Ionic Equilibrium · Chemistry · JEE Main

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

$\mathrm{M}_3 \mathrm{~A}_2$ is a sparingly soluble salt of molar mass $y \mathrm{~g} \mathrm{~mol}^{-1}$ and solubility $x \mathrm{~g} \mathrm{~L}^{-1}$. The ratio of the molar concentration of the anion $\left(\mathrm{A}^{3-}\right)$ to the solubility product of the salt is

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

A. $10 \mathrm{~mL} 0.2 \mathrm{M} \mathrm{Ca}(\mathrm{OH})_2+25 \mathrm{~mL} 0.1 \mathrm{M} \mathrm{HCl}$

B. $10 \mathrm{~mL} 0.01 \mathrm{M} \mathrm{H}_2 \mathrm{SO}_4+10 \mathrm{~mL} 0.01 \mathrm{M} \mathrm{Ca}(\mathrm{OH})_2$

C. $10 \mathrm{~mL} 0.1 \mathrm{M} \mathrm{H}_2 \mathrm{SO}_4+10 \mathrm{~mL} 0.1 \mathrm{M} \mathrm{KOH}$

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

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 $(\mathrm{X})$ ? $\left(\mathrm{pK}_{\mathrm{a}}\right.$ value of acetic acid is 4.75).

The first and second ionization constants of a weak dibasic acid H₂A are $8.1 \times 10^{-8}$ and $1.0 \times 10^{-13}$ respectively. 0.1 mol of H₂A was dissolved in 1 L of 0.1 M HCl solution. The concentration of 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 :
$K_a = 5 \times 10^{-4}$
$\mathrm{p}K_a = 3.3$
$\alpha \ll 1$

The solubility product constants of $\mathrm{Ag_2CrO_4}$ and $\mathrm{AgBr}$ are $32x$ and $4y$ respectively at 298 K.

The value of $$\left( \frac{\text{molarity of } \mathrm{Ag_2CrO_4}}{\text{molarity of } \mathrm{AgBr}} \right)$$ can be expressed as :

Consider a weak base ' B ' of $\mathrm{pK}_{\mathrm{b}}=5.699$. ' $x$ ' mL of 0.02 M HCl and ' y ' mL of 0.02 M weak base ' B ' are mixed to make 100 mL of a buffer of pH 9 at $25^{\circ} \mathrm{C}$. The values of ' $x$ ' and ' $y$ ' respectively are :

[Given : $\log 2=0.3010, \log 3=0.4771, \log 5=0.699$ ]

Which of the following mixture gives a buffer solution with $\mathrm{pH}=9.25$ ?

Given : $\mathrm{pK}_{\mathrm{b}}\left(\mathrm{NH}_4 \mathrm{OH}\right)=4.75$

An aqueous solution of HCl with pH 1.0 is diluted by adding equal volume of water (ignoring dissociation of water). The pH of HCl solution would

$($ Given $\log 2=0.30)$

40 mL of a mixture of $\mathrm{CH}_3 \mathrm{COOH}$ and HCl (aqueous solution) is titrated against 0.1 M NaOH solution conductometrically. Which of the following statement is correct?

If equal volumes of $A B_2$ and $X Y$ (both are salts) aqueous solutions are mixed, which of the following combination will give a precipitate of $\mathrm{AY}_2$ at 300 K ? (Given $\mathrm{K}_{\mathrm{sp}}\left(\right.$ at 300 K ) for $\mathrm{AY}_2=5.2 \times 10^{-7}$ )

Arrange the following in increasing order of solubility product :

$\mathrm{Ca}(\mathrm{OH})_2, \mathrm{AgBr}, \mathrm{PbS}, \mathrm{HgS}$

A weak acid HA has degree of dissociation x . Which option gives the correct expression of ( pH - $\mathrm{pK}_{\mathrm{a}}$)?

