avogadro's number $(N_A) = 6.0\times10^{23}\,\mathrm{mol^{-1}}$]

Plotting $1/\Lambda_\mathrm{m}$ against $c\Lambda_\mathrm{m}$ for aqueous solutions of a monobasic weak acid (HX) resulted in a straight line with y-axis intercept of P and slope of S. The ratio $\mathrm{P}/\mathrm{S}$ is

[$\Lambda_\mathrm{m}$ = molar conductivity; $\Lambda^\circ_\mathrm{m}$ = limiting molar conductivity; c = molar concentration; $K_\mathrm{a}$ = dissociation constant of HX]

On decreasing the $p\mathrm{H}$ from 7 to 2, the solubility of a sparingly soluble salt (MX) of a weak acid (HX) increased from $10^{-4}\,\mathrm{mol\,L^{-1}}$ to $10^{-3}\,\mathrm{mol\,L^{-1}}$. The $pK_\mathrm{a}$ of HX is