Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • For a reaction at equilibrium <img alt="\mathrm{A(g)\rightleftharpoons B(g)+\frac{1}{2} \, C(g)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7BA%28g%29%5Crightlef

For a reaction at equilibrium

\mathrm{A(g)\rightleftharpoons B(g)+\frac{1}{2} \, C(g)}
the relation  between dissociation constant \mathrm{\left ( K \right )},  degree of dissociation \mathrm{\left ( \alpha \right )}  and equilibrium pressure \mathrm{\left ( p \right )} is given by :

Option: 1

\mathrm{K}=\frac{\alpha^{\frac{1}{2}} \mathrm{p}^{\frac{3}{2}}}{\left(1+\frac{3}{2} \alpha\right)^{\frac{1}{2}}(1-\alpha)}


Option: 2

\mathrm{K=\frac{\alpha^{\frac{3}{2}} \mathrm{p}^{\frac{1}{2}}}{(2+\alpha)^{\frac{1}{2}}(1-\alpha)}}


Option: 3

\mathrm{K=\frac{(\alpha\, p)^{\frac{3}{2}}}{\left(1+\frac{3}{2} \alpha\right)^{\frac{1}{2}}(1-\alpha)}}


Option: 4

\mathrm{\mathrm{K}=\frac{(\alpha \, \mathrm{p})^{\frac{3}{2}}}{(1+\alpha)(1-\alpha)^{\frac{1}{2}}}}


Answers (1)

best_answer

                  \mathrm{A\quad\rightleftharpoons \quad B\quad+\quad\frac{C}{2}}

\mathrm{t=0 \quad p_{0}\quad\quad \ \ \quad -\quad\quad \quad -}

\mathrm{{teq}\:\ \ \ p_{0}(1-\alpha) \quad p_{0} \alpha \ \ \ \quad \frac{p_{0} \, \alpha}{2}}

\mathrm{\therefore\, P_{\text {Total }} =p=p_{0}\left(1+\frac{\alpha}{2}\right)}
      \mathrm{\Rightarrow \, p_{0} =\frac{p}{\left(1+\frac{\alpha}{2}\right)} }

\mathrm{\therefore\,\, K_{P}=\frac{p_{B} \cdot p_{C}^{1 / 2}}{p_{A}} =\frac{p_{0} \alpha \cdot\left(p_{0} \frac{\alpha}{2}\right)^{1 / 2}}{p_{0}(1-\alpha)}}
                                         \mathrm{=\frac{p_{0}^{1 / 2} \alpha^{3 / 2}}{(1-\alpha) 2^{1 / 2}} }
                                         \mathrm{=\frac{p^{1 / 2} \alpha^{3 / 2}}{2^{1 / 2}\left(1+\frac{\alpha}{2}\right)^{1 / 2}(1-\alpha)} }
                                         \mathrm{=\frac{p^{1 / 2} \alpha^{3 / 2}}{(2+\alpha)^{1 / 2}(1-\alpha)} }

Hence, the correct answer is Option (2)

Posted by

Gautam harsolia

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question