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JEE Mains | PYQ

\(20 \, \text{mL}\) of \(0.1 \, \text{M}\) \(\mathrm{NaOH}\) is added to \(50 \, \text{mL}\) of \(0.1 \, \text{M}\) acetic acid solution. The \(\mathrm{pH}\) of the resulting solution is __________ \( \times 10^{-2} \) \((\text{Nearest integer})\)
Given: \( \mathrm{p}K_a(\mathrm{CH_3COOH}) = 4.76 \)
 \( \log 2 = 0.30 \)
\( \log 3 = 0.48 \)

\( 20 \, \text{mL} \) 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)

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

\( 600 \, \text{mL} \) 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 : \( \log 2 = 0.30 \), \( \log 3 = 0.48 \), \( \log 5 = 0.69 \), \( \log 7 = 0.84 \), \( \log 11 \, = 1.04 \) ]

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 _______.

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:

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)

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.

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)

\( 25.0 \, \text{mL} \) 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)

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:

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: \( pK_b(\mathrm{NH_3}) = 4.745 \), \( \log 2 = 0.301 \), \( \log 3 = 0.477 \), \( T = 298 \ \mathrm{K} \)]