Problem 1 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

A sample of clay contains \(50 \%\) silica and \(10 \%\) water. The sample is partially dried by which it loses \(8 \mathrm{~g}\) water. If the percentage of silica in the partially dried clay is 52 , what is the percentage of water in the partially dried clay? (a) \(2.0 \%\) (b) \(6.4 \%\) (c) \(10.4 \%\) (d) \(2.4 \%\)

Step-by-Step Solution

Answer

The percentage of water in the partially dried clay is 48%.

Step 1: Determine the Initial Mass of the Clay Sample

Since the sample loses 8 g of water and this results in a change from 10% to some new percentage of water, we first need to determine the initial mass of the clay sample. This can be done by understanding that the initial 10% water is equivalent to 8 g.

Step 2: Calculate the Initial Mass of the Clay

If 10% is equal to 8 g, then 100% (the total mass of the clay) is calculated as: Initial Mass of Clay = (100 / 10) * 8 g = 80 g.

Step 3: Determine the new Mass of the Clay Sample

After losing 8 g of water, the new mass of the clay will be the initial mass minus the mass of the water lost.New Mass of Clay = Initial Mass of Clay - Mass of Water LostNew Mass of Clay = 80 g - 8 g = 72 g.

Step 4: Calculate the Mass of Silica in the Partially Dried Sample

Since the partially dried sample is 52% silica by the given information, its mass can be calculated as:Mass of Silica = (52 / 100) * New Mass of ClayMass of Silica = 0.52 * 72 g = 37.44 g.

Step 5: Calculate the New Percentage of Water

First calculate the new mass of water in the clay, which is the initial mass minus the mass of silica.Mass of Water in Partially Dried Clay = New Mass of Clay - Mass of SilicaMass of Water in Partially Dried Clay = 72 g - 37.44 gMass of Water in Partially Dried Clay = 34.56 g.Finally, we find the new percentage of water by dividing the mass of water by the new mass of the clay and multiplying by 100.Percentage of Water = (Mass of Water in Partially Dried Clay / New Mass of Clay) * 100Percentage of Water = (34.56 g / 72 g) * 100Percentage of Water = 48%.The water content percentage must add up with the silica content percentage to 100%. As the silica content is 52%, the water content is:Percentage of Water = 100% - 52%Percentage of Water = 48%

Key Concepts

Chemical Composition

Chemical composition refers to the identification and quantification of the different elements or compounds present within a substance. For example, a sample of clay can contain various elements such as silica (silicon dioxide), water (H2O), and other minerals. A clear understanding of the composition is critical for fields like materials science and chemistry where the properties of a sample can dramatically change with slight variations in composition. In the context of our exercise, the clay's composition is crucial since it determines how the percentages of silica and water will vary after the sample is partially dried.

It's important to recognize that the chemical composition of a sample is frequently expressed in terms of percentage by mass. This is the case with the given clay sample, which is initially reported to contain certain percentages of silica and water. When the sample is dried and experiences a change in mass due to water loss, the ratio of silica to the new total mass changes accordingly, which, in the given problem, is calculated to determine the new percentage composition of the clay.

Mass Percentage Calculation

Mass percentage calculation is a way to express the concentration of an element or a compound in a mixture. It is defined as the mass of a component divided by the total mass of the mixture, multiplied by 100. In simpler terms, it answers the question, 'What fraction of the total mass of this sample comes from a specific component?' This calculation is an essential part of stoichiometry and plays a significant role when dealing with chemical reactions and formulations.

In the given exercise, we start by determining that the initial 10% of water in the clay corresponds to 8 g. By finding the initial total mass, we can calculate how the mass percentages adjust after some of the water is removed. The mass percentage of water is recalculated after drying using the new total mass of the sample, illustrating how weight loss affects concentrations. Mastering the concept of mass percentage allows students to predict and understand the composition of substances as they undergo physical changes or chemical reactions.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It involves calculations of the masses and moles of substances involved. Stoichiometry is grounded in the conservation of mass, where the total mass of reactants equals the total mass of products. In practice, it helps chemists convert from one chemical substance to another and can be applied beyond reactions, such as to situations involving physical changes.

In our specific problem, stoichiometry is not directly dealing with a reaction but rather the change in mass due to water loss. While not a chemical reaction, the conservation of mass still applies; elements are neither created nor destroyed. The initial percentage of water and silica is a starting point, and the new percentage after drying requires stoichiometric calculations to understand the change in weight and, therefore, the percentage composition. The exercise aims to provide a clear example of how stoichiometry can apply to everyday situations and demonstrates its importance in accurately determining the composition of elements in a substance after a physical change.