To answer this question, we need to use stoichiometry and the balanced chemical equation for the reaction between hydrochloric acid (HCl) and magnesium (Mg).
First, let's write the balanced equation for the reaction:
2HCl + Mg -> MgCl2 + H2
From the balanced equation, we can see that 2 moles of HCl react with 1 mole of Mg. Now, let's calculate the number of moles of magnesium (Mg) we have:
Number of moles = Mass / molar mass
The molar mass of magnesium (Mg) is 24.31 g/mol, so:
Number of moles of Mg = 3.00 g / 24.31 g/mol = 0.1235 mol (rounded to 4 decimal places)
Since the stoichiometric ratio between HCl and Mg is 2:1, the number of moles of HCl required to react with 0.1235 moles of Mg is double that amount:
Number of moles of HCl = 2 * 0.1235 mol = 0.247 mol
Finally, we can determine the volume of 5.0 M HCl needed. The molarity (M) of a solution is defined as the number of moles of solute per liter of solution.
Volume of HCl = Number of moles / Molarity
Volume of HCl = 0.247 mol / 5.0 mol/L = 0.0494 L
To convert the volume from liters to milliliters, multiply by 1000:
Volume of HCl = 0.0494 L * 1000 mL/L = 49.4 mL
Therefore, approximately 49.4 mL of 5.0 M HCl is required to react completely with 3.00 g of magnesium.