Question

In a combustion reaction, 46.0 g of ethanol reacts with 96.0 g of oxygen to produce water and carbon dioxide. If 54.0 g of water is produced, what mass of carbon dioxide is produced?

Short answer

The mass of carbon dioxide produced in the combustion of ethanol is 88.0 g.

Step-by-step solution

Write the balanced chemical equation for the combustion of ethanol.

The combustion of ethanol (C2H5OH) with oxygen (O2) produces water (H2O) and carbon dioxide (CO2). To balance the equation, we must ensure that there are the same number of atoms of each element on both sides of the equation: C2H5OH + O2 -> H2O + CO2 Balanced equation: C2H5OH + 3O2 -> 2H2O + 2CO2

Calculate the moles of ethanol and oxygen

First, we need to find the moles of ethanol and oxygen present in the reaction. To do this, we will use the given masses and the molar masses of ethanol and oxygen. Given mass of ethanol: 46.0 g Molar mass of ethanol: 12.01 g/mol (C) * 2 + 1.01 g/mol (H) * 6 + 16.00 g/mol (O) = 46.07 g/mol Moles of ethanol = mass of ethanol / molar mass of ethanol = 46.0 g / 46.07 g/mol ≈ 1.0 mol Given mass of oxygen: 96.0 g Molar mass of oxygen: 16.00 g/mol (O) * 2 = 32.00 g/mol Moles of oxygen = mass of oxygen / molar mass of oxygen = 96.0 g / 32.00 g/mol = 3.0 mol

Identify the limiting reactant

Now, we can determine which reactant is the limiting reactant. The reactant that produces fewer moles of product is the limiting reactant. Based on the balanced chemical equation, 1 mole of ethanol reacts with 3 moles of oxygen. Ratio of moles of ethanol to moles of oxygen: 1.0 mol / 3.0 mol = 1/3 Since the ratio matches the stoichiometric ratio in the balanced equation, there is no excess reactant, and both reactants are completely consumed in the reaction.

Calculate the moles of carbon dioxide produced

Now, we can use stoichiometry to determine the moles of carbon dioxide produced in the reaction. According to the balanced equation, 1 mole of ethanol produces 2 moles of carbon dioxide: 1.0 mol ethanol * (2 mol CO2 / 1 mol ethanol) = 2.0 mol CO2

Calculate the mass of carbon dioxide produced

Finally, we can convert the moles of carbon dioxide produced to mass using its molar mass: Molar mass of carbon dioxide: 12.01 g/mol (C) + 16.00 g/mol (O) * 2 = 44.01 g/mol Mass of carbon dioxide = moles of carbon dioxide * molar mass of carbon dioxide = 2.0 mol * 44.01 g/mol = 88.0 g

Answer

The mass of carbon dioxide produced in the combustion of ethanol is 88.0 g.

Key concepts

Ethanol

Ethanol, scientifically known as C\(_2\)H\(_5\)OH, is a common alcohol that is widely used as a fuel and in alcoholic beverages. In chemical terms, it's an organic compound composed of carbon, hydrogen, and oxygen. Each molecule consists of two carbon atoms, six hydrogen atoms, and one oxygen atom.
Ethanol is a key component in the combustion reaction because it burns in the presence of oxygen to produce energy, carbon dioxide, and water. This process is represented in chemical equations where the elements in ethanol rearrange to form the products.

• Used in alcoholic beverages
• Common fuel source
• Contains carbon, hydrogen, and oxygen

A unique feature of ethanol is that it can undergo complete combustion, a process that generates a clean burn with fewer pollutants. This makes it a preferred choice for environmentally friendly fuels.
Understanding ethanol's structure and properties helps in comprehending how it plays a vital role in combustion reactions.

Limiting Reactant

In chemical reactions, the concept of a limiting reactant is crucial to determining how much product a reaction can produce. The limiting reactant is the substance that is completely consumed first, stopping the reaction from continuing past a certain point. It essentially "limits" the amount of product that can form.
When you perform a reaction, the reactants are generally not present in exact amounts needed to completely react with each other. In the context of the original exercise, if we compare the available moles of ethanol and oxygen, both were completely consumed in the reaction.

• Stops a reaction when exhausted
• Helps control product quantity
• Not all reactants are present in "perfect" proportions

Determining the limiting reactant helps predict the theoretical yield of products, like water and carbon dioxide in a combustion reaction. It's a critical step in reaction stoichiometry, allowing chemists to calculate the exact amounts of substances needed for reactions to occur efficiently.

Stoichiometry

Stoichiometry is the area of chemistry that involves calculating the relative quantities of reactants and products in chemical reactions. It uses balanced chemical equations to predict the outcomes of reactions under different conditions.
In stoichiometry, you start by examining the balanced chemical equation, which acts like a recipe in cooking. It tells you how much of each ingredient (reactant) you need to produce a set amount of product.

• Predicts how substances react
• Uses molar ratios from chemical equations
• Similar to a recipe in cooking

The simple act of balancing a chemical equation in the original exercise reveals the proportions of ethanol needed to react with oxygen. With these proportions, you can calculate how much water and carbon dioxide will be formed when these components react.
Using stoichiometry helps in scaling chemical reactions for different purposes, ensuring that you know exactly how much of each substance is needed or will be produced.

Balanced Chemical Equation

A balanced chemical equation is crucial for interpreting and predicting the outcomes of chemical reactions, like the combustion of ethanol. This equation ensures that the number of each type of atom is the same on both sides of the chemical reaction.
To balance an equation, adjust the coefficients (the numbers before each molecule), not the subscripts (the numbers within the chemical formula). This maintains the law of conservation of mass, which states that matter cannot be created or destroyed in a closed system.

• Reflects atomic balance in reactions
• Obeys conservation of mass
• Adjust coefficients, not subscripts

In our combustion reaction example, balancing involved making sure there were equal numbers of carbon, hydrogen, and oxygen atoms among the reactants and products. Without a balanced equation, stoichiometric calculations and predicting the limiting reactant would be inaccurate.
Mastering the skill of writing balanced chemical equations ensures precise predictions and computations in chemistry.