Question

A 0.662 gram sample of a metal, M, reacts completely with sulfuric acid according to: M(s) + H2SO4(aq) ----> MSO4(aq) +H2(g). A volume of 257 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 degrees C. Calculate the atomic mass of the metal.

Answer 1

In this problem we can use ideal gas equation

             That is

                         PV =nRT

Rearrange the above equation to solve for mols of hydrogen

                          n = PV/RT

next we can do a molar ratio between hydrogen and the metal.

convert Torr in to atm

where I atm = 760 torr

therefore

P = 756.0 torr x1 atm/760 torr = 0.995 atm

  

convert degree celcius in to kelvin
T = 273 + 25

    = 298 K

convert mL in to L

V = 257 mL x 1 L/ 1000 mL = 0.263 L

R= gas constant = 0.08206 L*atm/mol*k

Therefore

nH2 = (0.995 atm)(0.257L)/(0.08206 L*atm/mol*k)(298 K)

note atm , L & k units are cancelled

         = 0.25572 / 24.45

      nH2   = 1.046x 10^-2 mol

therefore the n M are

1.045 x 10^-2 mol H2 x 1 mol M/ 1 mol H2 = 1.045 x 10^-2 mol M

Molar mass = Mass/Mols

mass of metal = 0.662 g

So we can find the molar mass of the unknown metal.

Molar mass of M = (0.662 g)/(1.045 x 10^-2 mol) = 63.35 g/mol

so the unknown metal is copper (Cu)