A 0.200-g sample of cobalt metal reacted with hydrochloric acid according to the following balanced chemical equation: Co (s) + 2 HCl (aq) ➝ CoCl2 (aq) + H2 (g) The volume of hydrogen gas collected over water was 87.5 mL at 20 °C and a barometer reading of 763 mm Hg. Referring to Example Exercise 1, the adjusted volume of the H2 gas is

V H2 (g) = 83.13 mL

Explanation:

Dalton's law:

Pgas = Pbar - P*H2O

∴ vapor pressure (P*)

⇒ P*H2O (20°C) = 17.5 mmHg

∴ Pbar = 763 mmHg

⇒ PH2 = 763 mmHg - 17.5 mmHg = 745.5 mmHg = 0.9809 atm

Co (s) + 2 HCl (aq) → CoCl2 (aq) + H2 (g)

∴ Mw Co (s) = 58.933 g/mol

⇒ mol Co (s) = (0.200 g Co) * (mol/58.933 g) = 3.394 E-3 mol Co

⇒ n H2 (g) = (3.394 E-3 mol Co) (mol H2 / mol Co) = 3.394 E-3 mol H2 (g)

ideal gas:

PV = RTn

∴ R = 0.082 atm. L/K. mol

∴ T = 20°C ≅ 293 K

the adjusted volume H2 (g):

⇒ V H2 (g) = ((0.082 atm. L/K. mol) (293 K) (3.394 E-3 mol)) / (0.9809 atm)

⇒ V H2 (g) = 0.08313 L

⇒ V H2 (g) = 83.13 mL