$\mathrm{K}_{\mathrm{sp}}$ for $\mathrm{Cr}(\mathrm{OH})_3$ is $1.6 \times 10^{-30}$. What is the molar solubility of this salt in water?

pH of water is 7 at $25^{\circ} \mathrm{C}$. If water is heated to $80^{\circ} \mathrm{C}$., it's pH will :

Which of the following happens when $\mathrm{NH}_4 \mathrm{OH}$ is added gradually to the solution containing 1 M $\mathrm{A}^{2+}$ and $1 \mathrm{M} \mathrm{B}^{3+}$ ions?

Given : $\mathrm{K}_{\text {sp }}\left[\mathrm{A}(\mathrm{OH})_2\right]=9 \times 10^{-10}$ and $\mathrm{K}_{\mathrm{sp}}\left[\mathrm{B}(\mathrm{OH})_3\right]=27 \times 10^{-18}$ at 298 K.

The molar solubility(s) of zirconium phosphate with molecular formula $\left(\mathrm{Zr}^{4+}\right)_3\left(\mathrm{PO}_4^{3-}\right)_4$ is given by relation :

For a sparingly soluble salt $$\mathrm{AB}_2$$, the equilibrium concentrations of $$\mathrm{A}^{2+}$$ ions and $$B^{-}$$ ions are $$1.2 \times 10^{-4} \mathrm{M}$$ and $$0.24 \times 10^{-3} \mathrm{M}$$, respectively. The solubility product of $$\mathrm{AB}_2$$ is :

Given below are two statements :

Statement (I) : A Buffer solution is the mixture of a salt and an acid or a base mixed in any particular quantities

Statement (II) : Blood is naturally occurring buffer solution whose $$\mathrm{pH}$$ is maintained by $$\mathrm{H}_2 \mathrm{CO}_3 / \mathrm{HCO}_3{ }^{\ominus}$$ concentrations.

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

The equilibrium $$\mathrm{Cr}_2 \mathrm{O}_7^{2-} \rightleftharpoons 2 \mathrm{CrO}_4^{2-}$$ is shifted to the right in :

Given below are two statements :

Statement (I) : Aqueous solution of ammonium carbonate is basic.

Statement (II) : Acidic/basic nature of salt solution of a salt of weak acid and weak base depends on $$K_a$$ and $$K_b$$ value of acid and the base forming it.

In the light of the above statements, choose the most appropriate answer from the options given below :

$$25 \mathrm{~mL}$$ of silver nitrate solution (1M) is added dropwise to $$25 \mathrm{~mL}$$ of potassium iodide $$(1.05 \mathrm{M})$$ solution. The ion(s) present in very small quantity in the solution is/are :

When the hydrogen ion concentration [H$$^+$$] changes by a factor of 1000, the value of pH of the solution __________

$$200 \mathrm{~mL}$$ of $$0.01 \,\mathrm{M} \,\mathrm{HCl}$$ is mixed with $$400 \mathrm{~mL}$$ of $$0.01 \,\mathrm{M} \,\mathrm{H}_{2} \mathrm{SO}_{4}$$. The $$\mathrm{pH}$$ of the mixture is _________.

Given: $$\log {2}=0.30, \log 3=0.48, \log 5=0.70, \log 7=0.84, \log 11=1.04$$

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R

Assertion A : Permanganate titrations are not performed in presence of hydrochloric acid.

Reason R : Chlorine is formed as a consequence of oxidation of hydrochloric acid.

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

The plot of $$\mathrm{pH}$$-metric titration of weak base $$\mathrm{NH}_{4} \mathrm{OH}$$ vs strong acid HCl looks like :

Class XII students were asked to prepare one litre of buffer solution of $$\mathrm{pH} \,8.26$$ by their Chemistry teacher: The amount of ammonium chloride to be dissolved by the student in $$0.2\, \mathrm{M}$$ ammonia solution to make one litre of the buffer is :

(Given: $$\mathrm{pK}_{\mathrm{b}}\left(\mathrm{NH}_{3}\right)=4.74$$

Molar mass of $$\mathrm{NH}_{3}=17 \mathrm{~g} \mathrm{~mol}^{-1}$$

Molar mass of $$\mathrm{NH}_{4} \mathrm{Cl}=53.5 \mathrm{~g} \mathrm{~mol}^{-1}$$ )

$${K_{{a_1}}}$$, $${K_{{a_2}}}$$ and $${K_{{a_3}}}$$ are the respective ionization constants for the following reactions (a), (b) and (c).

