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Question: The rate of \(S{O_3}\) in the following reaction \(2S{O_2} + {O_2} \to 2S{O_2}\) is \(100g{\min ^{ -...

The rate of SO3S{O_3} in the following reaction 2SO2+O2→2SO22S{O_2} + {O_2} \to 2S{O_2} is 100gmin⁡−1100g{\min ^{ - 1}}. Hence, the rate of disappearance of O2{O_2} is:
(A). 2gmin⁡−12g{\min ^{ - 1}}
(B). 20gmin⁡−120g{\min ^{ - 1}}
(C). 200gmin⁡−1200g{\min ^{ - 1}}
(D). 50gmin⁡−150g{\min ^{ - 1}}

Explanation

Solution

The rate of chemical reaction is the change in concentration over the change in time.
Rate⁡of disappearance = −△(Reactants⁡)△t\operatorname{Rate} of \, disappearance {\text{ = }}\dfrac{{ - \vartriangle \left( {\operatorname{Reactants} } \right)}}{{\vartriangle t}} . The reaction rate is defined as the speed at which a chemical reaction takes place or the speed at which the reactants are converted into products.

Complete step by step answer:
For the given reaction
2SO2+O2→2SO32S{O_2} + {O_2} \to 2S{O_3}
The differential equation can be written as
12−d[SO2]dt=−d[O2]dt=12d[SO3]dt\dfrac{1}{2}\dfrac{{ - d\left[ {S{O_2}} \right]}}{{dt}} = \dfrac{{ - d\left[ {{O_2}} \right]}}{{dt}} = \dfrac{1}{2}\dfrac{{d\left[ {S{O_3}} \right]}}{{dt}}
d[SO3]dt=100gmin⁡−1=10080mol⁡min⁡−1\dfrac{{d\left[ {S{O_3}} \right]}}{{dt}} = 100g{\min ^{ - 1}} = \dfrac{{100}}{{80}}\operatorname{mol} {\min ^{ - 1}}
−d[O2]dt=12(10080)mol⁡min⁡−1\dfrac{{ - d\left[ {{O_2}} \right]}}{{dt}} = \dfrac{1}{2}\left( {\dfrac{{100}}{{80}}} \right)\operatorname{mol} {\min ^{ - 1}}
=12×10080×32gmin⁡−1= \dfrac{1}{2} \times \dfrac{{100}}{{80}} \times 32g{\min ^{ - 1}}
=20gmin⁡−1= 20g{\min ^{ - 1}}
Hence, option (B) is the correct one.

Additional Information:
i). The rate of disappearance of reactants
=−△(Reactants⁡)△t= \dfrac{{ - \vartriangle \left( {\operatorname{Reactants} } \right)}}{{\vartriangle t}}
Note this is negative because it measures the rate of disappearance of the reactants.
ii). The Rate of Formation of Products.
=△(Products)△t= \dfrac{{\vartriangle \left( {Products} \right)}}{{\vartriangle t}}
This is the rate at which the products are formed.
They both are linked are the balanced chemical reactions and can be used to measure the reaction rate.
Rate of Reaction: The reaction rate or rate of reaction is the speed at which a chemical reaction is the speed at which a chemical reaction takes place. Reactions rate is defined as speed at which reactants are converted into products.
Factors affecting rate of Reaction.
I. Surface area of solid reactant.
II. Concentration and pressure of a reactant
III. Temperature.
IV. Nature of reactant
V. Presence/absence of catalyst.
As the temperature increases, the kinetic energy of the reactants also increases. This results in the increased movement of the reactants. Thus, with the reactants moving faster, the number of collisions also increases. Due to this, the reactants start to convert into products. Hence, the rate of reaction is increased. Moreover, the minimum kinetic energy required for a reaction to occur is called activation energy.

Note: There is a significance of positive and negative sign in rate of reaction. The position sign shows the rate of formation of product where the negative sign shows that rate of disappearance of reactant in the rate of reaction.