Problem 1 - Chemistry in 30 days

Question

Maximum number of mole of oxygen gas that can be obtained by the electrolytic decom- position of \(90 \mathrm{~g}\) of water will be $$ \begin{array}{llll}\text { pos } & \text { (c) } 5 & \text { (d) } 9\end{array} $$ (a) 1 (b) \(2.5\)

Step-by-Step Solution

Answer

The maximum number of moles of oxygen gas obtained is 2.5 moles.

Step 1: Understanding the Chemical Reaction

Electrolytic decomposition of water involves the reaction: \[ 2H_2O(l) \rightarrow 2H_2(g) + O_2(g) \] This indicates that every 2 moles of water produce 1 mole of oxygen gas.

Step 2: Calculate Moles of Water

First, calculate the number of moles of water. The molar mass of water (\(H_2O\)) is \(18 \,g/mol\). Thus: \[ \text{moles of } H_2O = \frac{90 \,g}{18 \,g/mol} = 5 \,mol \]

Step 3: Determine the Moles of Oxygen Gas

Since the reaction \(2H_2O \rightarrow O_2\) shows that 2 moles of water produce 1 mole of \(O_2\), and we have 5 moles of \(H_2O\), we calculate: \[ 5 \,mol \, H_2O \times \frac{1 \,mol \, O_2}{2 \,mol \, H_2O} = 2.5 \,mol \, O_2 \]

Key Concepts

Molar Mass

The molar mass is a key concept in chemistry used to convert between the mass of a substance and the amount in moles. It helps you understand how much of a compound is present in a given mass. Here, the molar mass of water plays a crucial role. To calculate this for water (chemical formula: \( H_2O \)), we need to know the atomic masses of hydrogen and oxygen:

• Hydrogen (H): \(1 \,g/mol\)
• Oxygen (O): \(16 \,g/mol\)

A water molecule consists of two hydrogen atoms and one oxygen atom. Therefore, the molar mass of water is calculated as:\[ 2 \times 1 + 16 = 18 \,g/mol\]In the exercise, we have 90 grams of water. To find out how many moles of water this represents, we use the molar mass:\[ \text{moles of } H_2O = \frac{90 \,g}{18 \,g/mol} = 5 \,mol\] Understanding molar mass is essential to solving such exercises as it directly aids in converting given mass to moles, which further helps in predicting the products of chemical reactions.

Chemical Reactions

Chemical reactions describe how substances change and form new compounds. In the case of electrolytic decomposition of water, we must look at the reaction:\[ 2H_2O(l) \rightarrow 2H_2(g) + O_2(g) \]This equation shows that:

• 2 moles of water decompose to produce 1 mole of oxygen gas and 2 moles of hydrogen gas.
• This is an example of a balanced chemical equation where both sides of the equation have equal numbers of each type of atom.

Balanced equations are vital as they maintain the law of conservation of mass, ensuring that atoms are not lost or gained in a reaction but merely rearranged. Understanding the stoichiometry of the equation helps in predicting the amounts of products formed. For our exercise, this understanding allows us to determine that for every 2 moles of water decomposed, 1 mole of oxygen gas is produced, making it possible for us to calculate the resultant moles of oxygen.

Moles of Oxygen Gas

Calculating the moles of oxygen gas produced in a reaction relies on the balanced chemical equation and involves understanding the stoichiometry. Based on the reaction\[ 2H_2O \rightarrow O_2\]we can deduce:

• 2 moles of water produce 1 mole of oxygen gas.
• Therefore, if 5 moles of water were decomposed, the amount of oxygen gas produced would be:

\[ \text{moles of } O_2 = 5 \,mol \, H_2O \times \frac{1 \,mol \, O_2}{2 \,mol \, H_2O} = 2.5 \,mol \, O_2\] This conversion is important, as it directly ties the theoretical calculations to the actual experiment results. It showcases how chemical reaction equations provide ratios between reactants and products, serving as a recipe for predicting the amounts of different substances formed in a chemical process.