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JEE Mains | PYQ

The solubility of \( \mathrm{CdSO_4} \) in water is \( 8.0 \times 10^{-4} \, \mathrm{mol \, L^{-1}} \). Its solubility in \( 0.01 \, \mathrm{M} \, \mathrm{H_2SO_4} \) solution is _____ \( \times 10^{-6} \, \mathrm{mol \, L^{-1}} \). (Assume that solubility is much less than \( 0.01 \, \mathrm{M} \))

\( \mathrm{A_3B_2} \) is a sparingly soluble salt of molar mass \( M \) (\( \mathrm{g\, mol^{-1}} \)) and solubility \( x \) \( \mathrm{g\, L^{-1}} \). The solubility product satisfies \( K_{sp} = a \left( \frac{x}{M} \right)^{5} \). The value of \( a \) is ____________ . (Integer answer)

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 \( \mathrm{OH^-} \) 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 \( K_b = 1.8 \times 10^{-5} \)]

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 \\)]

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

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)

\( 0.01 \) 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 \( \ll 1 \)]

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) [\( \log 2.5 = 0.3979 \)]