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Using solubility data of a solid in a specified liquid, explain how you would determine the mass fraction of the solid in the liquid at the interface at a specified temperature.

Short Answer

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Answer: To calculate the mass fraction of a solid in a liquid, use the following steps: 1. Obtain the solubility data for the solid in the liquid at the specified temperature 2. Convert the solubility data to mass fraction by expressing it in terms of mass of solute per total mass of the solution, using the density of the solvent 3. Calculate the mass fraction using the formula: Mass fraction = Mass of solute / (Mass of solute + Mass of solvent) Using the specific solubility data and the density of the solvent, follow the steps above to find the mass fraction of the solid in the liquid at the given temperature.

Step by step solution

01

Obtain the solubility data

Consult a table or other source for the solubility of the given solid in the specified liquid at the given temperature. Solubility data is usually expressed in terms of mass of solute per volume or mass of solvent (e.g., g/100 mL or g/100 g).
02

Convert solubility data to mass fraction

To calculate the mass fraction of the solid in the liquid, we need to express the solubility data in terms of mass of solute per total mass of the solution. If the solubility is in g/100 mL (grams of solute per 100 mL of solvent), we will first need to convert it to g/100 g (grams of solute per 100 g of solvent) by using the density of the solvent: Mass of solvent = Volume of solvent * Density of solvent For example, if the solubility data is given as 20 g/100 mL and the density of the solvent is 1 g/mL, then: Mass of solvent = 100 mL * 1 g/mL = 100 g Now we have the solubility as 20 g of solute per 100 g of solvent.
03

Calculate the mass fraction of the solid

To calculate the mass fraction of the solid in the liquid, we use this formula: Mass fraction = Mass of solute / (Mass of solute + Mass of solvent) Using the solubility data from Step 2 (20 g/100 g), we can determine the mass fraction: Mass fraction = (20 g) / (20 g + 100 g) = 20/120 = 1/6 So, the mass fraction of the solid in the liquid at the given temperature is 1/6 or approximately 0.167 (16.7%). Remember to replace the values in these calculations with the specific solubility data and the density of the solvent for the given solid and liquid.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Solubility Data Interpretation
Understanding solubility data is crucial for scientists and engineers working with solutions. Solubility indicates how much of a solute can dissolve in a solvent at a specific temperature to form a saturated solution. It is often found in handbooks or experimental data sources and is expressed in various units like grams per 100 milliliters (g/100 mL) or grams per 100 grams (g/100g).

To interpret this data accurately, you'll need to consider the units provided and the context of the problem. For instance, solubility in g/100mL implies a volume-based measurement which requires knowledge of the density of the solvent to convert to a mass-based metric if needed. The latter, g/100g, directly relates to the mass of the substance and is used in mass fraction calculations without further conversions.

When you're given solubility data, ensure you've adjusted for temperature, which can significantly impact the amount of solute that will dissolve. Knowing how to interpret and correctly manipulate solubility data is the foundation for calculating mass fractions and understanding the effects of temperature on solubility.
Mass Fraction Calculation
The mass fraction, an essential concept in many scientific and engineering disciplines, represents the ratio of a solute's mass to the total mass of the solution (the sum of the solute's mass and the solvent's mass).

To compute the mass fraction of a solid solute in a liquid solvent, one must employ the equation:
\[ \text{Mass fraction} = \frac{\text{Mass of solute}}{(\text{Mass of solute} + \text{Mass of solvent})} \]

For practical exercises where solubility data is provided, typically, you'd convert this data into a mass-on-mass basis if it isn’t already. After conversion, use the formula above, dividing the solute's mass by the total mass of the solution. The result is a dimensionless number ranging from 0 (no solute present) to 1 (pure solute), which can also be expressed as a percentage.

Calculating mass fractions accurately is critical in industries such as pharmaceuticals, where precise concentrations of ingredients are required for safety and efficacy. This calculation helps in formulating mixtures with proper concentrations and is vital for quality control processes.
Temperature Influence on Solubility
Temperature plays a pivotal role in the solubility of substances, generally causing an increase in solubility for solid solutes as it rises. However, this isn't a uniform rule; some substances decrease in solubility with an increase in temperature.

In a typical solubility curve, which plots solubility against temperature, one can observe how a substance’s solubility changes as temperature varies. For many solids, the curve slopes upward indicating greater solubility at higher temperatures – a fact crucial when dealing with solutions in chemical reactions, food preparations, and manufacturing processes.

When calculating the mass fraction of a solute at a specific temperature, it's imperative to use the solubility data corresponding to that temperature. If you're working with scenarios that involve temperature fluctuations, you’ll have to account for these changes in your calculations. Knowledge about temperature influence on solubility ensures successful processes in temperature-sensitive applications, reinforcing the importance of thermodynamics in chemistry and material science.

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Most popular questions from this chapter

Exposure to high concentration of gaseous ammonia can cause lung damage. The acceptable shortterm ammonia exposure level set by the Occupational Safety and Health Administration (OSHA) is 35 ppm for 15 minutes. Consider a vessel filled with gaseous ammonia at \(30 \mathrm{~mol} / \mathrm{L}\), and a 10 -cm- diameter circular plastic plug with a thickness of \(2 \mathrm{~mm}\) is used to contain the ammonia inside the vessel. The ventilation system is capable of keeping the room safe with fresh air, provided that the rate of ammonia being released is below \(0.2 \mathrm{mg} / \mathrm{s}\). If the diffusion coefficient of ammonia through the plug is \(1.3 \times 10^{-10} \mathrm{~m}^{2} / \mathrm{s}\), determine whether or not the plug can safely contain the ammonia inside the vessel.

The molar analysis of a gas mixture at \(290 \mathrm{~K}\) and \(250 \mathrm{kPa}\) is 65 percent \(\mathrm{N}_{2}, 20\) percent \(\mathrm{O}_{2}\), and 15 percent \(\mathrm{CO}_{2}\). Determine the mass fraction and partial pressure of each gas.

Write down the relations for steady one-dimensional heat conduction and mass diffusion through a plane wall, and identify the quantities in the two equations that correspond to each other.

Mark these statements as being True or False for a binary mixture of substances \(A\) and \(B\). (a) The density of a mixture is always equal to the sum of the densities of its constituents. (b) The ratio of the density of component \(A\) to the density of component \(B\) is equal to the mass fraction of component \(A\). (c) If the mass fraction of component \(A\) is greater than \(0.5\), then at least half of the moles of the mixture are component \(A\). (d) If the molar masses of \(A\) and \(B\) are equal to each other, then the mass fraction of \(A\) will be equal to the mole fraction of \(A\). (e) If the mass fractions of \(A\) and \(B\) are both \(0.5\), then the molar mass of the mixture is simply the arithmetic average of the molar masses of \(A\) and \(B\).

A heated piece of steel, with a uniform initial carbon concentration of \(0.20 \%\) by mass, was exposed to a carburizing atmosphere for an hour. Throughout the entire process, the carbon concentration on the surface was \(0.70 \%\). If the mass diffusivity of carbon in steel in this process was uniform at \(1 \times\) \(10^{-11} \mathrm{~m}^{2} / \mathrm{s}\), determine the percentage of mass concentration of carbon at \(0.2 \mathrm{~mm}\) and \(0.4 \mathrm{~mm}\) below the surface after the process.

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