JEE Main 2021 (Online) 27th August Evening Shift

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Numerical

The first order rate constant for the decomposition of CaCO₃ at 700 K is 6.36 $$\times$$ 10^$$-$$3s^$$-$$1 and activation energy is 209 kJ mol^$$-$$1. Its rate constant (in s^$$-$$1) at 600 K is x $$\times$$ 10^$$-$$6. The value of x is ___________. (Nearest integer)

[Given R = 8.31 J K^$$-$$ mol^$$-$$1; log 6.36 $$\times$$ 10^$$-$$3 = $$-$$2.19, 10^$$-$$4.79 = 1.62 $$\times$$ 10^$$-$$5]

Your Input ________

Answer

Correct Answer is 16

Explanation

K₇₀₀ = 6.36 $$\times$$ 10^$$-$$3s^$$-$$1;

K₆₀₀ = x $$\times$$ 10^$$-$$6s^$$-$$1

E_a = 209 kJ/mol

Applying;

$$\log \left( {{{{K_{{T_2}}}} \over {{K_{{T_1}}}}}} \right) = {{ - {E_a}} \over {2.303R}}\left( {{1 \over {{T_2}}} - {1 \over {{T_1}}}} \right)$$

$$\log \left( {{{{K_{700}}} \over {{K_{600}}}}} \right) = {{ - {E_a}} \over {2.303R}}\left( {{1 \over {700}} - {1 \over {600}}} \right)$$

$$\log \left( {{{6.36 \times {{10}^{ - 3}}} \over {{K_{600}}}}} \right) = {{ + 209 \times 1000} \over {2.303 \times 8.31}}\left( {{{100} \over {700 \times 600}}} \right)$$

log(6.36 $$\times$$ 10^$$-$$3) $$-$$ logK₆₀₀ = 2.6

$$\Rightarrow$$ logK₆₀₀ = $$-$$2.19 $$-$$ 2.6 = $$-$$4.79

$$\Rightarrow$$ K₆₀₀ = 10^$$-$$4.79 = 1.62 $$\times$$ 10^$$-$$5

= 1.62 $$\times$$ 10^$$-$$6

= x $$\times$$ 10^$$-$$6

$$\Rightarrow$$ x = 16

JEE Main 2021 (Online) 27th August Morning Shift

Numerical

The reaction that occurs in a breath analyser, a device used to determine the alcohol level in a person's blood stream is

$$2{K_2}C{r_2}{O_7} + 8{H_2}S{O_4} + 3{C_2}{H_6}O \to 2C{r_2}{(S{O_4})_3} + 3{C_2}{H_4}{O_2} + 2{K_2}S{O_4} + 11{H_2}O$$

If the rate of appearance of Cr₂(SO₄)₃ is 2.67 mol min^$$-$$1 at a particular time, the rate of disappearance of C₂H₆O at the same time is _____________ mol min^$$-$$1. (Nearest integer)

Your Input ________

Answer

Correct Answer is 4

Explanation

$$\left( {{{Rate\,of\,disappearance\,of\,{C_2}{H_6}O} \over 3}} \right)$$

$$ = \left( {{{Rate\,of\,disappearance\,of\,C{r_2}{{(S{O_4})}_3}} \over 2}} \right)$$

$$ \Rightarrow \left( {{{2.67\,mol/\min \, \times 3} \over 2}} \right) = $$ rate of disappearance of C₂H₆O.

$$\Rightarrow$$ Rate of disappearance of C₂H₆O = 4.005 mol/min.

JEE Main 2021 (Online) 26th August Evening Shift

Numerical

The reaction rate for the reaction

[PtCl₄]^2$$-$$ + H₂O $$\rightleftharpoons$$ [Pt(H₂O)Cl₃]^$$-$$ + Cl^$$-$$

was measured as a function of concentrations of different species. It was observed that $${{ - d\left[ {{{\left[ {PtC{l_4}} \right]}^{2 - }}} \right]} \over {dt}} = 4.8 \times {10^{ - 5}}\left[ {{{\left[ {PtC{l_4}} \right]}^{2 - }}} \right] - 2.4 \times {10^{ - 3}}\left[ {{{\left[ {Pt({H_2}O)C{l_3}} \right]}^ - }} \right]\left[ {C{l^ - }} \right]$$.

where square brackets are used to denote molar concentrations. The equilibrium constant K_c = ____________ . (Nearest integer)

Your Input ________

Answer

Correct Answer is 50

Explanation

[PtCl₄]^2$$-$$ + H₂O $$\rightleftharpoons$$ [Pt(H₂O)Cl₃]^$$-$$ + Cl^$$-$$

$${{ - d{{\left[ {PtC{l_4}} \right]}^{ - 2}}} \over {dt}} = 4.8 \times {10^{ - 5}}\left[ {PtC{l_4}^{ - 2}} \right] - 2.4 \times {10^{ - 3}}[Pt({H_2}O)C{l_3}][\mathop u\limits^o ]$$

$$ \Rightarrow {K_{eq}} = {{{k_f}} \over {{k_b}}} = {{4.8 \times {{10}^{ - 5}}} \over {2.4 \times {{10}^{ - 3}}}} = 0.02$$

JEE Main 2021 (Online) 26th August Evening Shift

Numerical

The overall stability constant of the complex ion [Cu(NH₃)₄]²⁺ is 2.1 $$\times$$ 10¹³. The overall dissociations constant is y $$\times$$ 10^$$-$$14. Then y is __________. (Nearest integer)

Your Input ________