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1

### JEE Main 2021 (Online) 27th August Evening Shift

Numerical
When 5.1 g of solid NH4HS is introduced into a two litre evacuated flask at 27$$^\circ$$C, 20% of the solid decomposes into gaseous ammonia and hydrogen sulphide. The Kp for the reaction at 27$$^\circ$$C is x $$\times$$ 10$$-$$2. The value of x is _____________. (Integer answer) [Given R = 0.082 L atm K$$-$$1 mol$$-$$]

## Explanation

moles of NH4HS initially taken = $${{5.1g} \over {51g/mol}}$$ = 0.1 mol

volume of vessel = 2 litre

$$\Rightarrow$$ partial pressure of each component

$$P = {{nRT} \over V} = {{0.1 \times 0.2 \times 0.082 \times 300} \over 2}$$

= 0.246 atm

$$\Rightarrow$$ kP = P$$N{H_3}$$ $$\times$$ P$${H_2}S$$ = (0.246)2 = 0.060516

= 6.05 $$\times$$ 10$$-$$2

$$\therefore$$ x = 6
2

### JEE Main 2021 (Online) 27th August Morning Shift

Numerical
The number of moles of NH3, that must be added to 2L of 0.80 M AgNO3 in order to reduce the concentration of Ag+ ions to 5.0 $$\times$$ 10$$-$$8 M (Kformation for [Ag(NH3)2]+ = 1.0 $$\times$$ 108) is ____________. (Nearest integer)

[Assume no volume change on adding NH3]

## Explanation

$${{0.8} \over {(5 \times {{10}^{ - 8}})\left( {{a \over 2} - 1.6} \right)}} = {10^8}$$

$$\Rightarrow$$ $${{a \over 2}}$$ $$-$$ 1.6 = 0.4 $$\Rightarrow$$ a = 4
3

### JEE Main 2021 (Online) 26th August Evening Shift

Numerical
The equilibrium constant Kc at 298 K for the reaction A + B $$\rightleftharpoons$$ C + D is 100. Starting with an equimolar solution with concentrations of A, B, C and D all equal to 1M, the equilibrium concentration of D is ___________ $$\times$$ 10$$-$$2 M. (Nearest integer)

## Explanation

$$\therefore$$ $${K_C} = {\left( {{{1 + x} \over {1 - x}}} \right)^2}$$

$$100 = {\left( {{{1 + x} \over {1 - x}}} \right)^2}$$

$${{1 + x} \over {1 - x}} = 10$$

$$x = {9 \over {11}}$$

Moles of D = 1 + x

$$= 1 + {9 \over {11}} = {{20} \over {11}}$$

$$= 1.818 = 181.8 \times {10^{ - 2}} = 181.8 \times {10^{ - 2}}$$

$$\cong 182 \times {10^{ - 2}}$$ M

4

### JEE Main 2021 (Online) 26th August Morning Shift

Numerical
The OH$$-$$ concentration in a mixture of 5.0 mL of 0.0504 M NH4Cl and 2 mL of 0.0210 M NH3 solution is x $$\times$$ 10$$-$$6 M. The value of x is ___________. (Nearest integer)

[Given Kw = 1 $$\times$$ 10$$-$$14 and Kb = 1.8 $$\times$$ 10$$-$$5]

## Explanation

$$\left[ {NH_4^ + } \right]$$ = 0.0504 & [NH3] = 0.0210

So, $${K_b} = {{[NH_4^ + ][H{O^ - }]} \over {[N{H_3}]}}$$

$$[H{O^ - }] = {{{K_b} \times [N{H_3}]} \over {[NH_4^ + ]}} = 1.8 \times {10^{ - 5}} \times {2 \over 5} \times {{210} \over {504}} = 3 \times {10^{ - 6}}$$

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