Question

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

Short answer

To react completely with 3.00g of magnesium metal, 49.2 mL of 5.0 M HCl is required.

Step-by-step solution

Write the balanced chemical equation

The balanced chemical equation for the reaction between hydrochloric acid (HCl) and magnesium metal (Mg) is: \(Mg_{(s)} + 2HCl_{(aq)} \rightarrow MgCl_{2(aq)} + H_{2(g)}\)

Calculate the number of moles of magnesium

We are given the mass of magnesium (3.00g), and we need to find the corresponding moles. Using the molar mass of magnesium (Mg) which is 24.31 g/mol, we can calculate the moles as follows: Moles of Mg = \( \frac{mass}{molar\:mass} \) Moles of Mg = \( \frac{3.00\:g}{24.31\:g/mol} \) = 0.123 mol

Determine the number of moles of hydrochloric acid

According to the balanced chemical equation, 1 mole of Mg reacts with 2 moles of HCl. Thus, we can now find the number of moles of HCl that will completely react with 0.123 mol of Mg: Moles of HCl = moles of Mg × \( \frac{2\:mol\:HCl}{1\:mol\:Mg} \) Moles of HCl = 0.123 mol × \( \frac{2}{1} \) = 0.246 mol

Calculate the volume of 5.0M HCl needed

Lastly, we need to find the volume of 5.0M HCl needed to react with 0.246 mol of HCl. We know the molarity (M) is a measure of moles of solute per liter of solution, so we can use the formula: Molarity (M) = \( \frac{moles}{volume\:in\:liters} \) To find the volume of HCl needed, we can rearrange the formula and plug in the values: Volume in L = \( \frac{moles}{molarity} \) Volume in L = \( \frac{0.246\:mol}{5.0\:M} \) = 0.0492 L To convert liters to milliliters, we multiply by 1000: Volume in mL = 0.0492 L × 1000 = 49.2 mL Therefore, 49.2 mL of 5.0 M HCl are required to react completely with 3.00g of magnesium metal.

Key concepts

Understanding the Mole Concept

In chemistry, the mole is a fundamental concept that provides a bridge between the microscopic world of atoms and molecules and the macroscopic world we observe. A mole is a unit that measures the amount of substance. One mole of any substance contains exactly 6.02214076 × 10²³ entities, which is Avogadro's number, and this could be atoms, molecules, ions, or any other particles.

When we refer to one mole of an element, we are talking about a mass that is equal to the atomic mass of that element expressed in grams. For example, the atomic mass of magnesium (Mg) is approximately 24.31 atomic mass units (amu). Therefore, one mole of magnesium weighs 24.31 grams.

Using this concept, we can establish the number of moles of magnesium in a given sample by dividing the sample's mass by the molar mass of magnesium. This provides a quantitative measure that allows chemists to count the number of particles in a sample by weighing it, bridging the gap between the observable and the atomic scale.

To put it into perspective in our exercise, knowing that there are 3.00g of magnesium and the molar mass of magnesium is 24.31g/mol, the conversion demonstrates the power of the mole concept. It allows us to calculate that we have 0.123 moles of magnesium readily quantifiable for further stoichiometric calculations.

Molarity Calculation Explained

Molarity, commonly represented by the symbol 'M', is a very useful concentration metric in chemistry. It is defined as the number of moles of a solute per liter of solution, enabling chemists to understand the strength of a solution in terms of how much solute is present in a certain volume of solvent.

To calculate molarity, we can use the formula:
Molarity (M) = \( \frac{moles\;of\;solute}{volume\;of\;solution\;in\;liters} \)

This formula elucidates the direct proportionality between molarity and the amount of substance, and an inverse proportionality with the volume. Therefore, if you need to prepare a solution with a specific molarity, knowing the quantity (in moles) of your solute and the desired volume of your solution, you can manipulate the equation accordingly to work out either variable.

In the textbook problem, we inverted this formula to find out the volume of a hydrochloric acid solution needed to react with a given amount of magnesium. By knowing the number of moles of hydrochloric acid and its concentration (5.0M), we could determine that a volume of 49.2 mL is required – showcasing the practical application of molarity calculation in determining reactant volumes in chemical reactions.

Balancing Chemical Reaction Equations

Balancing chemical reaction equations is a critical skill that enforces the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction. This law implies that the number of each type of atom on the reactant side must equal the number of the same atoms on the product side of the equation.

To balance an equation, one must adjust the coefficients – the numbers in front of the chemical formulas – to ensure that there is the same number of each type of atom on both sides of the equation.
In the case of our hydrochloric acid and magnesium reaction:
\( Mg_{(s)} + 2HCl_{(aq)} \rightarrow MgCl_{2(aq)} + H_{2(g)} \)

This equation shows one magnesium atom reacting with two molecules of hydrochloric acid to form one molecule of magnesium chloride and one molecule of hydrogen gas. The coefficients (1 Mg, 2 HCl, 1 MgCl₂, and 1 H₂) illustrate a balanced equation where the atoms are conserved. Once a reaction is balanced, it provides the mole ratio of reactants to products necessary for stoichiometric calculations. In our exercise, it showed that one mole of Mg requires two moles of HCl, a stoichiometric ratio crucial for accurately determining the required volumes and amounts of reactants in chemical processes.