Problem 69 - General Chemistry

Question

Convert: a \(68^{\circ} \mathrm{F}\) to degrees Celsius b \(-23^{\circ} \mathrm{F}\) to degrees \(\mathrm{Celsius}\) c \(26^{\circ} \mathrm{C}\) to degrees Fahrenheit d \(-81^{\circ} \mathrm{C}\) to degrees Fahrenheit

Step-by-Step Solution

Answer

a) 20°C b) -31.67°C c) 78.8°F d) -113.8°F

Step 1: Understanding Conversion Formula for F to C

To convert Fahrenheit to Celsius, use the formula: \(C = (F - 32) \times \frac{5}{9}\).

Step 2: Calculate Part (a)

For part (a), convert \(68^{\circ}F\) to Celsius. Using the formula: \[C = (68 - 32) \times \frac{5}{9} = 36 \times \frac{5}{9} = 20^{\circ}C\]\.

Step 3: Calculate Part (b)

For part (b), convert \(-23^{\circ}F\) to Celsius. Using the formula: \[C = (-23 - 32) \times \frac{5}{9} = -55 \times \frac{5}{9} \approx -31.67^{\circ}C\]\.

Step 4: Understanding Conversion Formula for C to F

To convert Celsius to Fahrenheit, use the formula: \(F = C \times \frac{9}{5} + 32\).

Step 5: Calculate Part (c)

For part (c), convert \(26^{\circ}C\) to Fahrenheit. Using the formula: \[F = 26 \times \frac{9}{5} + 32 = 46.8 + 32 = 78.8^{\circ}F\]\.

Step 6: Calculate Part (d)

For part (d), convert \(-81^{\circ}C\) to Fahrenheit. Using the formula: \[F = -81 \times \frac{9}{5} + 32 = -145.8 + 32 = -113.8^{\circ}F\]\.

Key Concepts

Fahrenheit to Celsius

Temperature conversion is a handy skill, especially when traveling or studying sciences. The process of converting Fahrenheit to Celsius can seem daunting, but it becomes easy with practice. The key is to remember the correct conversion formula. First, understand that Celsius and Fahrenheit are based on different reference points. Celsius sets the freezing point of water at 0°C and the boiling point at 100°C. Fahrenheit sets these points at 32°F and 212°F, respectively. This makes direct comparison impossible without conversion.

To convert from Fahrenheit to Celsius, use the formula:

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

The formula subtracts 32 from the Fahrenheit temperature, which accounts for the different starting point. Then, multiplying by \(\frac{5}{9}\) scales it to the Celsius range. This formula simplifies the conversion process and ensures accuracy.

Celsius to Fahrenheit

When converting from Celsius to Fahrenheit, the process is slightly different but just as straightforward. This conversion is common in many everyday situations, like reading non-digital thermometers or old recipes. Understanding this formula allows easy conversion from Celsius to Fahrenheit without confusion.

The formula for this conversion is:

• \[ F = C \times \frac{9}{5} + 32 \]

First, multiply the Celsius temperature by \(\frac{9}{5}\), which stretches the Celsius degree to match the Fahrenheit scale. Finally, adding 32 shifts the starting point to align with Fahrenheit's reference point. Using this formula ensures your conversions are both correct and consistent.

Conversion Formula

The conversion formulas between Fahrenheit and Celsius play a crucial role in temperature calculations. These formulas bridge the gap between two systems with different base temperatures and unit scales. Each formula has a specific purpose and understanding them helps solving problems accurately.

The two primary conversion formulas are:

• Fahrenheit to Celsius: \[ C = (F - 32) \times \frac{5}{9} \]
• Celsius to Fahrenheit: \[ F = C \times \frac{9}{5} + 32 \]

Both formulas use simple arithmetic operations but require attention to detail to apply correctly. Having them memorized or easily accessible allows you to move between temperature scales effortlessly, whether for science class, traveling, or cooking. Constant practice and usage will bolster your confidence and precision in temperature conversion.

Step-by-Step Solution

Following a step-by-step solution makes understanding temperature conversion easy, even for complex calculations. Let's break down the steps using the provided exercise as an example.

First, when converting from Fahrenheit to Celsius, start by using the formula \( C = (F - 32) \times \frac{5}{9} \). Subtract 32 from the Fahrenheit temperature, then multiply by \(\frac{5}{9}\) to find the Celsius equivalent. For example, converting \(68^{\circ}F\) results in:

• Subtract 32 from 68: \(68 - 32 = 36\)
• Multiply by \(\frac{5}{9}\): \[36 \times \frac{5}{9} = 20^{\circ}C\]

On the other hand, converting from Celsius to Fahrenheit requires you to use \( F = C \times \frac{9}{5} + 32 \). Multiply the Celsius measurement by \(\frac{9}{5}\) and then add 32. For instance, converting \(26^{\circ}C\) to Fahrenheit becomes:

• Multiply by \(\frac{9}{5}\): \[26 \times \frac{9}{5} = 46.8\]
• Add 32: \[46.8 + 32 = 78.8^{\circ}F\]

This methodical approach helps in confirming each step and ensures that no part of the transformation is overlooked or miscalculated.