Question

A 0.595 g sample of a metal, M, reacts completely with sulfuric acid according to the reaction M ( s ) + H 2 SO 4 ( aq ) ⟶ MSO 4 ( aq ) + H 2 ( g ) A volume of 231 mL of hydrogen gas is collected over water; the water level in the collecting vessel is the same as the outside level. Atmospheric pressure is 1.0079 bar and the temperature is 25 °C. The vapor pressure of water at 25 °C is 0.03167 bar. Calculate the molar mass of the metal.

Answer 1

molar mass M(s) = 65.326 g/mol

Step-by-step explanation:

• M(s) + H2SO4(aq) → MSO4(aq) + H2(g)

∴ VH2(g) = 231 mL = 0.231 L

∴ P atm = 1.0079 bar

∴ PvH2O(25°C) = 0.03167 bar

Graham´s law:

⇒ PH2(g) = P atm - PvH2O(25°C)

⇒ PH2(g) = 1.0079 bar - 0.03167 bar = 0.97623 bar = 0.9635 atm

∴ nH2(g) = PV/RT

⇒ nH2(g) = ((0.9635 atm)(0.231 L))/((0.082 atmL/Kmol)(298 K))

⇒ nH2(g) = 9.1082 E-3 mol

⇒ n M(s) = ( 9.1082 E-3 mol H2(g) )(mol M(s)/mol H2(g))

⇒ n M(s) = 9.1082 E-3 mol

∴ molar mass M(s) [=] g/mol

⇒ molar mass M(s) = (0.595 g) / (9.1082 E-3 mol)

⇒ molar mass M(s) = 65.326 g/mol