Question

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

Short answer

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

Step-by-step solution

1. Write the balanced chemical equation for the reaction.

The balanced chemical equation for the reaction between magnesium (Mg) and hydrochloric acid (HCl) is given by: \[Mg(s) + 2HCl(aq) \rightarrow MgCl_2(aq) + H_2(g)\]

2. Convert the mass of magnesium to moles.

To convert the mass of magnesium to moles, we will use the molar mass of magnesium (24.31 g/mol). The formula to calculate the moles of magnesium is: Moles of Mg = (mass of Mg) / (molar mass of Mg) Moles of Mg = \(\frac{3.00\, g}{24.31\, g/mol} = 0.123\, mol\)

3. Use stoichiometry to find the moles of HCl required for the reaction.

From the balanced chemical equation, we observe that the stoichiometric ratio of Mg to HCl is 1:2. This means that for every one mole of Mg, two moles of HCl are required. Therefore, we can calculate the moles of HCl needed, using the moles of Mg: Moles of HCl = 2 × (moles of Mg) Moles of HCl = 2 × (0.123 mol) = 0.246 mol

4. Calculate the volume of 5.0 M HCl solution needed.

We are given the concentration of HCl solution, which is 5.0 M (moles per liter). We can use this information to calculate the volume of HCl solution required by using the formula: Volume of HCl solution = (moles of HCl) / (concentration of HCl solution) Volume of HCl solution = \(\frac{0.246\, mol}{5.0\, M} = 0.0492\, L\) To get the volume in milliliters, we can convert liters to milliliters: Volume of HCl solution = 0.0492 L × 1000 mL/L = 49.2 mL So, 49.2 mL of 5.0 M HCl is required to react completely with 3.00 g of magnesium.

Key concepts

Balanced Chemical Equation

When dealing with chemical reactions, the first key step is to write a balanced chemical equation. This ensures that the law of conservation of mass is upheld, meaning the same number of each type of atom is present on both sides of the equation.
In the reaction between magnesium (\( \text{Mg} \)) and hydrochloric acid (\( \text{HCl} \)), magnesium chloride (\( \text{MgCl}_2 \)) and hydrogen gas (\( \text{H}_2 \)) are produced. The balanced chemical equation for this reaction is:\[ \text{Mg}(s) + 2\text{HCl}(aq) \rightarrow \text{MgCl}_2(aq) + \text{H}_2(g) \]

• One atom of magnesium combines with two molecules of hydrochloric acid.
• This forms one formula unit of magnesium chloride and one molecule of hydrogen gas.

Balancing requires that the number of each type of atom be equal on both sides, which guides further calculations and predictions about the reaction.

Molar Mass

The concept of molar mass is crucial in stoichiometry as it allows us to convert between mass and moles, the fundamental unit in chemistry. Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol).
To find the molar mass of any element or compound, one simply sums the atomic masses of all the atoms in the formula, which are available from the periodic table.
For magnesium, the molar mass is 24.31 g/mol. This means one mole of magnesium weighs 24.31 grams. Hence, when we want to calculate how many moles are in a given mass, we use the formula:\[\text{Moles of substance} = \frac{\text{mass of substance}}{\text{molar mass of substance}}\]In our problem, 3.00 g of magnesium equates to 0.123 moles, calculated as:\[\text{Moles of Mg} = \frac{3.00 \text{ g}}{24.31 \text{ g/mol}} = 0.123 \text{ mol}\]

Conversion of Moles to Volume

After determining the moles of a reactant, we often need to find the volume of a solution needed to completely react with it. This involves conversion using the concentration of the solution, typically expressed in moles per liter (M).
For hydrochloric acid (\( \text{HCl} \)), in this exercise, a 5.0 M solution is mentioned. The concentration indicates that one liter of this solution contains 5 moles of HCl.
The formula to convert moles to volume when given the concentration (Molarity) is:\[\text{Volume} = \frac{\text{moles of solute}}{\text{Molarity of solution}}\]In our case, we calculated that 0.246 moles of HCl are required, which translates to a volume of:\[\text{Volume of HCl solution} = \frac{0.246 \text{ mol}}{5.0 \text{ M}} = 0.0492 \text{ L}\]This can be converted to milliliters by multiplying by 1000, giving us 49.2 mL of HCl needed.

Reaction of Magnesium with Hydrochloric Acid

This reaction is a common example used to illustrate fundamental stoichiometric principles. It involves the reaction of a metal, magnesium, with an acid, hydrochloric acid, producing hydrogen gas, which is combustible, and salt, magnesium chloride.

• Magnesium displaces the hydrogen ions in HCl, forming magnesium chloride, an ionic compound that dissolves in water.
• Hydrogen gas is released as a byproduct, often visibly as bubbles.

This type of reaction is classified as a single displacement reaction, where magnesium replaces hydrogen. From a real-world perspective, it's crucial in processes where rapid gas production is needed, such as hydrogen production for fuel. It also helps students understand reactive metals' behavior with acids.