A solution of HCl gas dissolved in water (sold commercially as "muriatic acid," a solution used to clean masonry surfaces) has 20.22 g of HCl per 100.0 g of solution, and its density is 1.10 g/mL.

What is its molarity?
What is its mole fraction?

[HCl] = 6.09 M

Xm HCl = 0.11

Explanation:

Let's analyse data:

20.22 g of solute / 100 g of solution

Solution's density = 1.10 g/mL

As we have the mass of solution and its density we determine solution's volume to stablish [M]

Density = Mass / volume → 1.10 g/mL = 100 g / Volume

100 g / 1.10g/mL = 90.9 mL

Let's convert the volume to L → 90.9 mL . 1L/ 1000mL = 0.0909L

We convert the mass of solute to moles → 20.22 g . 1mol/ 36.45g =

0.554 moles

[M] = Molarity (moles of solute /1L of solution) = 0.554 mol/0.0909L = 6.09M

Mole fraction (Xm) = Moles of solute / Total moles

Total moles = Moles of solute + Moles of solvent

Mass of solvent = Mass of solution - Mass of solute

Mass of solvent = 100 g - 20.22 g = 79.78g

We convert the mass to moles → 79.78 g / 18g/mol = 4.43 moles

Total moles = 4.43 moles + 0.554moles = 4.984 moles

Xm = 0.554 / 4.984 = 0.11