Verified Answer :

taskmasters

The balanced chemical reaction is:

2SO2 + O2=2SO3

We are given the amounts of the reactants to be consumed in the reaction. These amounts are the starting point for the calculations.

5.0 L SO2 ( 1 mol / 22.4 L ) = 0.2232 mol SO2
3.0 L O2  ( 1 mol / 22.4 L ) = 0.1339 mol O2

From the chemical reaction, the mole ratio of the reactants 2:1. Therefore, the limiting reactant is SO2.

0.2232 mol SO2 ( 1 mol SO3 / 2 mol SO2) ( 22.4 L / 1 mol ) = 2.4998 L SO3

Answer : The volume of mixture is, 4.99 liters.

Explanation :

First we have to calculate the moles of \(SO_2\) and \(O_2\).

As we know that at STP, 1 mole of substance contains 22.4 L volume of substance.

As, 22.4 L volume of \(SO_2\) present in 1 mole of \(SO_2\)

So, 5 L volume of \(SO_2\) present in \(\frac{5}{22.4}=0.223\) mole of \(SO_2\)

And,

As, 22.4 L volume of \(O_2\) present in 1 mole of \(O_2\)

So, 3 L volume of \(O_2\) present in \(\frac{3}{22.4}=0.134\) mole of \(O_2\)

Now we have to calculate the limiting and excess reagent.

The balanced chemical reaction is,

\(2SO_2+O_2\rightarrow 2SO_3\)

From the balanced reaction we conclude that

As, 2 mole of \(SO_2\) react with 1 mole of \(O_2\)

So, 0.223 moles of \(SO_2\) react with \(\frac{0.223}{2}=0.1115\) moles of \(O_2\)

From this we conclude that, \(O_2\) is an excess reagent because the given moles are greater than the required moles and \(SO_2\) is a limiting reagent and it limits the formation of product.

Now we have to calculate the moles of \(SO_3\)

From the reaction, we conclude that

As, 2 mole of \(SO_2\) react to give 2 mole of \(SO_3\)

So, 0.223 moles of \(SO_2\) react to give 0.223 moles of \(SO_3\)

Now we have to calculate the volume of \(SO_3\).

As, 1 mole of \(SO_3\) gas occupy 22.4 L volume of \(SO_3\)

So, 0.223 mole of \(SO_3\) gas occupy \(0.223\times 22.4=4.99L\) volume of \(SO_3\)

Therefore, the volume of the mixture is 4.99 liters.