Question

A 0.442 gram sample of a metal, M, reacts completely with sulfuric acid according to:

M(s) + H₂SO₄(aq) --> MSO₄(aq) + H₂(g)

A volume of 201 mL of hydrogen is collected over water; the water level in the collecting vessel is the same as the outside level. Atmospheric pressure is 756.0 Torr and the temperature is 25 °C. The vapor pressure of water at various temperatures can be found in this table. Calculate the molar mass of the metal.

Answer 1

Answer.

Given that,

Atmospheric pressure (P_a) = 756 Torr

Vapor Pressure (P_w) (at 25 ^oC) = 23.8 Torr

Temperature (T) = 25 + 273.15 = 298.15 K

Volume (V) = 201 mL = 0.201 L

Universal gas constant (R) = 0.08205 L-atm/mol-K

Total Pressure (P) = P_a-P_w = 756-23.8/(760) = 732.2/760 = 0.9634 atm

Using ideal gas equation PV=nRT, we have

0.9634*0.201 = n*0.08205*298.15

n = 0.0079 moles

Since 1 mole of H₂ is produced from 1 mole of Metal (M),

0.0079 mole of H₂ will be produced from 0.0079 mole of Metal (M)

Sinc Molar mass = mass/mole, therefore

Molar mass (M) = 0.442/0.0079 = 55.95 g/mol.