(a) $${H_2}{C_2}{O_4} \mathbin{\lower.3ex\hbox{$\buildrel\textstyle\rightarrow\over {\smash{\leftarrow}\vphantom{_{\vbox to.5ex{\vss}}}}$}} {H^ + } + H{C_2}O_4^ - $$

(b) $$H{C_2}O_4^ - \mathbin{\lower.3ex\hbox{$\buildrel\textstyle\rightarrow\over {\smash{\leftarrow}\vphantom{_{\vbox to.5ex{\vss}}}}$}} {H^ + } + {C_2}O_4^{2 - }$$

(c) $${H_2}{C_2}O_4^{} \mathbin{\lower.3ex\hbox{$\buildrel\textstyle\rightarrow\over {\smash{\leftarrow}\vphantom{_{\vbox to.5ex{\vss}}}}$}} 2{H^ + } + {C_2}O_4^{2 - }$$

The relationship between $${K_{{a_1}}}$$, $${K_{{a_2}}}$$ and $${K_{{a_3}}}$$ is given as :

$$20 \mathrm{~mL}$$ of $$0.1\, \mathrm{M} \,\mathrm{NH}_{4} \mathrm{OH}$$ is mixed with $$40 \mathrm{~mL}$$ of $$0.05 \mathrm{M} \mathrm{HCl}$$. The $$\mathrm{pH}$$ of the mixture is nearest to :

(Given : $$\mathrm{K}_{\mathrm{b}}\left(\mathrm{NH}_{4} \mathrm{OH}\right)=1 \times 10^{-5}, \log 2=0.30, \log 3=0.48, \log 5=0.69, \log 7=0.84, \log 11= 1.04)$$

The solubility of AgCl will be maximum in which of the following?

A student needs to prepare a buffer solution of propanoic acid and its sodium salt with pH 4. The ratio of $${{[C{H_3}C{H_2}CO{O^ - }]} \over {[C{H_3}C{H_2}COOH]}}$$ required to make buffer is ___________.

Given : $${K_a}(C{H_3}C{H_2}COOH) = 1.3 \times {10^{ - 5}}$$

The K_sp for bismuth sulphide (Bi₂S₃) is 1.08 $$\times$$ 10^$$-$$73. The solubility of Bi₂S₃ in mol L^$$-$$1 at 298 K is :

Given below are two statements one is labelled as Assertion A and the other is labelled as Reason R :

Assertion A : The amphoteric nature of water is explained by using Lewis acid/base concept.

Reason R : Water acts as an acid with NH₃ and as a base with H₂S.

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

The pH of a solution obtained by mixing 5 mL of $0.1 \mathrm{M} \mathrm{NH}_4 \mathrm{OH}$ solution with 250 mL of $0.1 \mathrm{M} \mathrm{NH}_4 \mathrm{Cl}$ solution is $\_\_\_\_$ $\times 10^{-2}$.(Nearest integer) Given: $\mathrm{pK}_{\mathrm{b}}\left(\mathrm{NH}_4 \mathrm{OH}\right)=4.74$

$$ \begin{aligned} & \log 2=0.30 \\ & \log 3=0.48 \\ & \log 5=0.70 \end{aligned} $$

Consider the dissociation equilibrium of the following weak acid

$$ \mathrm{HA} \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{A}^{-}(\mathrm{aq}) $$

If the pKa of the acid is 4 , then the pH of 10 mM HA solution is $\_\_\_\_$ .(Nearest integer)

[Given: The degree of dissociation can be neglected with respect to unity]

Consider two Group IV metal ions $\mathrm{X}^{2+}$ and $\mathrm{Y}^{2+}$.

