Magnesium metal reacts with HCl solution, liberating H2 gas and generating Mg2+ cations in solution. A 1.890-g sample of Mg metal is added to 125.0 mL of a 4.00 M HCl solution, and the reaction goes to completion. How many grams of H2 are formed?
To find the number of grams of H2 gas formed, we need to use stoichiometry.
First, we need to determine the limiting reactant. The limiting reactant is the one that will be completely consumed in the reaction, thereby determining the maximum amount of product that can be formed.
To find the limiting reactant, we need to compare the number of moles of each reactant. Then, we can determine which reactant produces fewer moles of the product. Let's calculate the moles of each reactant:
Moles of Mg = mass / molar mass
Molar mass of Mg = 24.31 g/mol
Moles of Mg = 1.890 g / 24.31 g/mol = 0.0777 mol
Moles of HCl = concentration x volume
Moles of HCl = 4.00 M x 0.1250 L = 0.500 mol
The balanced chemical equation for the reaction indicates that 1 mole of Mg reacts with 2 moles of HCl to produce 1 mole of H2.
From the stoichiometry, we can see that the ratio of moles of HCl to moles of H2 is 2:1. That means 2 moles of HCl will produce 1 mole of H2.
Now let's compare the moles of HCl and Mg:
Moles of HCl = 0.500 mol
Moles of H2 produced by HCl = 0.500 mol x (1 mol H2 / 2 mol HCl) = 0.250 mol
Since the molar ratio of HCl to H2 is 2:1, we have 0.250 mol of H2.
Finally, let's calculate the mass of H2:
Mass of H2 = moles of H2 x molar mass of H2
Molar mass of H2 = 2.02 g/mol
Mass of H2 = 0.250 mol x 2.02 g/mol = 0.505 g
Therefore, the mass of H2 formed is 0.505 grams.