Question

Water can be synthesized according to the following unbalanced chemical equation: $$\mathrm{H}_{2}+\mathrm{O}_{2} \rightarrow \mathrm{H}_{2} \mathrm{O}$$ a. Balance the reaction. b. How many moles of \(\mathrm{H}_{2} \mathrm{O}\) can be produced if you have \(2.72 \mathrm{~mol}\) of \(\mathrm{O}_{2}\) and an unlimited amount of \(\mathrm{H}_{2}\) ? c. How many moles of \(\mathrm{H}_{2}\) would be necessary to produce \(10.0 \mathrm{~g}\) of water? d. How many grams of water would be formed by the complete reaction of \(2.5 \mathrm{~g}\) of \(\mathrm{H}_{2}\) ?

Short answer

a) The balanced equation is \(2\mathrm{H}_{2} + \mathrm{O}_{2} \rightarrow 2\mathrm{H}_{2}\mathrm{O}\). b) \(5.44\mathrm{~mol}\) of \(\mathrm{H}_{2}\mathrm{O}\) can be produced with \(2.72\mathrm{~mol}\) of \(\mathrm{O}_{2}\). c) \(0.555\mathrm{~mol}\) of \(\mathrm{H}_{2}\) is needed to produce \(10.0\mathrm{~g}\) of water. d) Complete reaction of \(2.5\mathrm{~g}\) of \(\mathrm{H}_{2}\) would form \(22.30\mathrm{~g}\) of water.

Step-by-step solution

Balancing the chemical equation

To balance the given reaction \(\mathrm{H}_{2}+\mathrm{O}_{2} \rightarrow \mathrm{H}_{2} \mathrm{O}\), ensure an equal number of each type of atom on both sides. Place a coefficient of 2 before \(\mathrm{H}_{2}\mathrm{O}\) to have the same number of oxygen atoms on both sides. The balanced equation is \(\mathrm{H}_{2} + \frac{1}{2}\mathrm{O}_{2} \rightarrow \mathrm{H}_{2}\mathrm{O}\). Now, use whole numbers by multiplying all the coefficients by 2. The fully balanced equation is \(2\mathrm{H}_{2} + \mathrm{O}_{2} \rightarrow 2\mathrm{H}_{2}\mathrm{O}\).

Calculating moles of \(\mathrm{H}_{2}\mathrm{O}\) produced

From the balanced equation, 1 mole of \(\mathrm{O}_{2}\) produces 2 moles of \(\mathrm{H}_{2}\mathrm{O}\). Given \(2.72 \mathrm{~mol}\) of \(\mathrm{O}_{2}\), the number of moles of \(\mathrm{H}_{2}\mathrm{O}\) produced will be twice this amount, which is \(2 \times 2.72 \mathrm{~mol} = 5.44 \mathrm{~mol}\) of water.

Calculating moles of \(\mathrm{H}_{2}\) to produce 10.0 g of water

First, find the molar mass of \(\mathrm{H}_{2}\mathrm{O}\), which is approximately \(18.02 \mathrm{g/mol}\). Next, convert the mass of water to moles: \(10.0 \mathrm{~g} \div 18.02 \mathrm{~g/mol} = 0.555 \mathrm{~mol}\) of \(\mathrm{H}_{2}\mathrm{O}\). Since 2 moles of \(\mathrm{H}_{2}\) produce 2 moles of \(\mathrm{H}_{2}\mathrm{O}\), \(0.555 \mathrm{~mol}\) of water will require \(0.555 \mathrm{~mol}\) of \(\mathrm{H}_{2}\).

Calculating grams of water from \(2.5 \mathrm{~g}\) of \(\mathrm{H}_{2}\)

Calculate the molar mass of \(\mathrm{H}_{2}\), which is about \(2.02 \mathrm{g/mol}\). Convert the mass of \(\mathrm{H}_{2}\) to moles: \(2.5 \mathrm{~g} \div 2.02 \mathrm{~g/mol} = 1.238 \mathrm{~mol}\) of \(\mathrm{H}_{2}\). From the balanced equation, 1 mole of \(\mathrm{H}_{2}\) produces 1 mole of water, so \(1.238 \mathrm{~mol}\) of \(\mathrm{H}_{2}\) will produce the same number of moles of water. Multiply this by the molar mass of water to find the mass: \(1.238 \mathrm{~mol} \times 18.02 \mathrm{~g/mol} = 22.30 \mathrm{~g}\) of \(\mathrm{H}_{2}\mathrm{O}\).

Key concepts

Stoichiometry

Stoichiometry is a foundational concept in chemistry that involves the quantitative relationship between reactants and products in a chemical reaction. It's like a recipe for chemistry where you need the exact amount of ingredients (reactants) to make the perfect dish (product). Understanding stoichiometry is crucial because it enables you to predict the outcomes of reactions, such as how much product will form from given amounts of reactants.

When we balance a chemical equation, we are applying the principles of stoichiometry to ensure the conservation of mass. For example, when we balance the water synthesis equation, we determine that exactly two hydrogen molecules react with one oxygen molecule to produce two water molecules. This tells us the exact molar ratio of reactants to products, which is central to solving stoichiometry problems.

In the given problem, stoichiometry allows us to calculate not only the amount of water produced from a known quantity of oxygen, but also the amount of hydrogen needed to produce a certain mass of water, and the mass of water produced from a given mass of hydrogen.

Mole Concept

The mole concept is a bridge between the microscopic world of atoms and the macroscopic world we experience everyday. One mole is defined as Avogadro's number (\(6.022 \times 10^{23}\) entities) of particles, whether they are atoms, molecules, or ions. This concept is useful when dealing with chemical reactions because it allows us to count particles by weighing them, since we can't count each individual atom or molecule.

When we speak about moles in relation to the synthesis of water, we are essentially counting the number of water molecules produced or required in a reaction. For instance, when given the number of moles of one reactant, we can use the mole ratio from the balanced chemical equation to calculate the number of moles of any other substance in the reaction. In our textbook problem, knowing the amounts in moles translates directly into understanding how much of a substance we're using or producing.

Molar Mass

Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It is a crucial conversion factor in stoichiometry, allowing us to switch between the mass of a substance and the amount in moles. Each element's molar mass is found on the periodic table and can be used to calculate the molar mass of compounds by adding together the molar masses of their constituent elements.

For the synthesis of water, we use the molar mass of water, which is approximately 18.02 g/mol, to find how many grams are in a mole of water, and vice versa. This is how you can calculate the mass of water that will be produced (or react) from a given number of moles of substances, as seen in parts c and d of our exercise problem. The molar mass essentially acts as the conversion factor between the amount of a substance in moles and its mass in grams.

Chemical Reaction

A chemical reaction is a process where reactants are transformed into products through the breaking and forming of chemical bonds. Every chemical reaction is governed by laws, such as the conservation of mass and energy. The equation representing a chemical reaction must reflect these laws, which is why balancing chemical equations is a must.

Balancing a chemical equation ensures that the same number of each type of atom is present on both sides of the equation. This reflects the fact that in a closed system, atoms are not created or destroyed. Following our textbook example, we started with the unbalanced equation for the synthesis of water and then adjusted the coefficients to balance it. This equation then serves as the blueprint for all stoichiometric calculations related to that reaction. Understanding the underlying chemical reaction is essential to grasp the stoichiometry, mole concept, and molar mass calculations associated with it.