A solution containing $0.01 \mathrm{M} \mathrm{X}^{2+}$ and $0.01 \mathrm{M} \mathrm{Y}^{2+}$ is saturated with $\mathrm{H}_2 \mathrm{~S}$. The pH at which the metal sulphide YS will form as a precipitate is $\_\_\_\_$ . (Nearest integer)

(Given: $\mathrm{K}_{\mathrm{sp}}(\mathrm{XS})=1 \times 10^{-22}$ at $25^{\circ} \mathrm{C}, \mathrm{K}_{\mathrm{sp}}(\mathrm{YS})=4 \times 10^{-16}$ at $25^{\circ} \mathrm{C}$, $\left[\mathrm{H}_2 \mathrm{~S}\right]=0.1 \mathrm{M}$ in solution, $\mathrm{K}_{a 1} \times \mathrm{K}_{a 2}\left(\mathrm{H}_2 \mathrm{~S}\right)=1.0 \times 10^{-21}, \log 2=0.30$, $\log 3=0.48, \log 5=0.70)$

The first and second ionization constants of H₂X are $2.5 \times 10^{-8}$ and $1.0 \times 10^{-13}$ respectively.

The concentration of ${X^{2-}}$ in $0.1\ \mathrm{M}$ H₂X solution is ______ $\times 10^{-15}\ \mathrm{M}$. (Nearest Integer)

One litre buffer solution was prepared by adding 0.10 mol each of $\mathrm{NH}_3$ and $\mathrm{NH}_4 \mathrm{Cl}$ in deionised water. The change in pH on addition of 0.05 mol of HCl to the above solution is ______________ $\times 10^{-2}$.

(Nearest integer)

Given : $\mathrm{pK}_{\mathrm{b}}$ of $\mathrm{NH}_3=4.745$ and $\log _{10} 3=0.477$

The percentage dissociation of a salt $\left(\mathrm{MX}_3\right)$ solution at given temperature (van't Hoff factor $\mathrm{i}=2$ ) is ___________ %(Nearest integer)

The molar conductance of an infinitely dilute solution of ammonium chloride was found to be $185 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ and the ionic conductance of hydroxyl and chloride ions are 170 and $70 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$, respectively. If molar conductance of 0.02 M solution of ammonium hydroxide is $85.5 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$, its degree of dissociation is given by $x \times 10^{-1}$. The value of $x$ is __________ . (Nearest integer)

$x \mathrm{mg}$ of $\mathrm{Mg}(\mathrm{OH})_2($ molar mass $=58)$ is required to be dissolved in 1.0 L of water to produce a pH of 10.0 at 298 K . The value of $x$ is ________ mg. (Nearest integer)

(Given : $\mathrm{Mg}(\mathrm{OH})_2$ is assumed to dissociate completely in $\mathrm{H}_2 \mathrm{O}$ ]

The pH of a 0.01 M weak acid $\mathrm{HX}\left(\mathrm{K}_a=4 \times 10^{-10}\right)$ is found to be 5 . Now the acid solution is diluted with excess of water so that the pH of the solution changes to 6 . The new concentration of the diluted weak acid is given as $x \times 10^{-4} \mathrm{M}$. The value of $x$ is _________ (nearest integer)

The observed and normal molar masses of compound $\mathrm{MX}_2$ are 65.6 and 164 respectively. The percent degree of ionisation of $\mathrm{MX}_2$ is __________%. (Nearest integer)

If 1 mM solution of ethylamine produces $\mathrm{pH}=9$, then the ionization constant $\left(\mathrm{K}_{\mathrm{b}}\right)$ of ethylamine is $10^{-x}$. The value of $x$ is _________ (nearest integer).

[The degree of ionization of ethylamine can be neglected with respect to unity.]

