Question

Complete and balance the following equations: (a) \(\mathrm{NaH}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow\) (b) \(\mathrm{Fe}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow\) (c) \(\mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) \longrightarrow\) (d) \(\mathrm{Na}(l)+\mathrm{H}_{2}(g) \longrightarrow\) (e) \(\mathrm{PbO}(s)+\mathrm{H}_{2}(g)\)

Short answer

The short answers for the balanced equations are: (a) \(NaH(s) + H_2O(l) \rightarrow H_2(g) + NaOH(aq)\) (b) \(Fe(s) + H_2SO_4(aq) \rightarrow H_2(g) + FeSO_4(aq)\) (c) \(H_2(g) + Br_2(g) \rightarrow 2 HBr(g)\) (d) \(Na(l) + H_2(g) \rightarrow NaH(s)\) (e) \(PbO(s) + H_2(g) \rightarrow Pb(s) + H_2O(l)\)

Step-by-step solution

a) Balancing NaH + H2O → ...

To balance this equation, we start by writing down the products we expect from the reaction. NaH is a metal hydride and will react with water to produce hydrogen gas (H2) and a sodium hydroxide (NaOH). So the complete equation is given by: NaH(s) + H2O(l) → H2(g) + NaOH(aq) Now, we balance the equation: - There is 1 Na atom on both sides; - There are 2 H atoms in NaH and H2O and 2 H atoms in H2 and NaOH; - There is 1 O atom in H2O and 1 in NaOH; So, the balanced equation is: NaH(s) + H2O(l) → H2(g) + NaOH(aq)

b) Balancing Fe + H2SO4 → ...

Iron (Fe) reacts with sulfuric acid (H2SO4) to produce hydrogen gas (H2) and a salt, ferrous sulfate (FeSO4). So the complete equation is given by: Fe(s) + H2SO4(aq) → H2(g) + FeSO4(aq) Now, we balance the equation: - There is 1 Fe atom on both sides; - There are 2 H atoms in H2SO4 and 2 H atoms in H2; - There is 1 S atom in H2SO4 and 1 in FeSO4; - There are 4 O atoms in H2SO4 and 4 in FeSO4; So, the balanced equation is: Fe(s) + H2SO4(aq) → H2(g) + FeSO4(aq)

c) Balancing H2 + Br2 → ...

Hydrogen gas (H2) reacts with bromine gas (Br2) to form hydrogen bromide gas (HBr). The complete equation is given by: H2(g) + Br2(g) → HBr(g) To balance the equation, we need to adjust the coefficient of HBr to balance the numbers of H and Br atoms: H2(g) + Br2(g) → 2 HBr(g) Now, - There are 2 H atoms in H2 and 2 H atoms in 2 HBr; - There are 2 Br atoms in Br2 and 2 Br atoms in 2 HBr; So, the balanced equation is: H2(g) + Br2(g) → 2 HBr(g)

d) Balancing Na + H2 → ...

Sodium (Na) reacts with hydrogen gas (H2) to form the metal hydride sodium hydride (NaH). The complete equation is given by: Na(l) + H2(g) → NaH(s) In this equation, the number of each element is already balanced: - There is 1 Na atom on both sides; - There are 2 H atoms in H2 and 2 H atoms in NaH; So, the balanced equation is: Na(l) + H2(g) → NaH(s)

e) Balancing PbO + H2 → ...

Lead(II) oxide (PbO) reacts with hydrogen gas (H2) to form elemental lead (Pb) and water (H2O). The complete equation is given by: PbO(s) + H2(g) → Pb(s) + H2O(l) To balance the equation, we need to make sure we have the same number of each element on both sides, and in this case, it's already balanced. - There is 1 Pb atom in PbO and 1 Pb atom in Pb; - There is 1 O atom in PbO and 1 O atom in H2O; - There are 2 H atoms in H2 and 2 H atoms in H2O; So, the balanced equation is: PbO(s) + H2(g) → Pb(s) + H2O(l)

Key concepts

Chemical Reactions

Imagine a world where ingredients come together to create something entirely new - that's precisely the magic of a chemical reaction. It's a process where substances, known as reactants, transform into completely new substances, called products.

Take the classic reaction of baking soda and vinegar. When mixed, they create a fizzing commotion, producing carbon dioxide gas - a brand new substance. In the textbook problems, for example, when sodium hydride (NaH) meets water (H₂O), the result is hydrogen gas (H₂) and sodium hydroxide (NaOH), a completely different set of substances than what you started with.

These transformations follow strict rules. Atoms don't appear out of thin air or vanish; they rearrange. That's where the importance of balancing chemical equations comes in. Ensuring that the number of atoms for each element remains constant throughout the reaction is not just good bookkeeping; it's a fundamental law of nature, known as the law of conservation of mass.

Stoichiometry

Equations are not just symbols on paper; they're reflections of reality, and stoichiometry is the tool we use to make sure our chemical equations mirror the real world. It's like a recipe in cooking - stoichiometry tells us the precise proportions of all the reactants we need to use to get our desired products.

For instance, our textbook exercises reveal various stoichiometric relationships, like how one mole of iron (Fe) reacts with one mole of sulfuric acid (H₂SO₄) to produce one mole of hydrogen gas (H₂) and one mole of ferrous sulfate (FeSO₄).

Understanding stoichiometry not only helps us predict how much product we'll get from a given amount of reactants but also informs us about the energy changes during the reaction. It's a perfect blend of qualitative and quantitative analysis of a chemical reaction, making it a vital concept in the world of chemistry.

Law of Conservation of Mass

The universe has a fundamental rule that applies to all chemical reactions: the law of conservation of mass. This principle states that mass is neither created nor destroyed in a chemical reaction.

It's like a cosmic version of balancing your checkbook. If we take our textbook problem where lead(II) oxide (PbO) reacts with hydrogen gas (H₂), the total mass of lead (Pb) and water (H₂O) produced must equal the total mass of PbO and H₂ we started with.

The meticulous process of balancing chemical equations directly applies this law. By ensuring that each element has the same number of atoms on the reactant and product sides of the equation, we're respecting the law of conservation of mass. The atoms rearrange during the chemical reaction, but the total mass remains constant. So, when students learn to balance equations, they are not just learning a chemical procedure; they are seeing a fundamental law of nature in action.