Problem 97 - Chemistry: Atoms First

Question

Convert the boiling temperature of liquid ammonia, -28.1 ^ ^ F, into degrees Celsius and kelvin.

Step-by-Step Solution

Answer

Boiling temperature of liquid ammonia in Celsius is \( C = -33.39 \) degrees, and in Kelvin, it is \( K = 239.76 \) Kelvin.

Step 1: Convert Fahrenheit to Celsius

Use the formula to convert temperature from Fahrenheit to Celsius: \( C = \frac{5}{9}(F - 32) \). Substitute \( F = -28.1 \) into the formula to get \( C = \frac{5}{9}(-28.1 - 32) \).

Step 2: Perform the Calculation

Perform the arithmetic in the formula: \( C = \frac{5}{9}(-28.1 - 32) = \frac{5}{9}(-60.1) \). Calculate the numerical value to get the result in Celsius.

Step 3: Convert Celsius to Kelvin

Use the formula to convert Celsius to Kelvin: \( K = C + 273.15 \). Substitute the value of \( C \) that we found in Step 2 into the formula to get the temperature in Kelvin.

Step 4: Perform the Calculation for Kelvin

Perform the arithmetic to find the temperature in Kelvin using the Celsius value obtained from the previous steps.

Key Concepts

Fahrenheit to Celsius

Understanding how to convert temperatures from Fahrenheit to Celsius is essential in various scientific fields, including chemistry and physics. The formula for converting Fahrenheit to Celsius is given by:
\[ C = \frac{5}{9}(F - 32) \]
To put this into practice with the given exercise, where the boiling temperature of liquid ammonia is -28.1 degrees Fahrenheit, we substitute the Fahrenheit temperature into the formula:
\[ C = \frac{5}{9}(-28.1 - 32) \]
It's crucial to perform the arithmetic carefully:
\[ C = \frac{5}{9}(-60.1) \]
Keeping track of negative signs is particularly important to avoid errors. After calculating, you'll obtain the temperature in degrees Celsius. This step is fundamental in fields such as meteorology, where temperature readings usually need to be reported in Celsius rather than Fahrenheit.

Celsius to Kelvin

Conversion from degrees Celsius to Kelvin is a common task in the scientific study of temperature, particularly in the field of thermochemistry. The Kelvin scale is an absolute temperature scale used in the physical sciences to represent thermodynamic temperature. The relationship between Celsius and Kelvin is linear and is described by the formula:
\[ K = C + 273.15 \]
In this exercise, after converting the Fahrenheit temperature of liquid ammonia to Celsius, we apply this formula to find the Kelvin temperature. For instance, if the Celsius temperature is calculated to be -33.4 degrees, the conversion to Kelvin would be simply:
\[ K = -33.4 + 273.15 \]
Performing this calculation, you will obtain the temperature in Kelvin. No matter what the Celsius temperature is, adding 273.15 will give the correct Kelvin temperature. This step is particularly critical when studying chemical reactions or physical processes where absolute temperatures are required.

Thermochemistry

Thermochemistry is the branch of chemistry that deals with the energy changes associated with chemical reactions and phase changes. Knowing how to convert temperatures between different units is vital in this field, as measurements may be taken or reported in Fahrenheit, Celsius, or Kelvin. Thermochemical calculations often require temperatures in Kelvin because it is the SI unit for thermodynamic temperature and indicates the absolute scale, starting at absolute zero.
Understanding the relationship between different temperature scales becomes crucial when considering energetics of reactions, where even small temperature changes can significantly affect the outcome. For example, the boiling or freezing points of substances, including the boiling temperature of liquid ammonia in our exercise, are key indicators in the study of enthalpies of vaporization and fusion.
When studying or working in thermochemistry, it's imperative to be thorough in temperature unit conversions to ensure accuracy in experimental results and to effectively communicate findings with the scientific community.