Problem 122 - General Chemistry

Question

Iodine is a bluish-black solid. It forms a violetcolored vapor when heated. The solid melts at \(236^{\circ} \mathrm{F}\). What is this temperature in degrees Celsius? in kelvins?

Step-by-Step Solution

Answer

The temperature is \(113.333^{\circ} C\) and \(386.483 \text{ K}\).

Step 1: Convert Fahrenheit to Celsius Formula

The formula to convert Fahrenheit to Celsius is \( C = \frac{5}{9}(F - 32) \). Identify the Fahrenheit temperature given, which is \( 236^{\circ} F \).

Step 2: Calculate the Temperature in Celsius

Substitute \(236\) for \(F\) in the conversion formula: \[ C = \frac{5}{9}(236 - 32) \]Calculate:\[ C = \frac{5}{9} \times 204 = 113.333 \ ^{\circ} \text{C} \]

Step 3: Convert Celsius to Kelvin Formula

The formula to convert Celsius to Kelvin is \( K = C + 273.15 \). Use the Celsius temperature we just calculated: \(113.333^{\circ} C\).

Step 4: Calculate the Temperature in Kelvin

Substitute \(113.333\) for \(C\) in the conversion formula:\[ K = 113.333 + 273.15 \]Calculate the sum:\[ K = 386.483 \]

Key Concepts

Fahrenheit to Celsius

Converting temperatures between different scales is an important skill, especially in scientific contexts. When we're converting Fahrenheit to Celsius, we use the formula: \( C = \frac{5}{9}(F - 32) \). This formula allows us to transform a Fahrenheit temperature into its equivalent in Celsius.

• First, identify the given temperature in Fahrenheit. In this exercise, it's \(236^{\circ} \text{F}\).
• Next, subtract 32 from this value. This step adjusts for the baseline difference between the two scales.
• Then, multiply by \(\frac{5}{9}\). This ratio represents the difference in interval sizing between Fahrenheit and Celsius scales.

Applying these steps to \(236^{\circ} \text{F}\):

• Subtract 32: \(236 - 32 = 204\).
• Multiply by \(\frac{5}{9}\): \(\frac{5}{9} \times 204 = 113.333\ ^{\circ} \text{C}\).

Understanding this conversion is key to smoothly transitioning temperatures from Fahrenheit to Celsius.

Celsius to Kelvin

Once you have a temperature in Celsius, converting it to Kelvin is straightforward, as both scales are metric and linear. The conversion involves a simple addition: \( K = C + 273.15 \). This constant amount, 273.15, compensates for the starting point difference between the Celsius and Kelvin scales.

• The Kelvin scale starts at absolute zero, which is \(-273.15^{\circ} \text{C}\).
• The size of one degree Celsius is the same as one Kelvin.
• This consistency makes the conversion an addition problem, only dealing with the offset.
  

For our \(113.333^{\circ} \text{C}\):

• Add 273.15: \(113.333 + 273.15 = 386.483 \ \text{K}\).

Kelvin is often used in scientific studies since it starts at absolute zero, making it simpler for calculations involving thermodynamics.

Iodine Properties

Iodine is a fascinating element, noted for its distinct bluish-black solid state and its dramatic transformation into a violet gas when heated. This transition occurs without turning into a liquid first, a process called sublimation.

• It is solid at room temperature but when heated, it transitions from solid directly to gas.
• This property makes iodine handy in various scientific applications, particularly in demonstrations of sublimation.
• Iodine's melting point, \(236^{\circ} \text{F}\), corresponds to \(113.333^{\circ} \text{C}\) or \(386.483 \ \text{K}\), showing how properties can be mapped across temperature scales.
  

Understanding iodine's basic properties and behavior in different temperature scales helps in appreciating its role in chemical processes and real-world applications.