Question

How many moles of oxygen gas can be produced during electrolytic decomposition of \(180 \mathrm{~g}\) of \(\begin{array}{ll}\text { Water? } & \text { (b) } 5 \text { moles }\end{array}\) (a) \(2.5\) moles (c) 10 moles (d) 7 moles

Short answer

5 moles of oxygen gas can be produced.

Step-by-step solution

Find the molar mass of water

Water (H2O) has a molar mass of approximately 18 g/mol, which is the sum of the molar masses of two hydrogen atoms (1 g/mol each) and one oxygen atom (16 g/mol).

Calculate the moles of water

Using the formula n = m/M, where n is the number of moles, m is the mass of the substance, and M is the molar mass, calculate the moles of water present in 180 g. n = 180 g / 18 g/mol

Apply the stoichiometry of the reaction

The electrolytic decomposition of water produces oxygen gas (O2) and hydrogen gas (H2) according to the balanced chemical equation: 2 H2O(l) -> 2 H2(g) + O2(g). From every 2 moles of water, 1 mole of oxygen gas is produced.

Calculate the moles of oxygen gas

If 180 g of water equals 10 moles of water, then according to the reaction stoichiometry, we will have half the moles of oxygen, which gives us 10 moles H2O x (1 mole O2 / 2 moles H2O) = 5 moles O2.

Key concepts

Molar Mass Calculation

Understanding the molar mass of a substance is a foundational concept in chemistry, acting as a bridge between the atomic scale and the macroscopic world. The molar mass is defined as the mass of one mole of a substance, expressed in grams per mole (\text{g/mol}). For example, to calculate the molar mass of water (\text{H}_2\text{O}), we sum the molar masses of the individual atoms in a molecule.

Each hydrogen atom contributes approximately 1 \text{g/mol}, and with two hydrogen atoms in each water molecule, we have 2 \text{g/mol}. The oxygen atom contributes approximately 16 \text{g/mol}. Therefore, the molar mass of water is calculated as: \[ M_{\text{H}_2\text{O}} = 2 \times M_{\text{H}} + M_{\text{O}} = 2 \times 1 \text{g/mol} + 16 \text{g/mol} = 18 \text{g/mol} \]With the molar mass of water, we can convert between mass and moles, unlocking the ability to perform various calculations and predictions about chemical reactions.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It's like the 'recipe' for a chemical process, telling us how much of each substance is needed or produced. In the case of the electrolytic decomposition of water, stoichiometry tells us that from every 2 moles of water, we can produce 1 mole of oxygen gas (\text{O}_2).

The balanced chemical equation for the decomposition of water is: \[ 2 \text{H}_2\text{O}(l) \rightarrow 2 \text{H}_2(g) + \text{O}_2(g) \]When we have 10 moles of water, we can apply this 2-to-1 ratio to find the moles of oxygen gas produced. Thus, we have: \[ 10 \text{ moles H}_2\text{O} \times \frac{1 \text{ mole O}_2}{2 \text{ moles H}_2\text{O}} = 5 \text{ moles O}_2 \]Stoichiometry is essential for predicting the amounts of substances consumed and produced, allowing us to control and optimize chemical reactions effectively.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products, following the laws of conservation of mass and energy. They are described by chemical equations which need to be balanced to reflect these laws. In our chemical reaction of interest, water undergoes electrolytic decomposition, which separates it into hydrogen and oxygen gases.

Electrolysis requires an electric current to induce the chemical change, with water acting as an electrolyte. This process is instrumental in various applications, such as the production of pure gases for industrial or medical use.

The reaction's stoichiometry helps us to understand and quantify the changes occurring during the reaction, making it a vital aspect of chemical sciences. By mastering the concepts of molar mass, stoichiometry, and the process of a chemical reaction, students lay the groundwork for understanding more complex phenomena in chemistry and related fields.