Problem 55 - Chemistry Matter and Change

Question

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

Step-by-Step Solution

Answer

The mass of carbon dioxide produced in the reaction is 264 g.

Step 1: Identify the given masses

We are given the following masses: - Mass of glucose: 180 g - Mass of oxygen: 192 g - Mass of water produced: 108 g Our task is to find the mass of carbon dioxide produced.

Step 2: Use the law of conservation of mass

According to the law of conservation of mass, the total mass of reactants before the reaction is equal to the total mass of products after the reaction. Therefore, we can write the equation for the total mass: Mass of reactants = Mass of products Mass of glucose + Mass of oxygen = Mass of water + Mass of carbon dioxide

Step 3: Substitute the given values

Now we substitute the given values into the equation: 180 g (glucose) + 192 g (oxygen) = 108 g (water) + Mass of carbon dioxide

Step 4: Solve for the mass of carbon dioxide

We need to solve for the mass of carbon dioxide. We can rearrange the equation and solve for the unknown: Mass of carbon dioxide = (180 g + 192 g) - 108 g Mass of carbon dioxide = 372 g - 108 g Mass of carbon dioxide = 264 g

Step 5: Write the final answer

The mass of carbon dioxide produced in the reaction is 264 g.

Key Concepts

Mass of Reactants

The concept of the mass of reactants is fundamental in chemistry, especially when applying the law of conservation of mass. In any chemical reaction, the reactants are the starting substances that undergo a transformation to become products. In our exercise, the reactants are glucose and oxygen.
It is crucial to quantify these reactants' masses to predict the outcome of the reaction accurately. Here, we have:

• Glucose: 180 g
• Oxygen: 192 g

Recognizing these masses helps set up a clear understanding of the reaction's balance. The total mass of these starting materials gives us the initial mass before the reaction occurs.

Mass of Products

The mass of products is the total mass of substances resulting from a chemical reaction. According to the law of conservation of mass, the mass of products should equal the mass of reactants. This means that the atoms in the reactants are simply rearranged to form the products, and no mass is lost or gained.
In our example, the products are:

• Water, with a mass of 108 g
• Carbon dioxide, with an unknown mass initially

Calculating the mass of carbon dioxide is essential to verify the conservation of mass, allowing us to identify that the mass accounted for after the reaction indeed matches the mass present at the start.

Chemical Equation

A chemical equation symbolizes a chemical reaction, showing the reactants and products along with their quantities. It is a concise way to describe how reactants transform into products. For glucose combustion, the chemical equation is:\[ C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O \]This equation tells us four main points:

• The formula of each reactant and product.
• The mole ratio between reactants and products, which indicates how much of each substance is involved.
• The transformation that occurs during combustion.
• How matter is conserved throughout the reaction.

Understanding this equation is crucial. It aligns the stoichiometry with the principles of mass conservation observed in tangible measurements.

Glucose Combustion

Glucose combustion is an exothermic reaction where glucose burns in oxygen to produce carbon dioxide and water. This process is like respiration in living organisms where energy is released.The formula for this combustion reaction, \[ C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O \]depicts how one mole of glucose reacts with six moles of oxygen.
Some important insights of glucose combustion include:

• Both water and carbon dioxide are generated as products, confirming the mass of these products equal the initial mass of reactants.
• The mole concept illustrates the atom and electron rearrangement, which sustains the law of conservation.
• The energy released provides biological systems the required energy to function.

Grasping these aspects of glucose combustion helps appreciate its role not just in chemistry but in biological energy production too.