To determine the number of grams of H2 gas formed in the reaction, we need to use stoichiometry and the principle of conservation of mass.
First, let's write the balanced chemical equation for the reaction:
Mg(s) + 2HCl(aq) -> MgCl2(aq) + H2(g)
From the balanced equation, we can see that 1 mole of Mg reacts with 2 moles of HCl to produce 1 mole of H2.
Step 1: Calculate the moles of Mg in the 2.970 g sample.
To do this, we need to use the molar mass of Mg, which is 24.31 g/mol.
Moles of Mg = Mass of Mg / Molar mass of Mg
Moles of Mg = 2.970 g / 24.31 g/mol
Moles of Mg = 0.122 moles
Step 2: Use stoichiometry to determine the moles of H2 formed.
Since the reaction is 1:1 between Mg and H2, the moles of H2 formed will also be 0.122 moles.
Step 3: Convert the moles of H2 to grams.
To do this, we need to use the molar mass of H2, which is 2.016 g/mol.
Mass of H2 = Moles of H2 x Molar mass of H2
Mass of H2 = 0.122 moles x 2.016 g/mol
Mass of H2 = 0.246 g
Therefore, approximately 0.246 grams of H2 gas are formed in the reaction.