Question

Hydrobromic acid dissolves solid iron according to the reaction: $$ \mathrm{Fe}(s)+2 \mathrm{HBr}(a q) \longrightarrow \mathrm{FeBr}_{2}(a q)+\mathrm{H}_{2}(g) $$ What mass of HBr (in g) do you need to dissolve a 3.2 -g pure iron bar on a padlock? What mass of \(\mathrm{H}_{2}\) would the complete reaction of the iron bar produce?

Short answer

To dissolve a 3.2 g iron bar, you need 112.51 g of HBr. The complete reaction of the iron bar would produce 0.02988 g of H2.

Step-by-step solution

Calculate moles of Iron (Fe)

First, determine the moles of iron using its given mass and its molar mass. The molar mass of Fe is 55.845 g/mol. Using the formula: moles of Fe = mass of Fe / molar mass of Fe. So, moles of Fe = 3.2 g / 55.845 g/mol.

Determine moles of HBr required

Use the stoichiometry of the balanced equation to find the moles of HBr needed to dissolve the iron. According to the equation, 1 mole of Fe reacts with 2 moles of HBr. So, moles of HBr required = 2 * moles of Fe.

Calculate mass of HBr required

Now, determine the mass of HBr needed using its molar mass, which is 80.9119 g/mol. Mass of HBr = moles of HBr * molar mass of HBr.

Determine moles of H2 produced

The balanced chemical equation shows that 1 mole of Fe produces 1 mole of H2. Therefore, the moles of H2 produced equals the moles of Fe.

Calculate mass of H2 produced

Finally, calculate the mass of H2 using its molar mass which is 2.01588 g/mol. Mass of H2 = moles of H2 * molar mass of H2.

Key concepts

Molar Mass Calculation

Understanding how to calculate molar mass is a fundamental skill in chemistry, essential for solving various stoichiometry problems. Molar mass, typically measured in grams per mole (g/mol), is the total mass of one mole of a substance. It's calculated by adding the atomic masses of all the atoms in a given molecular formula.

For example, in the provided homework problem, iron (Fe) has a molar mass of 55.845 g/mol, which is derived from the periodic table. If a student needs to know the molar mass of a compound like HBr, they would add the molar masses of hydrogen (H, approximately 1.01 g/mol) and bromine (Br, approximately 79.90 g/mol) to get the molar mass of HBr, which is 80.9119 g/mol. This calculation enables the student to convert between mass and moles, a critical step in stoichiometry.

Chemical Reaction Stoichiometry

Chemical reaction stoichiometry involves using balanced chemical equations to calculate the relative quantities of reactants and products involved in a chemical reaction. This balancing act is crucial because it respects the conservation of mass and the idea that atoms aren't created or destroyed in chemical reactions.

In our exercise, the balanced equation \(\text{Fe}(s) + 2\text{HBr}(aq) \longrightarrow \text{FeBr}_{2}(aq) + \text{H}_{2}(g)\) tells us that one mole of iron reacts with two moles of HBr to produce one mole of iron(II) bromide and one mole of hydrogen gas. By understanding this proportionality, students can determine how much reactant is needed to fully react with a given amount of another reactant, or what quantity of a product will form.

Mass-Mole Conversion

Converting mass to moles and vice versa is a pivotal part of solving stoichiometry problems. The conversion relies on the molar mass of the substance, which acts as a conversion factor.

For instance, the problem requires calculating how much HBr is needed to dissolve a 3.2 g iron bar. To solve this, first calculate the number of moles of iron using its molar mass (step 1 of the solution). Multiply that by the stoichiometric factor from the balanced equation (step 2), and then reverse the process - convert moles of HBr to grams using its molar mass (step 3). Similarly, once we know the moles of hydrogen gas produced (equal to the moles of iron used), we can find out its mass by multiplying by the molar mass of hydrogen (step 5). These conversions are fundamental for quantifying substances in chemistry.