Question

In a zero order reaction for every $10 ^\circ $ rise in temperature,the rate is doubled.If the temperature is increased from $10 ^\circ C$ to $100 ^\circ C$ ,the rate of reaction will become
a) $256$ times
b) $512$ times
c) $64$ times
d) $128$ times

Answer 1

Hint: The relationship between the rate of a chemical reaction and the concentration of the species which are taking part in it is known as the order of the reaction.In simple terms the order of reaction also tells us how dependent the reaction is on reactant concentration.Most of the reactions have zero order,first order or second order of reaction.

Complete answer:
In the above example we are talking about an zero order reaction.Let us first understand what are zero order reaction.The chemical reactions in which the rate of the chemical reaction is independent of the concentration of reactants is known as zero order reactions.In simple terms we can say that no matter the variation in concentration of reactants the rate at which the reaction proceeds will not change.
Here it is given that for every $10 \circ $ rise in temperature,the rate of reaction is doubled,therefore
\[n = 1\]
Therefore the rate of reaction is given as,
$ = {2^n}$
Substituting the value of $n$ which we had got earlier,
$ = {2^1} = 2$
The rate of reaction thus corresponds with the condition given.
Here the temperature increases from $10 \circ C$ to $100 \circ C$ ,therefore the difference between the final and initial temperature is given as,
$100 - 10 = 90$
Therefore now the value of $n$ is $9$ .Hence the rate of reaction once the temperature is raised to $100 \circ C$ is given as,
${2^9} = 512$
Hence the rate of reaction will increase by $512$ times.Hence the correct option is b) $512$.

Note:
For zero order reactions it is worth noting that external factors like temperature and pressure will impact the rate of reaction.One of the most famous examples of zero-order reaction is the reverse Haber process because its rate is independent of the concentration of ammonia.