Question

At \[518^\circ C\], the rate of decomposition of a sample of gaseous acetaldehyde,initially at a pressure of \[363Torr\], was \[1.00Torr\] inverse when \[5\% \] had reacted and \[0.5Torr\]per second when had reacted.the order of the reaction is:
 \[\begin{gathered}
  A.1 \\
  B.0 \\
  C.2 \\
  D.3 \\
\end{gathered} \]

Answer 1

Hint: the rate of the reaction is given as \[\Bbbk {\left( {a - {\rm X}} \right)^q}\]
Further the order of a reaction is given by
\[\dfrac{{r1}}{{r2}} = {\left\{ {\dfrac{{\left( {a - {\rm X}} \right)}}{{\left( {a - {{\rm X}_2}} \right)}}} \right\}^q}\]
Where \[\left( {a - {\rm X}} \right)\]is the remaining concentration ,

Complete step-by-step answer:We firstly need to do is
Order of a reaction : the order of a reaction is defined as the power dependence of the rate on the concentration of each reactant.it is basically a determined parameter.
Consider the order of the reaction be=”q”
Rate of a reaction is defined as a speed by which a reaction is taking place.
Then we need to consider the rate of the reaction as \[\Bbbk {\left( {a - {\rm X}} \right)^q}\]
Where \[\left( {a - {\rm X}} \right)\]is the remaining concentration ,
Then let's consider two rates,
\[\dfrac{{r1}}{{r2}} = {\left\{ {\dfrac{{\left( {a - {\rm X}} \right)}}{{\left( {a - {{\rm X}_2}} \right)}}} \right\}^q}\]here we have used five per cent so,this concludes that ninety five per cent is left and also here we are talking about the leftover substance .in the second one the left one is sixty seven per cent as thirty three percent is already used up.therefore on solving the equation we get the order of the reaction to be two.
\[q = 2\]
The order of the reaction is calculated to be two in number.

Note: The order of the reaction should be calculated very carefully and the remaining quantity should be determined very carefully.