Problem 37 - General Chemistry

Question

A \(15.5 \mathrm{~g}\) sample of sodium carbonate is added to a solution of acetic acid weighing \(19.7 \mathrm{~g}\). The two substances react, releasing carbon dioxide gas to the atmosphere. After reaction, the contents of the reaction vessel weigh \(28.7 \mathrm{~g}\). What is the mass of carbon dioxide given off during the reaction?

Step-by-Step Solution

Answer

6.5 g of carbon dioxide was released.

Step 1: Understanding the Problem

We're given that sodium carbonate reacts with acetic acid to release carbon dioxide gas. We need to determine the mass of carbon dioxide that is released during the reaction.

Step 2: Collecting Initial Information

Initially, we have a 15.5 g sample of sodium carbonate and a 19.7 g solution of acetic acid. Thus, the total initial mass before the reaction is the sum of these two masses.

Step 3: Calculating Initial Mass

The initial mass of the system before the reaction is the sum of sodium carbonate and acetic acid. Thus, the total initial mass is 15.5 g + 19.7 g = 35.2 g.

Step 4: Considering Mass Conservation

According to the law of conservation of mass, the total mass of substances before a chemical reaction should equal the total mass of substances after the reaction, minus any gas lost to the atmosphere.

Step 5: Calculating Final Mass without Gas

The total mass of the reaction vessel contents after the reaction is given as 28.7 g. This is the mass of products formed by sodium carbonate and acetic acid, after losing CO2.

Step 6: Finding the Mass of Carbon Dioxide Released

The mass of the carbon dioxide released can be found by subtracting the final mass from the initial mass: 35.2 g (initial mass) - 28.7 g (final mass) = 6.5 g.

Key Concepts

Law of Conservation of Mass

The law of conservation of mass is a fundamental concept in chemistry that dictates that mass cannot be created or destroyed in a chemical reaction. Instead, it can only be rearranged or transformed. In a closed system, the total mass remains the same, no matter the transformations happening inside the system. The exercise illustrates this beautifully by demonstrating how mass is balanced even when some of the substances transform into gases or other states.

In our given problem, we begin with a specific mass from sodium carbonate and acetic acid. Despite the release of carbon dioxide gas, the initial mass and final mass can be accounted for and balanced, confirming this law. The calculation reflects that although carbon dioxide gas leaves the system, the total mass before and after the reaction accounts for this loss, maintaining equilibrium in the system.

Chemical Reactions

In the context of the problem, a chemical reaction occurs between sodium carbonate and acetic acid. When these two substances combine, they undergo a transformation that results in the creation of new products and the release of carbon dioxide gas. Chemical reactions involve breaking old bonds and forming new ones. They often include the absorption or release of energy, contributing to the formation of new substances.

During this specific reaction, the sodium ions, carbonate ions, hydrogen ions from the acetic acid, and various other components rearrange. The carbon dioxide and water are products of this reaction, with carbon dioxide being released into the atmosphere. Meticulous calculations and understanding reactions like this help chemists to predict and analyze outcomes of similar processes.

Mass Calculations

Mass calculations in chemical reactions play a crucial role in measuring and predicting the behaviour of substances involved. By determining the initial and final masses, one can find how much matter has transformed and whether gases have been emitted.

In the exercise at hand, calculating the initial mass involves simply adding the masses of the reactants: sodium carbonate and acetic acid. The given mass and the observed final mass provide enough data to deduce the mass of carbon dioxide released. By subtracting the final remaining mass from the initial mass, students can calculate the gas mass, which in this case turns out to be 6.5 grams.

Understanding this calculation process highlights the practical application of stoichiometry in daily chemical transactions and how vital precision is in solving real-world problems that involve chemical changes. This reinforces the law of conservation of mass and provides fundamental insight into the science of stoichiometry.