# Question 97471

Jun 29, 2015

The mole fraction of ${\text{SO}}_{2}$ is 9.3 × 10^(-10), and its molarity is 3.8 × 10^(-11) "mol/L".

#### Explanation:

Step 1. Calculate the mass of 1 mol of air.

$\text{Mass of air" = 24.5 cancel("L air") × (1000 cancel("mL air"))/(1 cancel("L air")) × (1.22 × 10^-6 "g air")/(1 cancel("mL air")) = 2.989 × 10^-2 "g air}$

Step 2. Calculate the mass of ${\text{SO}}_{2}$.

${\text{Mass of SO"_2 = 2.989 × 10^(-2) cancel("g air") × ("2.0 g SO"_2)/(10^6 cancel("g air")) = 5.98 ×10^(-8) "g SO}}_{2}$

Step 3. Calculate the moles of ${\text{SO}}_{2}$.

${\text{Moles of SO"_2 = 5.98 ×10^(-8) cancel("g SO"_2) × ("1 mol SO"_2)/(64.06 cancel("g SO"_2)) = 9.33 × 10^(-10) "mol SO}}_{2}$

Step 4. Calculate the mole fraction of ${\text{SO}}_{2}$.

"Mole fraction" = ("moles SO"_2)/"total moles" = (9.33 × 10^(-10)cancel("mol")) /(1 cancel("mol") + 9.33 × 10^(-10) cancel("mol")) = 9.3 × 10^(-10)#

Step 5. Calculate the molarity of ${\text{SO}}_{2}$.

$\text{Molarity" = "moles"/"litres" = (9.33 × 10^(-10) "mol")/"24.5 L" = 3.8 × 10^(-11) "mol/L}$