Consider the dissociation of the weak acid HX as given below

$$\mathrm{HX}(\mathrm{aq}) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{X}^{-}(\mathrm{aq}), \mathrm{Ka}=1.2 \times 10^{-5}$$

[$$\mathrm{K}_{\mathrm{a}}$$ : dissociation constant]

The osmotic pressure of $$0.03 \mathrm{M}$$ aqueous solution of $$\mathrm{HX}$$ at $$300 \mathrm{~K}$$ is _________ $$\times 10^{-2}$$ bar (nearest integer).

[Given : $$\mathrm{R}=0.083 \mathrm{~L} \mathrm{~bar} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$$]

The $$\mathrm{pH}$$ of an aqueous solution containing $$1 \mathrm{M}$$ benzoic acid $$\left(\mathrm{pK}_{\mathrm{a}}=4.20\right)$$ and $$1 \mathrm{M}$$ sodium benzoate is 4.5. The volume of benzoic acid solution in $$300 \mathrm{~mL}$$ of this buffer solution is _________ $$\mathrm{mL}$$. (given : $$\log 2=0.3$$)

The $$\mathrm{pH}$$ at which $$\mathrm{Mg}(\mathrm{OH})_2\left[\mathrm{~K}_{\mathrm{sp}}=1 \times 10^{-11}\right]$$ begins to precipitate from a solution containing $$0.10 \mathrm{~M} \mathrm{~Mg}^{2+}$$ ions is __________.

20 mL of $$0.1 ~\mathrm{M} ~\mathrm{NaOH}$$ is added to $$50 \mathrm{~mL}$$ of $$0.1 ~\mathrm{M}$$ acetic acid solution. The $$\mathrm{pH}$$ of the resulting solution is ___________ $$\times 10^{-2}$$ (Nearest integer)

Given : $$\mathrm{pKa}\left(\mathrm{CH}_{3} \mathrm{COOH}\right)=4.76$$

$$\log 2=0.30$$

$$\log 3=0.48$$

$$25.0 \mathrm{~mL}$$ of $$0.050 ~\mathrm{M} ~\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}$$ is mixed with $$25.0 \mathrm{~mL}$$ of $$0.020 ~\mathrm{M} ~\mathrm{NaF} . \mathrm{K}_{\mathrm{Sp}}$$ of $$\mathrm{BaF}_{2}$$ is $$0.5 \times 10^{-6}$$ at $$298 \mathrm{~K}$$. The ratio of $$\left[\mathrm{Ba}^{2+}\right]\left[\mathrm{F}^{-}\right]^{2}$$ and $$\mathrm{K}_{\mathrm{sp}}$$ is ___________.

(Nearest integer)

An analyst wants to convert $$1 \mathrm{~L} \mathrm{~HCl}$$ of $$\mathrm{pH}=1$$ to a solution of $$\mathrm{HCl}$$ of $$\mathrm{pH} ~2$$. The volume of water needed to do this dilution is __________ $$\mathrm{mL}$$. (Nearest integer)

The solubility product of $$\mathrm{BaSO}_{4}$$ is $$1 \times 10^{-10}$$ at $$298 \mathrm{~K}$$. The solubility of $$\mathrm{BaSO}_{4}$$ in $$0.1 ~\mathrm{M} ~\mathrm{K}_{2} \mathrm{SO}_{4}(\mathrm{aq})$$ solution is ___________ $$\times 10^{-9} \mathrm{~g} \mathrm{~L}^{-1}$$ (nearest integer).

Given: Molar mass of $$\mathrm{BaSO}_{4}$$ is $$233 \mathrm{~g} \mathrm{~mol}^{-1}$$

The titration curve of weak acid vs. strong base with phenolphthalein as indictor) is shown below. The $$\mathrm{K}_{\text {phenolphthalein }}=4 \times 10^{-10}$$.

