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JEE Mains | PYQ

\( \text{pH} \) of water is \( 7 \) at \( 25^\circ\text{C} \). If water is heated to \( 80^\circ\text{C} \), it’s \( \text{pH} \) will:

\( 20 \, \text{mL} \) of calcium hydroxide was consumed when it was reacted with \( 10 \, \text{mL} \) of unknown solution of \( \mathrm{H_2SO_4} \). Also \( 20 \, \text{mL} \) standard solution of \( 0.5 \, \mathrm{M} \) \( \mathrm{HCl} \) containing \( 2 \) drops of phenolphthalein was titrated with calcium hydroxide, the mixture showed pink colour when burette displayed the value of \( 35.5 \, \text{mL} \) whereas the burette showed \( 25.5 \, \text{mL} \) initially. The concentration of \( \mathrm{H_2SO_4} \) is: _______ \( \mathrm{M} \). (Nearest integer)

A student needs to prepare a buffer solution of propanoic acid and its sodium salt with pH 4.

The ratio of $\frac{[\text{CH}_3\text{CH}_2\text{COO}^-]}{[\text{CH}_3\text{CH}_2\text{COOH}]}$ required to make buffer is___________.

Given : $\text{K}_\text{a} (\text{CH}_3\text{CH}_2\text{COOH}) = 1.3 \times 10^{-5}$

The number of moles of \( \mathrm{NH_3} \), that must be added to \( 2 \, \text{L} \) of \( 0.80 \, \text{M} \) \( \mathrm{AgNO_3} \) in order to reduce the concentration of \( \mathrm{Ag^+} \) ions to \( 5.0 \times 10^{-8} \, \text{M} \) \( (K_{\text{formation}} \text{ for } [\mathrm{Ag(NH_3)_2}]^{+} = 1.0 \times 10^{8}) \) is __________. (Nearest integer)
[Assume no volume change on adding \( \mathrm{NH_3} \)]

In order to prepare a buffer solution of pH \( 5.74 \), sodium acetate is added to acetic acid. If the concentration of acetic acid in the buffer is \( 1.0 \) \( \mathrm{M} \), the concentration of sodium acetate in the buffer is __________ \( \mathrm{M} \). (Round off to the Nearest Integer).
[Given: \( \mathrm{p}K_a \) (acetic acid) = \( 4.74 \)]

Given below are two statements:
Statement I : In the titration between strong acid and weak base methyl orange is suitable as an indicator.
Statement II : For titration of acetic acid with \( \mathrm{NaOH} \) phenolphthalein is not a suitable indicator.
In the light of the above statements, choose the most appropriate answer from the options given below:

The molar solubility of \( \text{Zn(OH)}_2 \) in \( 0.1 \, \text{M} \) NaOH sodium is \( x \times 10^{-18} \, \text{M} \). The value of \( x \) is:
(Given: The solubility product of \( \text{Zn(OH)}_2 \) is \( 2 \times 10^{20} \) )

The titration curve of weak acid vs. strong base with phenolphthalein as indicator is shown below. The \( K_{\text{phenolphthalein}} = 4 \times 10^{-10} \). [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

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 pH is maintained by \( \mathrm{H_2CO_3} / \mathrm{HCO_3^\ominus} \) concentrations.
In the light of the above statements, choose the correct answer from the options given below ;

The element which shows only one oxidation state other than its elemental form is:

The \( \mathrm{OH^-} \) concentration in a mixture of \( 5.0 \, \mathrm{mL} \) of \( 0.0504 \, \mathrm{M} \) \( \mathrm{NH_4Cl} \) and \( 2 \, \mathrm{mL} \) of \( 0.0210 \, \mathrm{M} \) \( \mathrm{NH_3} \) solution is \( x \times 10^{-6} \, \mathrm{M} \). The value of \( x \) is __________. (Nearest Integer)
[Given \( K_w = 1 \times 10^{-14} \) and \( K_b = 1.8 \times 10^{-5} \)]

\( 600 \, \text{mL} \) of \( 0.01 \, \text{M} \) \( \mathrm{HCl} \) is mixing with \( 400 \, \text{mL} \) of \( 0.01 \, \text{M} \) \( \mathrm{H_2SO_4} \). The pH of the mixture is ______ \( \times 10^{-2} \). (Nearest integer) [Given : \( \log 2 = 0.30 \), \( \log 3 = 0.48 \), \( \log 5 = 0.69 \), \( \log 7 = 0.84 \), \( \log 11 \, = 1.04 \) ]

