Question

Show how only 9 grams of water can be produced by the combination of 8 grams of oxygen and 8 grams of hydrogen.

Short answer

9 grams of water can be produced by 0.25 moles of oxygen and excess hydrogen.

Step-by-step solution

Write the Chemical Reaction Equation

The chemical reaction for the formation of water from hydrogen and oxygen is given by the equation:\[ 2H_2 + O_2 ightarrow 2H_2O \] This indicates that two molecules of hydrogen react with one molecule of oxygen to form two molecules of water.

Determine the Molar Masses

Calculate the molar masses of the substances involved: - Molar mass of hydrogen \( (H_2) \) is \( 2 \times 1 = 2 \) g/mol.- Molar mass of oxygen \( (O_2) \) is \( 2 \times 16 = 32 \) g/mol.- Molar mass of water \( (H_2O) \) is \( 2 + 16 = 18 \) g/mol.

Calculate Moles of Reactants

Convert grams to moles for each reactant:- Moles of hydrogen: \( \frac{8}{2} = 4 \) moles- Moles of oxygen: \( \frac{8}{32} = 0.25 \) moles

Apply Stoichiometry

According to the balanced equation, 2 moles of \(H_2\) react with 1 mole of \(O_2\) to form 2 moles of \(H_2O\). Here, we have 4 moles of hydrogen which require 2 moles of oxygen. However, only 0.25 moles of oxygen are available, making oxygen the limiting reactant.

Calculate Moles of Water Produced

Since oxygen is the limiting reactant, we calculate the moles of water produced from 0.25 moles of oxygen. From the stoichiometry of the reaction:- 1 mole of \(O_2\) produces 2 moles of \(H_2O\)- 0.25 moles of \(O_2\) produce \(0.25 \times 2 = 0.5\) moles of \(H_2O\)

Convert Moles of Water to Grams

Convert the calculated moles of water to grams:- Grams of water: \( 0.5 \times 18 = 9 \) grams

Key concepts

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, transform into different substances, called products. During this transformation, the bonds between atoms in the reactants are broken and new bonds are formed to create the products.
In our example with water formation, hydrogen and oxygen are the reactants while water is the product. This reaction is important because it explains how water can be formed from its elemental gases.

• Reactants: Elements or compounds that start a reaction.
• Products: New elements or compounds formed as a result of the reaction.
• Activation energy: Minimum energy required to initiate a reaction.

Understanding chemical reactions gives us insight into how substances interact and change, which is essential for predicting reaction outcomes.

Molar Mass

Molar mass is crucial in chemistry as it helps relate the mass of a substance to the amount of molecules or atoms it contains. It is the mass of one mole of a substance, expressed in grams per mole (g/mol).

For instance, in the reaction to form water:

• The molar mass of hydrogen gas \(H_2\) is calculated as \(2 imes 1 = 2\) g/mol because each hydrogen atom has a mass of 1 g/mol.
• Oxygen gas \(O_2\) has a molar mass of \(2 imes 16 = 32\) g/mol, since each oxygen atom has a mass of 16 g/mol.
• Water \(H_2O\), composed of two hydrogen atoms and one oxygen atom, has a molar mass of \(2 + 16 = 18\) g/mol.

Molar mass enables us to convert between the mass of substances and amount in moles, allowing for accurate measurements and calculations in chemical reactions.

Limiting Reactant

The limiting reactant in a chemical reaction determines the maximum amount of product that can form. It is the reactant that is entirely consumed first, stopping the reaction from continuing.

In our water formation exercise, although we have 4 moles of hydrogen available, we only have 0.25 moles of oxygen. The balanced equation requires 1 mole of oxygen for every 2 moles of hydrogen. This means:

• Oxygen, being in shorter supply, is the limiting reactant.
• The reaction can only proceed until all the oxygen is consumed, limiting the total amount of water formed.

Identifying the limiting reactant is crucial for predicting the amount of products formed and optimizing resource use in chemical processes.

Balanced Chemical Equation

A balanced chemical equation is a way to represent a chemical reaction using symbols and formulas for the substances involved. It ensures that the number of atoms for each element is the same on both sides of the equation, reflecting the conservation of mass.

For the formation of water, the balanced equation is: \[2H_2 + O_2 \rightarrow 2H_2O\]
This equation tells us:

• Two molecules of hydrogen react with one molecule of oxygen to produce two molecules of water.
• The coefficients (numbers in front of the chemical formulas) indicate the ratio of reactants needed and products formed.

A balanced equation is vital for stoichiometry, which involves calculating relative quantities of reactants and products. It ensures reactions comply with the law of conservation of mass, meaning no atoms are lost or gained during the reaction.