To find the mass of Me, we need to use the ideal gas law equation to calculate the number of moles of H2.

First, convert the volume of H2 from liters to cubic meters:
V(H2) = 112 L = 0.112 m^3

Next, use the ideal gas law equation:
PV = nRT

Substitute the values:
(1 atm) (0.112 m^3) = n (0.0821 Latm/molK) * (298 K)

Solve for n (moles of H2):
n = (1 0.112) / (0.0821 298) = 0.004

Since the stoichiometry of the reaction shows a 1:1 ratio between Me and H2, the number of moles of H2 is equal to the number of moles of Me.

Therefore, the mass of Me is:
m(Me) = n(Me) MM(Me) = 0.004 mol 162.5 g/mol = 0.65 g

So, the mass of Me is 0.65 grams.