Chemistry, asked by Prep4JEEADV, 8 months ago

Two solids dissociate as follows :-

 A(s)\: \rightleftharpoons\:B(g)\:+\:C(g)\: ;K_{p_1}\:=\:x\:(atm}^2\\ \\ \\ D(s)\: \rightleftharpoons\:C(g)\:+\:E(g)\: ;K_{p_2}\:=\:x\:(atm}^2

The total pressure when both the solids dissociate simultaneously is _________ atm. JEE-M(2019) 12 Jan Shift-1​

Answers

Answered by Draxillus
6

Correct question :- Two solids dissociate as follows :-

 A(s)\: \rightleftharpoons\:B(g)\:+\:C(g)\: ;K_{p_1}\:=\:x\:(atm}^2\\ \\ \\ D(s)\: \rightleftharpoons\:C(g)\:+\:E(g)\: ;K_{p_2}\:=\:y\:(atm}^2

The total pressure when both the solids dissociate simultaneously is _________ atm.

Solutions

 A(s)\: \rightleftharpoons\:B(g)\:+\:C(g)\: ;K_{p_1}\:=\:x\:(atm}^2\\ \\ \\ D(s)\: \rightleftharpoons\:C(g)\:+\:E(g)\: ;K_{p_2}\:=\:y\:(atm}^2

Consider the attachment for the pressure of each of the species at equilibrium.

Considering equilibria 1.

 K_{P_1}\:=\:[B]\:[C] \\ \\ =>\:x\:=\:m \times (m\:+\:n).....eqn(1)

Considering equilibria 2.

 K_{P_2}\:=\:[E]\:[C] \\ \\ =>\:y\:=\:n \times (m\:+\:n).....eqn(2)

Dividing eqn(I) by eqn(ii)

 \dfrac{K_{P_1}}{K_{P_2}}\:=\: \dfrac{\:m \times (m\:+\:n)}{\:n \times (m\:+\:n)} \\ \\ \\   \dfrac{x}{y}\:=\: \dfrac{\:m \times (m\:+\:n)}{\:n \times (m\:+\:n)} \\ \\ \\ =>\: \dfrac{x}{y}\:=\: \dfrac{m}{n}

now, diving both sides by m² in quation (i)

 \: \dfrac{x}{m^2}=\:  (1\:+\: \dfrac{n}{m})\\ \\ \\ => \:  \dfrac{x}{m^2}\:=\:(1\:+\: \dfrac{y}{x})....(\because \:\:  \dfrac{x}{y}\:=\: \dfrac{m}{n}) \\ \\ \\ => \: \dfrac{x}{m^2}\:=\: \dfrac{x\:+\:y}{x}   \: \\ \\ \\ => \: m^2\:=\: \dfrac{x^2}{x\:+\:y}\\ \\ \\ => \: m\:=\: \dfrac{x}{\sqrt{x\:+\:y}}

Now using equation (I),we can find out the value of n.N comes :-

 n\:=\: \dfrac{y}{\sqrt{x\:+\:y}}

Total pressure is sum of pressures of [C], [B] ,[E]

= 2(m + n)

Substuting the value of m and n respectively, we get total pressure :-

 => \: 2(m\:+\:n)\:=\:2(\dfrac{x}{\sqrt{x\:+\:y}}\:+\:\dfrac{y}{\sqrt{x\:+\:y}}) \\ \\ \\ =\: 2(\dfrac{x\:+\:y}{\sqrt{x\:+y\:}})\\ \\ \\ =2(\sqrt{x\:+\:y})

 \boxed{\boxed{\green{Hence,\:the\:total\:pressure\:is\:2\sqrt{x\:+\:y}\: atm}}}

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Answered by Anonymous
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\huge\star\underbrace{\mathtt\red{✺A} \mathtt\green{N}\mathtt\blue{S} \mathtt\purple{W}\mathtt\orange{E} \mathtt\pink{R✺}}\star /:⋆

see in the attachments please

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