Question

When hydrochloric acid reacts with magnesium metal, hydrogen gas and aqueous magnesium chloride are produced. What volume of \(5.0 M \mathrm{HCl}\) is required to react completely with \(3.00 \mathrm{~g}\) of magnesium?

Short answer

The volume of \(5.0 \mathrm{M}\) \(\mathrm{HCl}\) required to react completely with \(3.00 \mathrm{~g}\) of magnesium is \(0.0492 \mathrm{~L}\) or \(49.2 \mathrm{~mL}\).

Step-by-step solution

Write down the balanced chemical equation

The reaction of hydrochloric acid with magnesium metal can be represented by the following balanced chemical equation: \( \mathrm{Mg} + 2\mathrm{HCl} \rightarrow \mathrm{MgCl_2} + \mathrm{H_2} \)

Convert the mass of magnesium to moles

To convert the mass of magnesium to moles, use the molar mass of magnesium, which is \(24.31\mathrm{~g/mol}\): \[ \text{moles of Mg} = \frac{\text{mass}}{\text{molar mass}} = \frac{3.00 \mathrm{~g}}{24.31 \mathrm{~g/mol}} = 0.123 \mathrm{~mol} \]

Determine moles of \(\mathrm{HCl}\) needed using stoichiometry

For every mole of \(\mathrm{Mg}\) that reacts, two moles of \(\mathrm{HCl}\) are required (from the balanced chemical equation). So, we multiply the moles of \(\mathrm{Mg}\) by a stoichiometric factor to find the moles of \(\mathrm{HCl}\) required: \[ \text{moles of HCl} = \text{moles of Mg} \times \frac{\text{moles of HCl}}{\text{moles of Mg}} = 0.123 \mathrm{~mol} \times \frac{2 \mathrm{~mol\ HCl}}{1 \mathrm{~mol\ Mg}} = 0.246 \mathrm{~mol\ HCl} \]

Convert the moles of \(\mathrm{HCl}\) to the volume of \(5.0 \mathrm{M}\) solution required

Use the formula \(\mathrm{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution}}\) to find the volume of \(5.0 \mathrm{M}\) \(\mathrm{HCl}\) solution required: \[ \text{volume of solution} = \frac{\text{moles of HCl}}{\text{Molarity}} = \frac{0.246 \mathrm{~mol}}{5.0 \mathrm{~M}} = 0.0492 \mathrm{~L} \] So, \(0.0492 \mathrm{~L}\) (\(49.2 \mathrm{~mL}\)) of \(5.0 \mathrm{M}\) \(\mathrm{HCl}\) is required to react completely with \(3.00 \mathrm{~g}\) of magnesium.

Key concepts

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and forming of chemical bonds. These processes can be depicted using balanced chemical equations, which represent the reaction in a concise and informational way.

For example, when hydrochloric acid (\text{HCl}) reacts with magnesium metal (\text{Mg}), it forms hydrogen gas (\text{H}_2) and aqueous magnesium chloride (\text{MgCl}_2). The balanced chemical equation for this reaction would be: \( \text{Mg} + 2\text{HCl} \rightarrow \text{MgCl}_2 + \text{H}_2 \).

The coefficients before the chemical formulas indicate the mole-to-mole ratio in which the reactants combine and the products form. It's crucial to balance a chemical equation so that the same number of atoms of each element are present on both sides, reflecting the law of conservation of mass.

Molar Mass

The molar mass of a substance is the mass of one mole of that substance, usually expressed in grams per mole (\text{g/mol}). It is a critical factor for converting between the mass of a substance and the amount in moles.

For instance, magnesium has a molar mass of 24.31 \text{g/mol}. Therefore, to convert 3.00 \text{g} of magnesium to moles, we divide the mass by the molar mass: \( \frac{3.00 \text{g}}{24.31 \text{g/mol}} = 0.123 \text{mol} \).

This allows us to work out the amount of magnesium in terms of moles, which then becomes the starting point for stoichiometric calculations in a chemical reaction.

Molarity

Molarity is a measure of the concentration of a solution, defined as the number of moles of solute (the substance being dissolved) per liter of solution. It is numerically represented in moles per liter (\text{M}).

For example, a 5.0 \text{M} solution of hydrochloric acid (\text{HCl}) contains 5.0 moles of \text{HCl} in every liter of the solution. If we have a certain number of moles of \text{HCl}, we can calculate the volume of this solution necessary for a reaction by rearranging the molarity formula: \( \text{Volume of solution} = \frac{\text{Moles of solute}}{\text{Molarity}} \).

This relationship is crucial in the laboratory when preparing solutions or determining the amounts needed for reactions.

Mole-to-Mole Ratio

The mole-to-mole ratio, derived from the coefficients in a balanced chemical equation, is pivotal in stoichiometry. It provides the direct relationship between the amounts in moles of any two substances involved in a chemical reaction.

In our exercise, the balanced equation \( \text{Mg} + 2\text{HCl} \rightarrow \text{MgCl}_2 + \text{H}_2 \) indicates that for every mole of magnesium, two moles of hydrochloric acid are needed. Consequently, if we have 0.123 moles of magnesium, based on the mole-to-mole ratio of magnesium to hydrochloric acid (1:2), we would require 0.246 moles of hydrochloric acid: \( 0.123 \text{mol Mg} \times \frac{2 \text{mol HCl}}{1 \text{mol Mg}} = 0.246 \text{mol HCl} \).

The mole-to-mole ratio is an essential concept enabling the quantitative prediction of products and reactants in a given chemical reaction.