| $[A] (mol\,L^{-1})$ | $[B] (mol\,L^{-1})$ | Initial Rate $(mol\, L^{-1}\,s^{-1} )$ |
| $0.05$ | $0.05$ | $0.045$ |
| $0.10$ | $0.05$ | $0.090$ |
| $0.20$ | $0.10$ | $0.72$ |
- ARate $= k[A]^2[B]^2$
- ✓Rate $= k[A][B]^2$
- CRate $= k[A][B]$
- DRate $= k[A]^2[B]$
| $[A] (mol\,L^{-1})$ | $[B] (mol\,L^{-1})$ | Initial Rate $(mol\, L^{-1}\,s^{-1} )$ |
| $0.05$ | $0.05$ | $0.045$ |
| $0.10$ | $0.05$ | $0.090$ |
| $0.20$ | $0.10$ | $0.72$ |
$0.045\, = \,K{(0.05)^x}{(0.05)^y}$ ...... $(1)$
$0.090\, = \,K{(0.10)^x}{(0.05)^y}$ .......$(2)$
$0.72\, = \,K{(0.20)^x}{(0.10)^y}$ ........$(3)$
Diving $(1)$ by $(2)$ We get
$\frac{{0.045}}{{0.090}}\, = \,{\left( {\frac{{0.05}}{{0.10}}} \right)^x}\, \Rightarrow \,x = 1$
Diving $(2)$ by $(3)$
$\frac{{0.090}}{{0.720}}\, = \,{\left( {\frac{{0.10}}{{0.20}}} \right)^x}\,{\left( {\frac{{0.05}}{{0.10}}} \right)^y}\, \Rightarrow \,y = 2\,$
Hence, $r\, = \,K[A]\,{[B]^2}$
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Statement $I :$ Potassium permanganate on heating at $573\, K$ forms potassium manganate.
Statement $II :$ Both potassium permanganate and potassium manganate are tetrahedral and paramagnetic in nature.
In the light of the above statements, choose the most appropriate answer from the options given below
$(A)$ The $pH$ of $1 \times 10^{-8}\,M\,HCl$ solution is $8$.
$(B)$ The conjugate base $H _2 PO _4^{-}$is $HPO _4{ }^{2-}$.
$(C)$ $K _{ w }$ increases with increase in temperature.
$(D)$ When a solution of weak monoprotic acid is titrated against a strong base at half neutralisation point, $pH =\frac{1}{2} pK _{ a }$
Choose the correct answer from the option given below.