The \( K_{sp} \) for bismuth sulphide \( (\mathrm{Bi_2S_3}) \) is \( 1.08 \times 10^{-73} \). The solubility of \( \mathrm{Bi_2S_3} \) in \( \mathrm{mol \, L^{-1}} \) at \( 298 \, \mathrm{K} \) is

\(\text{ K}_{a_1} \), \(\text{ K}_{a_2} \) and \(\text{ K}_{a_3} \) are the respective ionization constants for the following reactions (a), (b) and (c).
(a) \( \mathrm{H_2C_2O_4} \rightleftharpoons \mathrm{H^+} + \mathrm{HC_2O_4^-} \)
(b) \( \mathrm{HC_2O_4^-} \rightleftharpoons \mathrm{H^+} + \mathrm{C_2O_4^{2-}} \) 
(c) \( \mathrm{H_2C_2O_4} \rightleftharpoons 2\mathrm{H^+} + \mathrm{C_2O_4^{2-}} \) 
The relationship between \( K_{a_1} \), \( K_{a_2} \) and \( K_{a_3} \) is given as:

The solubility product of \\( \mathrm{PbI_2} \\) is \\( 8.0 \times 10^{-9} \\). The solubility of lead iodide in \\( 0.1 \\) molar solution of lead nitrate is \\( x \times 10^{-6} \, \text{mol/L} \\). The value of \\( x \\) is __________. (Rounded off to the nearest integer)
[Given \\( \sqrt{2} = 1.41 \\)]

At \( 298 \, \text{K} \), the solubility of silver chloride in water is \( 1.434 \times 10^{-3} \, \text{g L}^{-1} \). The value of \( -\log K_{sp} \) for silver chloride is __________.
(Given mass of Ag is \( 107.9 \, \text{g mol}^{-1} \) and mass of Cl is \( 35.5 \, \text{g mol}^{-1} \))

The solubility product of \( \mathrm{BaSO_4} \) is \( 1 \times 10^{-10} \) at \( 298 \, \mathrm{K} \). The solubility of \( \mathrm{BaSO_4} \) in \( 0.1 \, \mathrm{M} \, \mathrm{K_2SO_4(aq)} \) solution is ______ \( \times 10^{-9} \, \mathrm{g\, L^{-1}} \) (nearest integer).
Given : Molar mass of \( \mathrm{BaSO_4} \) is \( 233 \, \mathrm{g \, mol^{-1}} \)

The dissociation constant of acetic acid is \( x \times 10^{-5} \). When \( 25 \, \mathrm{mL} \) of \( 0.2 \, \mathrm{M} \) \( \mathrm{CH_3COONa} \) solution is mixed with \( 25 \, \mathrm{mL} \) of \( 0.02 \, \mathrm{M} \) \( \mathrm{CH_3COOH} \) solution, the pH of the resultant solution is found to be equal to \( 5 \). The value of \( x \) is \( \_\_\_\_\_ \).

For a concentrated solution of a weak electrolyte (\( K_{eq} \)= equilibrium constant) \( \text{A}_2\text{B}_3 \) of concentration '\( c \)', the degree of dissociation '\( \alpha \)' is:

When the hydrogen ion concentration \( [\mathrm{H}^+] \) changes by a factor of \( 1000 \), the value of \( \text{pH} \) of the solution _______.

\( K_a \) for \( \mathrm{CH_3COOH} \) is \( 1.8 \times 10^{-5} \) and \( K_b \) for \( \mathrm{NH_4OH} \) is \( 1.8 \times 10^{-5} \). The \( \mathrm{pH} \) of ammonium acetate solution will be ______.

Given below are two statements:
Statement I: Methyl orange is a weak acid.
Statement II: The benzenoid form of methyl orange is more intensity / deeply coloured than the quinonoid from.
In the light of the above statement, choose the most appropriate answer from the options given below:

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

The first and second ionization constants of a weak dibasic acid \( \mathrm{H_2A} \) are \( 8.1 \times 10^{-8} \) and \( 1.0 \times 10^{-13} \) respectively. \( 0.1 \) mol of \( \mathrm{H_2A} \) was dissolved in \( 1 \) L of \( 0.1 \, \mathrm{M} \) HCl solution. The concentration of \( \mathrm{HA^-} \) in the resultant solution is:

The solubility of \( \mathrm{AgCl} \) will be maximum in which of the following?

Which of the following compound CANNOT act as a Lewis base?