Given: $$\log 2=0.3$$

The number of following statement/s which is/are correct about phenolphthalein is ___________

A. It can be used as an indicator for the titration of weak acid with weak base.

B. It begins to change colour at $$\mathrm{pH}=8.4$$

C. It is a weak organic base

D. It is colourless in acidic medium

$$600 \mathrm{~mL}$$ of $$0.01~\mathrm{M} ~\mathrm{HCl}$$ is mixed with $$400 \mathrm{~mL}$$ of $$0.01~\mathrm{M} ~\mathrm{H}_{2} \mathrm{SO}_{4}$$. The $$\mathrm{pH}$$ of the mixture is ___________ $$\times 10^{-2}$$. (Nearest integer)

[Given $$\log 2=0.30$$

$$\log 3=0.48$$

$$\log 5=0.69$$

$$\log 7=0.84$$

$$\log 11=1.04]$$

Millimoles of calcium hydroxide required to produce 100 mL of the aqueous solution of pH 12 is $$x\times10^{-1}$$. The value of $$x$$ is ___________ (Nearest integer).

Assume complete dissociation.

A litre of buffer solution contains 0.1 mole of each of NH$$_3$$ and NH$$_4$$Cl. On the addition of 0.02 mole of HCl by dissolving gaseous HCl, the pH of the solution is found to be _____________ $$\times$$ 10$$^{-3}$$ (Nearest integer)

[Given : $$\mathrm{pK_b(NH_3)=4.745}$$

$$\mathrm{\log2=0.301}$$

$$\mathrm{\log3=0.477}$$

$$\mathrm{T=298~K]}$$

If the pKa of lactic acid is 5, then the pH of 0.005 M calcium lactate solution at 25$$^\circ$$C is ___________ $$\times$$ 10$$^{-1}$$ (Nearest integer)

The dissociation constant of acetic acid is $$x\times10^{-5}$$. When 25 mL of 0.2 $$\mathrm{M~CH_3COONa}$$ solution is mixed with 25 mL of 0.02 $$\mathrm{M~CH_3COOH}$$ solution, the pH of the resultant solution is found to be equal to 5. The value of $$x$$ is ____________

If the solubility product of PbS is 8 $$\times$$ 10^$$-$$28, then the solubility of PbS in pure water at 298 K is x $$\times$$ 10^$$-$$16 mol L^$$-$$1. The value of x is __________. (Nearest Integer)

[Given : $$\sqrt2$$ = 1.41]

$$\mathrm{K}_{\mathrm{a}}$$ for butyric acid $$\left(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{COOH}\right)$$ is $$2 \times 10^{-5}$$. The $$\mathrm{pH}$$ of $$0.2 \,\mathrm{M}$$ solution of butyric acid is __________ $$\times 10^{-1}$$. (Nearest integer)

[Given $$\log 2=0.30$$]

At $$310 \mathrm{~K}$$, the solubility of $$\mathrm{CaF}_{2}$$ in water is $$2.34 \times 10^{-3} \mathrm{~g} / 100 \mathrm{~mL}$$. The solubility product of $$\mathrm{CaF}_{2}$$ is ____________ $$\times 10^{-8}(\mathrm{~mol} / \mathrm{L})^{3}$$. (Give molar mass : $$\mathrm{CaF}_{2}=78 \mathrm{~g} \mathrm{~mol}^{-1}$$)

In the titration of $$\mathrm{KMnO}_{4}$$ and oxalic acid in acidic medium, the change in oxidation number of carbon at the end point is ___________.

The solubility product of a sparingly soluble salt A₂X₃ is 1.1 $$\times$$ 10^$$-$$23. If specific conductance of the solution is 3 $$\times$$ 10^$$-$$5 S m^$$-$$1, the limiting molar conductivity of the solution is $$x \,\times$$ 10^$$-$$3 S m² mol^$$-$$1. The value of x is ___________.

pH value of 0.001 M NaOH solution is ____________.

50 mL of 0.1 M CH₃COOH is being titrated against 0.1 M NaOH. When 25 mL of NaOH has been added, the pH of the solution will be _____________ $$\times$$ 10^$$-$$2. (Nearest integer)

(Given : pK_a (CH₃COOH) = 4.76)

log 2 = 0.30

log 3 = 0.48

log 5 = 0.69

log 7 = 0.84

log 11 = 1.04