Question

What are neutral oxides? Explain the nature of zinc oxide with the help of reactions. Define 'Molar Conductivity' and 'Zero order reaction'.
In a first-order reaction, $x \to y$, $40\% $ of the given sample of the compound remains unreacted in $45$ minutes. Calculate the rate constant of the reaction.

Answer 1

Hint: Neutral oxides can be inferred to those oxides which show neither basic properties nor acidic properties when they are reacted with water. Some of the examples are carbon monoxide ( $CO$ ) and nitrous oxide ( ${N_2}O$ ) which are only slightly soluble in water, and nitric oxide ( $NO$ ) which is appreciably soluble in cold water.

Complete answer:
Step 1: Defining Neutral oxides.
The neutral oxides can be inferred as those oxides which are neither acidic nor basic when they are reacted with water. Some of the examples are carbon monoxide ( $CO$ ) and nitrous oxide ( ${N_2}O$ ) which are only slightly soluble in water, and nitric oxide ( $NO$ ) which is appreciably soluble in cold water.
Step 2: Now, we will explain the nature of zinc oxides with the help of reactions,
Zinc oxide has an amphoteric nature and amphoteric refers to the compounds which exhibit acidic as well as basic properties as zinc oxide reacts with acids such as hydrochloric acid to give zinc chloride as a product, and zinc oxide reacts with bases such as sodium hydroxide which gives sodium zincate as a product it is called as an amphoteric oxide. The reactions are as follows,
$ZnO(s) + 2HCl(aq) \to ZnC{l_2}(s) + {H_2}O(l)$
$ZnO(s) + 2NaOH(aq) \to N{a_2}Zn{O_2}(aq) + {H_2}O(l)$
Step 3: Now we will define Molar conductivity and Zero-order reactions one by one,
Molar conductivity is a term of electrochemistry and is defined as the conductance (Conductance is defined as a degree of easiness of flow of current) of a volume of a solution containing $1$ mole of dissolved electrolyte when placed between two parallel electrodes 1cm apart.
Zero-order reaction: This is a term used in chemical kinetics and is a type of reaction whose rate (change in conc. of reactants or products with time) is independent of the reaction concentration and the rate remains constant throughout the reaction.
Step 4: Calculation of rate constant for the first order reaction:
Rate for the first order reaction is given by the following formula,
$k = \dfrac{{2.303}}{t}\log \dfrac{{{{[A]}_0}}}{{{{[A]}_t}}}$where,
$t$ = time of the reaction
$k$= rate constant for the reaction
${[A]_t}$ = concentration of reactant at time t
${[A]_0}$ = Initial concentration of the reaction at time= 0
Let the initial concentration of the reactant be “ $100$ ”, now as it is given that $40\% $ of the sample remains unreacted at $45$ minutes this means we can put the concentration of reactant at time= $45$ min as “ $40$ ”. Therefore, substituting the given values in the above equation we get;
$k = \dfrac{{2.303}}{{45}}\log \dfrac{{100}}{{40}}$
$k = \dfrac{{2.303}}{{45}}\log 2.5$
$k = \dfrac{{2.303}}{{45}} \times 0.3979$
$k = 0.02036{\min ^{ - 1}}$

Note:
The unit for the rate constant for a first-order reaction is ${\sec ^{ - 1}}$ when time is in second, and here as the time is in minutes so the unit for rate constant becomes ${\min ^{ - 1}}$.