Problem 103 - Chemistry

Question

How many grams of \(\mathrm{H}_{2} \mathrm{O}\) will be produced from the complete combustion of \(26.7 \mathrm{~g}\) of butane \(\left(\mathrm{C}_{4} \mathrm{H}_{10}\right) ?\)

Step-by-Step Solution

Answer

The complete combustion of 26.7g of butane will produce 41.4g of water.

Step 1: Identify the relevant stoichiometric ratio

In the balanced equation, one molecule of butane creates five molecules of water. This means that the ratio is 1:5.

Step 2: Convert mass of butane to moles

The molar mass of butane \(\mathrm{C}_{4} \mathrm{H}_{10}\) is approximately 58.1g/mol. To convert the mass into moles, use the formula \[\text{number of moles} = \frac{\text{mass}}{\text{molar mass}}\] Therefore, the number of moles of butane is given by: \[\frac{26.7 g }{58.1 g/mol} = 0.46 mol\]

Step 3: Calculate moles of water produced

Using the stoichiometric ratio (1:5), calculate the number of moles of water produced: the number of moles of water = \( 0.46 mol * 5 = 2.3 mol\)

Step 4: Convert moles of water to grams

Knowing the number of moles and the molar mass of water, which is approximately 18g/mol, calculate the mass of water produced by the reaction: \[mass_{H2O} = \text{number of moles} * \text{molar mass} = 2.3 mol * 18 g/mol = 41.4 g\]

Key Concepts

Combustion Reactions

Combustion reactions are a specific type of chemical reaction where a substance reacts with oxygen to produce energy in the form of light or heat. In most cases, these reactions involve hydrocarbons (compounds made of hydrogen and carbon) burning in the presence of oxygen to create carbon dioxide and water. Combustion is a crucial process often employed for heating, powering engines, and generating electricity.
Here are some key points:

• A combustion reaction typically yields water (H₂O) and carbon dioxide (CO₂).
• The general form of a combustion reaction is:
  \[ ext{Hydrocarbon} + O_2 ightarrow CO_2 + H_2O \]
• In the combustion of butane (C₄H₁₀), every mole of butane reacts with oxygen to produce water and carbon dioxide.

Understanding combustion reactions is essential in fields such as chemistry, environmental science, and engineering.

Molar Mass

Molar mass, a foundational concept in stoichiometry, is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It allows chemists to convert between the mass of a substance and the number of moles, which is necessary for understanding chemical reactions quantitatively.
To calculate the molar mass of a substance, sum the atomic masses of its constituent elements:

• For butane (C₄H₁₀): Each carbon (C) atom has an atomic mass of about 12 atomic mass units (amu), and each hydrogen (H) atom about 1 amu.
• This totals to:
  \[ (4 \times 12 \, \text{amu for C}) + (10 \times 1 \, \text{amu for H}) = 58 \, \text{amu} \]
• The molar mass is thus approximately 58 g/mol for butane.

Realizing the molar mass is crucial for converting mass to moles and vice versa, which is a frequent requirement in solving stoichiometric problems.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions. They depict the reactants (starting materials) on the left side and the products (substances formed) on the right, separated by an arrow indicating the direction of the reaction.
For example, the balanced equation for the combustion of butane is:

• \[ 2 \, C_4H_{10} + 13 \, O_2 ightarrow 8 \, CO_2 + 10 \, H_2O \]

A balanced equation ensures that the same number of atoms for each element are on both sides of the equation, which is a reflection of the law of conservation of mass.
Balancing chemical equations is essential because it tells us the exact proportions in which reactants combine and form products, crucial for any stoichiometric calculations.

• Each chemical symbol stands for a specific type of atom.
• The coefficients in front of each substance in the equation represent the number of moles involved.

Mole Concept

The mole is a fundamental concept in chemistry used to express amounts of a chemical substance. One mole is defined as the amount of substance that contains as many entities (usually atoms or molecules) as there are atoms in 12 grams of pure carbon-12. This number, Avogadro's number, is approximately \(6.022 \times 10^{23}\).
This concept simplifies chemical formulas and reactions, as it allows chemists to calculate exactly how much of a substance is needed or produced in a reaction. By using the mole concept, we can convert between mass, number of particles, and volumes in reactions involving gases:

• Moles link the micro world of atoms and molecules to the macroscopic world of grams and liters.
• This makes it easier to measure out reactants for a reaction since it describes amounts in a manner that relates directly back to the equations.

For students dealing with stoichiometry, mastering the mole concept is essential for success in understanding and solving chemical reaction problems.