An analyst wants to convert \( 1 \, \text{L} \) HCl of \( \text{pH} = 1 \) to a solution of HCl of \( \text{pH} \, 2 \). The volume of water needed to do this dilution is_____ \( \text{mL} \). (Nearest integer)

Given below are two statements one is labeled as Assertion A and the other is labeled 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 \( \text{\(NH_3\)} \) and as a base with \( \text{\(H_2S\)} \).
In the light of the above statements choose the correct answer from the options given below:

The \( \mathrm{pH} \) of a solution obtained by mixing \( 5 \, \text{mL} \) of \( 0.1 \, \text{M} \, \text{NH}_4\text{OH} \) solution with \( 250 \, \text{mL} \) of \( 0.1 \, \text{M} \, \text{NH}_4\text{Cl} \) solution is ________ \( \times 10^{-2} \). (Nearest integer)
Given: \( \mathrm{p}K_b(\text{NH}_4\text{OH}) = 4.74 \)

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

One litre buffer solution was prepared by adding \(0.10\) \(\text{mol}\) each of \(NH_3\) and \(NH_4Cl\) in deionized water. The change in \(\mathrm{pH}\) on addition of \(0.05\) \(\text{mol}\) of \(HCl\) to the above solution is ______ \(\times 10^{-2}\). (Nearest integer)
Given: \(pK_b\) of \(NH_3 = 4.745\) and \(\log_{10} 3 = 0.477\)

At \( 25^\circ \text{C} \), \( 20.0 \, \text{mL} \) of \( 0.2 \, \text{M} \) weak monoprotic acid \( \mathrm{HX} \) is titrated against \( 0.2 \, \text{M} \) \( \mathrm{NaOH} \). The pH of the solution (a) at the start of the titration (when \( \mathrm{NaOH} \) has not been added) and (b) when \( 10 \, \text{mL} \) of \( \mathrm{NaOH} \) is added respectively, are:

Given : \( K_a = 5 \times 10^{-4} \)
\( \mathrm{p}K_a = 3.3 \)
\( \alpha \ll 1 \)

The correct set of ions (aqueous solution) with same colour from the following is:

Millimoles of calcium hydroxide required to produce \( 100 \, \text{mL} \) of the aqueous solution of \( \text{pH} \, 12 \) is \( x \times 10^{-1} \). The value of \( x \) is _______ (Nearest integer).
Assume complete dissociation.

\( 20 \, \text{mL} \) of a solution of acetic acid required \( 28.4 \, \text{mL} \) of \( 0.1 \, \text{M} \) \( \mathrm{NaOH} \) for its neutralization. A solution \( (X) \) was prepared by mixing \( 20 \, \text{mL} \) of the above acetic acid and \( 14.2 \, \text{mL} \) of \( 0.1 \, \text{M} \) \( \mathrm{NaOH} \) solution. What is the \( \mathrm{pH} \) of the solution \( (X) \)? \( (\mathrm{p}K_a \) value of acetic acid is \( 4.75) \).

Consider a weak base ‘B’ of \( pK_b = 5.699 \). ‘\( x \)’ \( \mathrm{mL} \) of \( 0.02 \, \mathrm{M} \) \( \mathrm{HCl} \) and ‘\( y \)’ \( \mathrm{mL} \) of \( 0.02 \, \mathrm{M} \) weak base ‘B’ are mixed to make \( 100 \, \mathrm{mL} \) of a buffer of \( \mathrm{pH} \, 9 \) at \( 25^\circ \mathrm{C} \). The values of ‘\( x \)’ and ‘\( y \)’ respectively are:

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

What will be the decreasing order of basic strength of the following conjugate bases ?

$\text{ }^{-}\text{OH}, \text{R}\bar{\text{O}}, \text{CH}_3\text{CO}\bar{\text{O}}, \text{C}\bar{\text{l}}$

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

Which of the following mixture gives a buffer solution with \( \mathrm{pH} = 9.25 \)? Given: \( \mathrm{pK_b}(\mathrm{NH_4OH}) = 4.75 \)

The solubility product constants of \( \mathrm{Ag_2CrO_4} \) and \( \mathrm{AgBr} \) are \( 32x \) and \( 4y \) respectively at \( 298 \, \text{K} \). The value of \( (\dfrac{\text{molarity of } \mathrm{Ag_2CrO_4}}{\text{molarity of } \mathrm{AgBr}} )\) can be expressed as:

Arrange the following resultant mixtures in increasing order of their pH values
A. \( 10 \, \text{mL} \, 0.2 \, \text{M} \, \mathrm{Ca(OH)_{2}} + 25 \, \text{mL} \, 0.1 \, \text{M} \, \mathrm{HCl} \)
B. \( 10 \, \text{mL} \, 0.01 \, \text{M} \, \mathrm{H_{2}SO_{4}} + 10 \, \text{mL} \, 0.01 \, \text{M} \, \mathrm{Ca(OH)_{2}} \)
C. \( 10 \, \text{mL} \, 0.1 \, \text{M} \, \mathrm{H_{2}SO_{4}} + 10 \, \text{mL} \, 0.1 \, \text{M} \, \mathrm{KOH} \)
Choose the correct answer from the options given below:

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

The pH at which \( \text{Mg(OH)}_2 \) \( [K_{sp} = 1 \times 10^{-11}] \) begins to precipitate from a solution containing \( 0.10 \, \text{M} \) \( \text{Mg}^{2+} \) ions is ________.

Assuming that \( \mathrm{Ba(OH)_2} \) is completely ionised in aqueous solution under the given conditions the concentration of \( \mathrm{H_3O^+} \) ions in \( 0.005 \, \text{M} \) aqueous solution of \( \mathrm{Ba(OH)_2} \) at \( 298 \, \text{K} \) is _______ \( \times 10^{-12} \) \( \text{mol L}^{-1} \). (Nearest integer)

\( 25.0 \, \text{mL} \) of \( 0.050 \, \mathrm{M} \) \( \mathrm{Ba(NO_3)_2} \) is mixed with \( 25.0 \, \text{mL} \) of \( 0.020 \, \mathrm{M} \) \( \mathrm{NaF} \). \( K_{sp} \) of \( \mathrm{BaF_2} \) is \( 0.5 \times 10^{-6} \) at \( 298 \, \text{K} \). The ratio of \( [\mathrm{Ba}^{2+}][\mathrm{F}^-]^2 \) and \( K_{sp} \) is _______. (Nearest integer)

\( \mathrm{M_{3}A_{2}} \) is a sparingly soluble salt of molar mass \( y \, \text{g mol}^{-1} \) and solubility \( x \, \text{g L}^{-1} \). The ratio of the molar concentration of the anion \( (\mathrm{A^{3-}}) \) to the solubility product of the salt is:

An aqueous solution of \( \mathrm{HCl} \) with pH \( 1.0 \) is diluted by adding equal volume of water (ignoring dissociation of water). The pH of \( \mathrm{HCl} \) solution would . (Given \( \log 2 = 0.30 \))

\( 20 \,\mathrm{mL} \) of \( 0.1 \,\mathrm{M} \; \mathrm{NH_4OH} \) is mixed with \( 40 \,\mathrm{mL} \) of \( 0.05 \,\mathrm{M} \; \mathrm{HCl} \). The pH of the mixture is nearest to :
(Given : \( K_b(\mathrm{NH_4OH}) = 1 \times 10^{-5} \), \( \log 2 = 0.30 \), \( \log 3 = 0.48 \), \( \log 5 = 0.69 \), \( \log 7 = 0.84 \), \( \log 11 = 1.04 \))

For a sparingly soluble salt \( \mathrm{AB_2} \), the equilibrium concentrations of \( \mathrm{A^{2+}} \) ions and \( \mathrm{B^-} \) 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:

If \( 1 \, \text{mM} \) solution of ethylamine produces \( \text{pH} = 9 \), then the ionization constant (\( K_b \)) 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.]

\( 0.01 \) moles of a weak acid \( \mathrm{HA} (K_a = 2.0 \times 10^{-6}) \) is dissolved in \( 1.0 \, \text{L} \) of \( 0.1 \, \text{M} \) \( \mathrm{HCl} \) solution. The degree of dissociation of \( \mathrm{HA} \) is ______ \( \times 10^{-5} \) (Round off to the Nearest Integer) [Assume degree of dissociation \( \ll 1 \)]

Which of the following statement(s) is/are correct?
\( (1) \) The pH \( 1 \times 10^{-8} \,\text{M} \,\mathrm{HCl} \) solution is \( 8 \)
\( (2) \) The conjugate base of \( \mathrm{H_2PO_4^-} \) is \( \mathrm{HPO_4^{2-}} \)
\( (3) \) \( K_w \) increases with increase in temperature
\( (4) \) When a solution of a weak monoprotic acid is titrated against a strong base at half neutralization point, \( \mathrm{pH} = \dfrac{1}{2}\mathrm{p}K_a \)
Choose the correct answer from the options given below:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Phenolphthalein is a pH dependent indicator, remains colourless in acidic solution and gives pink colour in basic medium.
Reason R: Phenolphthalein is a weak acid. It doesn't dissociate in basic medium.
In the light of the above statements, choose the most appropriate answer from the options given below

