Question

You start with an equimolar mixture of the gases SO₂ and O₂ in a container. The SO₂ and O₂ react to completion to form SO₃. If the temperature after the reaction is 25°C and the pressure in the container is 1.25 atm, what is the density of the product gas mixture? Assume ideal behavior.

Answer 1

Explanation:

The given reaction is as follows.

         $SO_{2} + O_{2} \rightarrow SO_{3}$

Now, balancing the given equation by putting appropriate coefficients.

              $2SO_{2} + O_{2} \rightarrow 2SO_{3}$

It is given that equimolar $SO_{2}$ and $O_{2}$. Hence,

Therefore, during completion of the reaction,

          $SO_{2} + O_{2} \rightarrow SO_{3} + \frac{1}{2}O_{2}$    

Temperature (T) = $25^{o}C$ = (25 + 273) K = 298 K

Pressure (P) = 1.75 atm

R (gas constant) = 0.0820 L atm/mol K

As on completion of reaction there is $O_{2}$ and $SO_{3}$ remains in the mixture. Therefore, molar mass of the mixture is equal to the sum of molar mass of

Total molar mass = $O_{2} + SO_{3}$

                             = (32 + 80) g/mol

                             = 112 g/mol

Hence, according to the formula we will calculate the density as follows.

       Density = $\frac{P \times \text{molar mass}}{R \times T}$

                     = $\frac{1.25 atm \times 112 g/mol}{0.0820 Latm/mol K \times 298 K}$

                     = 5.73 g/L

Thus, we can conclude that density of the product gas mixture is 5.73 g/L.