An aqueous solution of hydrochloric acid (HC1, molar mass - 36.5 g/mol) has a de

Question

An aqueous solution of hydrochloric acid (HC1, molar mass - 36.5 g/mol) has a density of 1.18 g/mL and is 37 % HC1 by mass. The solvent is water (molar mass = 18.0 g/mol). Perform the calculations indicated below. A) the molality of HCl B) the mole fractions of HC1 and water C) the molarity of HCl Do the reverse calculations for the previous problems by using your answers for each part. A) mass percent from molality of HCl B) mass percent from the mole fractions of HCl and water C) mass percent from the molarity of HCl

Explanation / Answer

HCl molar mass = 36.5 g/mol

HCl density = 1.18 g/mL; i.e., 1180 kg/L

the mass percentage of HCl in HCl solution = 37%

The mass of HCl in 1 L HCl solution = 1180 X 37/100 = 436.6 gr

a) 1180 gr of HCl solution contains 436.6 g

therefore the wt. of HCl in 1000 g/ 1 kg = 1000/1180 X 436.6 = 370 g

the moles of HCl in 1 kg of HCl solution = 370/36.5 = 10.14 moles

the moles of HCl in 1 kg of HCl solution is called its molality

So, HCl solution molality = 10.14 m (mol/kg)

b) 1000 g of HCl solution contains 370 g (or) 10.14 moles of HCl.

remaing wt. of 1000g is the wt. of water = 630 g

water moles in 1 kg of HCl = 35 moles

Mole fraction of HCl = HCl moles/total moles = 10.14/45.14 = 0.225

Mole fraction of water = water moles/total moles = 35/45.14 = 0.775

c) The moles of HCl in 1 L HCl solution = 436.6/36.5 = 11.96 moles

The moles of HCl in 1 L HCl solution is called its molarity

therefore HCl molarity = 11.96 M (or) 11.96 mol/L

2. a) molality of HCl = 10.14 mol/kg

10.14 mol HCl = 10.14 X 36.5 = 370.11

mass percent of HCl soln. = 370.11/1000 X 100 = 37.01%

b) mass percent of HCl = (m. f of HCl X HCl M.Wt.)/ (m. f. of water X water m.wt. + m. f of HCl X HCl M.Wt.) X100

= (0.225 X 36.5)/ (0.775 X 18 + 0.225 X 36.5) X 100

= 37.05%

c) molarity of HCl = 11.96 mol/L

11.96 moles HCl wt. = 436.54 g

1 L of HCl solution wt. = 1180 g

therefore mass percent = 436.54/ 1180 X 100 = 36.99%

Best wishes.

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