Consider two Group IV metal ions \( X^{2+} \) and \( Y^{2+} \).
A solution containing \( 0.01 \, \text{M} \, X^{2+} \) and \( 0.01 \, \text{M} \, Y^{2+} \) is saturated with \( H_2S \). The pH at which the metal sulphide \( YS \) will form as a precipitate is _______. (Nearest integer)
(Given: \( K_{sp}(XS) = 1 \times 10^{-22} \) at \( 25^\circ \text{C} \), \( K_{sp}(YS) = 4 \times 10^{-16} \) at \( 25^\circ \text{C} \), \( [H_2S] = 0.1 \, \text{M} \) in solution, \( K_{a1} \times K_{a2}(H_2S) = 1.0 \times 10^{-21} \), \( \log 2 = 0.30 \), \( \log 3 = 0.48 \), \( \log 5 = 0.70 \))

At \( 310 \, \text{K} \), the solubility of \( \mathrm{CaF_2} \) in water is \( 2.34 \times 10^{-3} \, \text{g}/100 \, \text{mL} \). The solubility product of \( \mathrm{CaF_2} \) is _____ \( \times 10^{-8} \, (\text{mol}/\text{L})^3 \). (Give molar mass : \( \mathrm{CaF_2} = 78 \, \text{g mol}^{-1} \) )

\( 200 \, \text{mL} \) of \( 0.01 \, \text{M} \, \mathrm{HCl} \) is mixed with \( 400 \, \text{mL} \) of \( 0.01 \, \text{M} \, \mathrm{H_2SO_4} \). 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 :
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 :

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

The pH of a solution obtained by mixing \( 50 \, \text{mL} \) of \( 1 \, \text{M} \) HCl and \( 30 \, \text{mL} \) of \( 1 \, \text{M} \) NaOH is \( x \times 10^{-4} \). The value of \( x \) is ________ . (Nearest integer) [\( \log 2.5 = 0.3979 \)]

The plot of pH-metric titration of weak base \( \mathrm{NH_4OH} \) vs strong acid \( \mathrm{HCl} \) looks like:

pH value of \( 0.001 \, \mathrm{M} \) NaOH solution is ______.

If the solubility product of \( \mathrm{PbS} \) is \( 8 \times 10^{-28} \), then the solubility of \( \mathrm{PbS} \) in pure water at \( 298 \, \text{K} \) is \( x \times 10^{-16} \; \text{mol L}^{-1} \). The value of \( x \) is __________. (Nearest Integer)
[Given: \( \sqrt{2} = 1.41 \)]

A litre of buffer solution contains \(0.1\) mole of each of \( \mathrm{NH_3} \) and \( \mathrm{NH_4Cl} \). On the addition of \(0.02\) mole of \( \mathrm{HCl} \) by dissolving gaseous \( \mathrm{HCl} \), the pH of the solution is found to be _______ \( \times 10^{-3} \) (Nearest integer) [Given: \( pK_b(\mathrm{NH_3}) = 4.745 \), \( \log 2 = 0.301 \), \( \log 3 = 0.477 \), \( T = 298 \ \mathrm{K} \)]

\( 50 \, \text{mL} \) of \( 0.1 \, \text{M} \, \mathrm{CH_3COOH} \) is being titrated against \( 0.1 \, \text{M} \, \mathrm{NaOH} \). When \( 25 \, \text{mL} \) of \( \mathrm{NaOH} \) has been added, the pH of the solution will be ____________ \( \times 10^{-2} \). (Nearest integer)
(Given: \( pK_a(\mathrm{CH_3COOH}) = 4.76 \) )
\( \log 2 = 0.30 \)
\( \log 3 = 0.48 \)
\( \log 5 = 0.69 \)
\( \log 7 = 0.84 \)
\( \log 11 = 1.04 \)

If equal volumes of \( \text{AB}_2 \) and \( \text{XY} \) (both are salts) aqueous solutions are mixed, which of the following combination will give a precipitate of \( \text{AY}_2 \) at \( 300 \, \text{K} \)?
(Given \( K_{sp} \) (at \( 300 \, \text{K} \)) for \( \text{AY}_2 = 5.2 \times 10^{-7} \))

The first and second ionization constants of \( \mathrm{H_2X} \) are \( 2.5 \times 10^{-8} \) and \( 1.0 \times 10^{-13} \) respectively. The concentration of \( \mathrm{X^{2-}} \) in \( 0.1 \, \text{M} \, \mathrm{H_2X} \) solution is _____ \( \times 10^{-15} \, \text{M} \). (Nearest Integer)