Problem 44 - General Chemistry: Principles and Modern Applications

Question

A family/consumer science class is given an assignment in candy-making that requires a sugar mixture to be brought to a "soft-ball" stage \(\left(234-240^{\circ} \mathrm{F}\right)\). A student borrows a thermometer having a range from \(-10^{\circ} \mathrm{C}\) to \(110^{\circ} \mathrm{C}\) from the chemistry laboratory to do this assignment. Will this thermometer serve the purpose? Explain.

Step-by-Step Solution

Answer

No, the thermometer having a range from \(-10^{\circ} C\) to \(110^{\circ} C\) will not serve the purpose as it does not cover the 'soft-ball' stage temperature range that is \(112.22 - 115.56^{\circ} C\).

Step 1: Understand the temperature conversion formula

The formula to convert temperature from Fahrenheit to Celsius is given by \(C = (F - 32) \times \frac{5}{9}\). This formula will be used to convert the 'soft-ball' stage temperature range from Fahrenheit to Celsius.

Step 2: Convert the temperature range to Celsius

Apply the conversion formula to the 'soft-ball' stage temperature range (\(234 - 240^{\circ} F\)). The lower limit in Celsius is \((234-32) \times \frac{5}{9} \approx 112.22^{\circ}C\), and the upper limit is \((240-32) \times \frac{5}{9} \approx 115.56^{\circ}C\). So, the temperature range in Celsius is \(112.22 - 115.56^{\circ} C\).

Step 3: Compare the converted temperature range with the thermometer range

The thermometer can measure the temperature from \(-10^{\circ} C\) to \(110^{\circ} C\). Comparing this with the converted 'soft-ball' stage temperature range, \(112.22 - 115.56^{\circ} C\), it is clear that the thermometer does not cover the 'soft-ball' stage temperature range.

Key Concepts

Celsius to Fahrenheit

When dealing with temperature conversions, it's essential to understand how to go from Celsius to Fahrenheit. This conversion is particularly useful in various scientific and culinary fields where specific temperature settings are required. The formula for converting Celsius to Fahrenheit is:

• \( F = C \, \times \, \frac{9}{5} \, + \, 32 \)

This formula adds 32 degrees and scales the input from Celsius by multiplying it by \( \frac{9}{5} \). For example, to convert 100°C to Fahrenheit:

• First, multiply 100 by \( \frac{9}{5} \) which equals 180.
• Then, add 32 to get a result of 212°F.

Using this simple formula, you can easily determine the Fahrenheit equivalent for any temperature given in Celsius. This understanding is critical because temperature ranges are often specified in different units depending on the context and geographical location.
Knowing how to make these conversions ensures that you are using the correct setting in processes like cooking, manufacturing, or conducting experiments.

Fahrenheit to Celsius

Converting Fahrenheit to Celsius is equally important, especially when dealing with international standards in science or global travel. The process requires a bit of calculation but is straightforward with the correct formula:

• \( C = (F \, - \, 32) \, \times \, \frac{5}{9} \)

This formula involves subtracting 32 from the Fahrenheit temperature and then multiplying the result by \( \frac{5}{9} \). For instance, if you need to convert 68°F to Celsius:

• Subtract 32 from 68 to get 36.
• Multiply 36 by \( \frac{5}{9} \), resulting in 20°C.

Understanding this conversion helps in correctly interpreting temperature-related instructions, such as those in the example of candy-making, where precise temperatures are critical to getting the right consistency. Failure to convert temperature correctly can result in unsuccessful outcomes in chemical reactions or culinary processes.
If we consider the soft-ball candy stage temperature conversion, the same technique applies to ensure the thermometer in use can read the necessary range for the assignment.

Thermometer Range

Thermometers are essential tools in both scientific and everyday settings because they measure temperature accurately. However, different thermometers are designed with specific temperature ranges in mind. When using a thermometer, it is vital to ensure that its range matches the necessary measurement requirement.

• For example, a thermometer with a range from \(-10^{\circ}C\) to \(110^{\circ}C\) is unsuitable for tasks requiring temperatures above 110°C.
• When conducting experiments or cooking, this limitation can affect the validity and success of your work.

In the mentioned exercise, the borrowed thermometer from the chemistry lab had its range limited to \(110^{\circ}C\), which didn't suffice for the candy's soft-ball stage temperature, converted to be \(112.22 - 115.56^{\circ}C\). This discrepancy highlights the importance of checking the thermometer's suitability before starting any temperature-sensitive activity.Using a thermometer with the correct range ensures reliable measurements and helps avoid complications, such as burning or undercooking in culinary settings, or inaccuracies in scientific calculations.