Question

Convert each temperature. MISSED THIS? Read Section 1.6; Watch \(\mathrm{KCV} 1.6\) a. \(32^{\circ} \mathrm{F}\) to \({ }^{\circ} \mathrm{C}\) (temperature at which water freezes) b. \(77 \mathrm{~K}\) to \({ }^{\circ} \mathrm{F}\) (temperature of liquid nitrogen) c. \(-109^{\circ} \mathrm{F}\) to \({ }^{\circ} \mathrm{C}\) (temperature of dry ice) d. \(98.6^{\circ} \mathrm{F}\) to \(\mathrm{K}\) (body temperature)

Short answer

a. 0°C, b. -321.07°F, c. -78.33°C, d. 310.15 K

Step-by-step solution

Convert 32°F to °C

Use the formula \( (°F - 32) \times \frac{5}{9} = °C \). For 32°F, it becomes \( (32 - 32) \times \frac{5}{9} = °C \). Therefore, the temperature in Celsius is 0°C.

Convert 77 K to °F

Use the formula \( (K - 273.15) \times \frac{9}{5} + 32 = °F \). For 77 K, it is \( (77 - 273.15) \times \frac{9}{5} + 32 = °F \). After calculations, the temperature in Fahrenheit is approximately -321.07°F.

Convert -109°F to °C

Again, use the formula \( (°F - 32) \times \frac{5}{9} = °C \). For -109°F, the conversion is \( (-109 - 32) \times \frac{5}{9} = °C \). This gives a result of approximately -78.33°C.

Convert 98.6°F to K

We use the formula \( ((°F - 32) \times \frac{5}{9}) + 273.15 = K \). For 98.6°F, it is \( ((98.6 - 32) \times \frac{5}{9}) + 273.15 = K \). The body temperature in Kelvin is approximately 310.15 K.

Key concepts

Fahrenheit to Celsius conversion

Understanding how to convert temperature from Fahrenheit to Celsius is essential in chemistry, as it allows for consistent measurements across different scientific communities. The formula to convert Fahrenheit to Celsius is \[ (°F - 32) \times \frac{5}{9} = °C \].

To apply this formula, subtract 32 from the Fahrenheit temperature. The result is then multiplied by \(\frac{5}{9}\), or approximately 0.5556, to find the equivalent Celsius temperature. For example, the freezing point of water, which is 32°F, converted to Celsius is \[ (32°F - 32) \times \frac{5}{9} = 0°C \].

This conversion is a linear transformation, meaning any change in Fahrenheit results in a proportional change in Celsius. Memorizing this formula is useful, not only for chemistry students, but also for those traveling to countries where Celsius is the standard, or for interpreting cooking recipes from different regions.

Kelvin to Fahrenheit conversion

The Kelvin scale is named after Lord Kelvin and is used primarily in the field of science. Converting Kelvin to Fahrenheit might be less common in daily life, but it's a crucial skill in scientific practices where precise temperature measurements are required. The conversion formula is \[ (K - 273.15) \times \frac{9}{5} + 32 = °F \].

This equation begins with subtracting 273.15 from the Kelvin temperature, which adjusts it to the Celsius scale. The resulting Celsius temperature is converted to Fahrenheit by multiplying it by \(\frac{9}{5}\) (or 1.8), followed by adding 32. For instance, the temperature of liquid nitrogen at 77 K is \[ (77 K - 273.15) \times \frac{9}{5} + 32 \approx -321.07 °F \].

Kelvin is an absolute temperature scale with no negative numbers, thus it is useful in theoretical physics and chemistry to express temperatures on a scale where zero represents the theoretical absolute zero.

Temperature scales in chemistry

Chemistry often requires the understanding of different temperature scales, namely Celsius, Fahrenheit, and Kelvin. These scales are used for various reasons across the globe and in scientific research.

Celsius, denoted as °C, is used widely around the world and in science for its convenience in dealing with water's freezing and boiling points; 0°C for the former and 100°C for the latter. Fahrenheit, represented as °F, is still used in the United States for everyday temperature measurements. Lastly, Kelvin, the SI unit for temperature, is an absolute temperature scale commonly used in scientific studies, and does not have a degree symbol as it is not relative but absolute.

As temperature is a critical parameter in chemical reactions affecting rates, equilibria, and energy of processes, chemists need to be proficient in converting temperatures between these scales for precise communication and to ensure the reproducibility of experiments across the globe. It’s also important to appreciate that while temperature conversions are straightforward mathematically, they do have significant impacts on experimental results and the interpretation of those results in a broader scientific context.