Question

Electrolysis Determine the theoretical and percent yield of hydrogen gas if 36.0 g of water undergoes electrolysis to produce hydrogen and oxygen and 3.80 g of hydrogen is collected.

Short answer

The theoretical yield of hydrogen gas when 36.0 g of water undergoes electrolysis is 4.0 g, and the percent yield is 95%.

Step-by-step solution

Determine the moles of water

First, we need to calculate the number of moles of water (H₂0) present in 36.0 g. We can find this by using the formula: Number of moles = mass / molar mass The molar mass of water (H₂0) is 18.0 g/mol. So, the number of moles of water is: number_of_moles_of_water = \( \frac{36.0\,\text{g}}{18.0\,\text{g/mol}} \) number_of_moles_of_water = 2.0 mol

Determine the moles of hydrogen produced theoretically

Next, we need to find the number of moles of hydrogen produced theoretically. In the balanced chemical equation for the electrolysis of water: 2 H₂0(l) → 2 H₂(g) + O₂(g) From the stoichiometry, 2 moles of water produce 2 moles of hydrogen gas. So the moles of hydrogen produced theoretically equal the moles of water: number_of_moles_of_hydrogen = number_of_moles_of_water number_of_moles_of_hydrogen = 2.0 mol

Determine the theoretical yield of hydrogen

Now, we can calculate the theoretical yield of hydrogen by using the formula: mass = number of moles × molar mass The molar mass of hydrogen gas (H₂) is 2.0 g/mol. Therefore, the theoretical yield of hydrogen is: theoretical_yield_H₂ = 2.0 mol × 2.0 \( \frac{\text{g}}{\text{mol}} \) theoretical_yield_H₂ = 4.0 g

Determine the percent yield of hydrogen

Finally, we calculate the percent yield of hydrogen by using the formula: percent_yield = \( \frac{\text{actual yield}}{\text{theoretical yield}} \) × 100 The actual yield of hydrogen is 3.80 g, which was given in the problem. Thus, the percent yield of hydrogen is: percent_yield_H₂ = \( \frac{3.80\,\text{g}}{4.0\,\text{g}} \) × 100 = 95% The theoretical yield of hydrogen gas is 4.0 g, and the percent yield is 95%.

Key concepts

Stoichiometry

Stoichiometry is essentially a form of bookkeeping for chemistry; it allows us to predict the quantities of substances consumed and produced in chemical reactions. To grasp these predictions, it's crucial to understand the balanced chemical equation, which provides the mole ratio of reactants and products. In the case of water electrolysis:

2 H₂O(l) → 2 H₂(g) + O₂(g),
the balanced equation tells us that 2 moles of water yields 2 moles of hydrogen gas and 1 mole of oxygen gas. This stoichiometric relationship is the foundation for determining theoretical yield, a concept we'll explore in the next section.

Theoretical Yield

The theoretical yield is the maximum amount of product that could be formed from a given amount of reactants under perfect conditions. It is calculated using stoichiometry and the balanced chemical equation. When we say 'perfect conditions,' we're referring to a scenario with no side reactions, complete conversion of reactants to products, and no loss of materials. In the provided water electrolysis problem, the theoretical yield of hydrogen is calculated by first finding the moles of water (as shown in Step 1), then using stoichiometry to find the equivalent moles of hydrogen gas, and finally converting these moles to grams using the molar mass of hydrogen. It's helpful to remember that the theoretical yield is an idealized quantity that may not be achievable in actual practice due to various factors affecting the reaction.

Percent Yield

While theoretical yield is a prediction based on stoichiometry, percent yield is the measure of efficiency of a chemical reaction. It compares the actual yield (the amount of product actually obtained from the experiment) to the theoretical yield, with the formula:

percent_yield = (actual yield / theoretical yield) × 100.

It effectively tells us what percentage of the theoretical yield was actually produced. If the percent yield is below 100%, it could indicate that the reaction did not go to completion, that there were losses during product collection, or that impurities affected the outcome. Understanding and calculating percent yield helps chemists to evaluate the feasibility and cost-effectiveness of industrial chemical processes. For students working with laboratory experiments, it's an essential check on their technique and the reaction's behaviour.

Molar Mass

Molar mass is another fundamental concept in chemistry, defined as the mass of one mole of a substance. It is usually expressed in grams per mole (g/mol) and is calculated by summing the atomic masses of all the atoms in a molecule as given in the periodic table. In our water electrolysis example, the molar mass of water is 18.0 g/mol, derived from the atomic masses of hydrogen (1 g/mol for each hydrogen atom) and oxygen (16 g/mol). Likewise, the molar mass of hydrogen gas (H₂) is 2.0 g/mol, which is twice the atomic mass of hydrogen because each molecule contains two hydrogen atoms. Understanding how to find and use molar mass is essential for converting between moles and grams, which is a key step in many stoichiometric calculations.