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 1.65 atm, what is the density of the product gas mixture? Assume ideal behavior.

Answer 1

The density of the product gas mixture is 5.39 g/L

Explanation:

Given:

Temperature after the reaction = $25^0$C

Pressure in the container = 1.65 atm

The ideal gas equation PV = nRT

To find: Density of the product gas mixture

Step 1:

Molarity (M) = P/(RT)

$\[M=\frac{P}{R T}\] M=\frac{1.65 \mathrm{atm}}{\left(0.08206 \frac{L \cdot a t m}{m o l . K}\right)(298.15 K)}$

M = 0.0674 mol/L

Step 2:

The product of the given reaction is $SO_3$. Its molar mass is

1S x 32.066 g/mol = 32.066 g/mol

3O x 16 g/mol = 48 g/mol

Adding both we get 80.066 g/mol

Therefore the density of the product gas mixture is $0.0674 \frac{{mol}}{L} \times \frac{80.066 g}{1 \mathrm{mol}}$

= 5.39 g/L