Magnesium metal reacts with HCl solution, liberating H2 gas and generating Mg2+ cations in solution. A 2.970-g sample of Mg metal is added to 50.0 mL of a 4.00 M HCl solution, and the reaction goes to completion. How many grams of H2 are formed?
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.
To find the number of grams of H2 formed, we need to use stoichiometry and the balanced chemical equation for the reaction between magnesium and hydrochloric acid.
The balanced chemical equation for the reaction is:
Mg + 2HCl -> MgCl2 + H2
From the equation, we can see that 1 mole of magnesium reacts with 2 moles of hydrochloric acid to produce 1 mole of hydrogen gas.
First, let's calculate the number of moles of hydrochloric acid used in the reaction:
moles of HCl = (volume of HCl solution in liters) x (concentration of HCl in M)
Given that the volume of HCl solution is 50.0 mL (or 0.0500 L) and the concentration is 4.00 M, we can calculate the number of moles of HCl:
moles of HCl = 0.0500 L x 4.00 M = 0.200 mol
Since the reaction goes to completion, all of the moles of HCl react with magnesium, and we can infer that the number of moles of hydrogen gas formed is also 0.200 mol.
Now, we need to calculate the molar mass of hydrogen gas (H2), which is approximately 2.016 g/mol.
To find the mass of hydrogen gas formed, we can use the equation:
mass of H2 = moles of H2 x molar mass of H2
mass of H2 = 0.200 mol x 2.016 g/mol ≈ 0.4032 g
Therefore, approximately 0.4032 grams of hydrogen gas are formed in the reaction.