Problem 55 - Chemistry Matter and Change

Question

When burning 180 of glucose in the presence of 192 of oxygen, water and carbon dioxide are produced. If 108 gof water is produced, how much carbon dioxide is produced?

Step-by-Step Solution

Answer

264 g of carbon dioxide is produced.

Step 1: Write the Chemical Reaction Equation

The balanced chemical equation for the combustion of glucose (C_6H_{12}O_6) in the presence of oxygen (O_2) is:\[C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O\]This means that 1 mole of glucose reacts with 6 moles of oxygen to produce 6 moles of carbon dioxide and 6 moles of water.

Step 2: Calculate Moles from Given Mass

First, we find the moles of water produced using its molar mass (18 g/mol):\[\text{Moles of } H_2O = \frac{108 \, \text{g}}{18 \, \text{g/mol}} = 6 \, \text{moles}\]Since 6 moles of water are produced, this is consistent with the equation.

Step 3: Use Stoichiometry for Carbon Dioxide

According to the balanced equation, the production of 6 moles of water corresponds to the production of 6 moles of carbon dioxide, because the ratio of water to carbon dioxide is 1:1.

Step 4: Convert Moles of Carbon Dioxide to Mass

The molar mass of carbon dioxide (CO2) is 44 g/mol. Therefore, the mass of CO2 produced can be calculated as follows:\[\text{Mass of } CO_2 = 6 \, \text{moles} \times 44 \, \text{g/mol} = 264 \, \text{g}\]

Step 5: Conclude the Calculation

From the stoichiometry and given data, 264 g of carbon dioxide is produced when 108 g of water is formed in the reaction.

Key Concepts

Chemical Reaction Equation

A chemical reaction equation is a symbolic way to represent a chemical reaction. It shows how reactants transform into products. For the combustion of glucose, the equation is given by:

• In the formula: \[ C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O \]
• This indicates that glucose \(C_6H_{12}O_6\) and oxygen \(O_2\) react together.
• Products formed are carbon dioxide \(CO_2\) and water \(H_2O\).

The molecules on both sides of the equation accurately depict what happens during the chemical transformation. Remember, reactants are on the left, and products are on the right.

Balanced Equation

Balancing a chemical equation is crucial for accurately representing a reaction. A balanced equation ensures the same number of atoms of each element appear on both sides. For the glucose combustion reaction:

• The balanced form is:\[ C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O \]
• It reflects the principle of conservation of mass, as no mass is lost or gained.

Balancing is done by adjusting coefficients, the numbers placed before formulas to show the number of molecules. This step is essential to use the equation in stoichiometric calculations accurately.

Molar Mass

Molar mass is the mass of one mole of a substance, expressed in grams per mole \( ext{g/mol} \). It connects mass to the amount of substance involved in a reaction. For example:

• Water \(H_2O\) has a molar mass of 18 g/mol.
• Carbon dioxide \(CO_2\) has a molar mass of 44 g/mol.

Knowing these values allows us to convert between mass and moles, which is crucial in interpreting chemical equations and determining the quantities of reactants or products involved in reactions.

Combustion Reaction

A combustion reaction involves the burning of a substance in oxygen. It releases energy, often as heat and light. In the case of glucose combustion:

• Glucose \( C_6H_{12}O_6 \) combines with oxygen \( O_2 \).
• Produces carbon dioxide \( CO_2 \) and water \( H_2O \).
• This reaction is an exothermic reaction, meaning it releases energy.

Combustion reactions are vital in various processes, such as energy production in biological systems or fuel consumption in power plants. Understanding this type of reaction helps us comprehend how energy is harnessed and used in everyday life.