Problem 105 - Chemistry and Chemical Reactivity

Question

It is interesting how the Fahrenheit temperature scale was established. One report, given by Fahrenheit in a paper in \(1724,\) stated that the value of \(0^{\circ} \mathrm{F}\) was established as the freezing temperature of saturated solutions of sea salt. From the literature we find that the freezing point of a \(20 \%\) by mass solution of \(\mathrm{NaCl}\) is \(-16.46^{\circ} \mathrm{C}\) (This is the lowest freezing temperature reported for solutions of NaCl.) Does this value lend credence to this story of the establishment of the Fahrenheit scale?

Step-by-Step Solution

Answer

The freezing point of a 20% NaCl solution does not support the story for 0°F.

Step 1: Understanding the problem

We are checking whether the reported freezing point of a \(20\%\) NaCl solution aligns with the claimed origin of \(0^{\circ} \mathrm{F}\) on the Fahrenheit scale. Specifically, we need to verify if \(-16.46^{\circ} \mathrm{C}\) is equivalent to \(0^{\circ} \mathrm{F}\).

Step 2: Use the conversion formula

The formula to convert Celsius to Fahrenheit is \( F = \frac{9}{5}C + 32 \). Substituting \(-16.46^{\circ} \mathrm{C}\) into the formula will allow us to find the corresponding Fahrenheit temperature.

Step 3: Calculate the Fahrenheit temperature

Substitute \(-16.46\) for \(C\) in the equation: \[F = \frac{9}{5}(-16.46) + 32\]Calculating this gives: \[F = \frac{9}{5} \times (-16.46) + 32 = -29.628 + 32 = 2.372^{\circ} \mathrm{F}\]

Step 4: Compare the results

The calculated Celsius equivalent of \(0^{\circ} \mathrm{F}\) was \(2.372^{\circ} \mathrm{F}\), not \(0^{\circ} \mathrm{F}\). Thus, \(-16.46^{\circ} \mathrm{C}\) does not confirm that it aligns with \(0^{\circ} \mathrm{F}\).

Key Concepts

Celsius to Fahrenheit conversion

The conversion between Celsius and Fahrenheit is a foundational concept in understanding temperature measurements. The formula to convert a temperature from Celsius (C) to Fahrenheit (F) is \[ F = \frac{9}{5}C + 32 \].This equation enables us to translate the Celsius scale, commonly used worldwide, into the Fahrenheit scale, which is primarily used in the United States. For example, a temperature of \(-16.46^{\circ} \mathrm{C}\) converted to Fahrenheit is calculated by substituting into the formula:

• \( F = \frac{9}{5}(-16.46) + 32 \)
• \( F = -29.628 + 32 \)
• \( F = 2.372^{\circ} \mathrm{F} \)

This shows how Celsius and Fahrenheit scales differ, underscoring the importance of accurate conversion in scientific calculations and daily life. Recognizing these differences helps in understanding temperature references across various domains.

saturated solutions

Saturated solutions are a key concept in chemistry, involving a solution in which no more solute can be dissolved in the solvent at a given temperature and pressure. When a solution reaches saturation, the maximum concentration of solute is achieved, and any additional solute added will result in precipitation or crystallization. For example, when sodium chloride (NaCl), or table salt, is added to water, it dissolves until the point of saturation is reached. This particular state is critical in many natural and industrial processes because the solubility varies with temperature. In the context of the Fahrenheit scale establishment, a saturated solution of sea salt's freezing point was reportedly used as a reference point. Understanding how saturated solutions behave at different temperatures helps in various applications such as food preservation, chemical manufacturing, and even meteorology, making it a fundamental topic in science education.

freezing point depression

Freezing point depression refers to the phenomenon where the addition of a solute to a solvent decreases the freezing point of the solution compared to that of the pure solvent. This is a colligative property, which means it depends on the number of particles in the solution, not on the type of particles. Real-world examples of freezing point depression include using salt to melt ice on roads during winter or antifreeze in car radiators. In the situation described in the exercise, adding NaCl lowers the freezing point of water, illustrating how solute addition alters physical properties significantly.This concept helps explain why the \(-16.46^{\circ} \mathrm{C}\) freezing point for a 20% NaCl solution was historically significant when considering temperature scales. It shows the practical application of freezing point depression in setting certain scientific benchmarks and standards.

historical temperature scales

Temperature scales have evolved over time, rooted in historical contexts and scientific discovery. The Fahrenheit scale, created by Daniel Gabriel Fahrenheit in the early 18th century, is one of several temperature scales developed. It is based on mercury as a thermometric fluid and set several fixed points, including the freezing point of an ammonium chloride solution being \(0^{\circ} \mathrm{F}\).Other historical scales include the Celsius scale, which designates \(0^{\circ}\) for freezing water and \(100^{\circ}\) for boiling water under standard atmospheric conditions. While Fahrenheit was convenient for certain scientific and meteorological studies in the past, the Celsius scale became more widespread due to its decimal-based convenience.Understanding the legacy and reasoning behind these different scales illuminates the intricate journey scientific measurement has undergone. It helps us appreciate the blend of tradition and precision in recording temperature, which still impacts our daily weather forecasts and scientific research.