Question

You borrowed a thermometer from the chemistry lab to use in the kitchen. If you want to heat a mixture of sugar and cream to \(247^{\circ} \mathrm{F}\), what temperature do you need in \({ }^{\circ} \mathrm{C}\) ? What is this temperature in \(\mathrm{K}\) ?

Short answer

119.4 °C and 392.55 K

Step-by-step solution

- Converting Fahrenheit to Celsius

We start by using the formula to convert Fahrenheit to Celsius:\[ C = (F - 32) \times \frac{5}{9} \]Substitute the given Fahrenheit value, 247:\[ C = (247 - 32) \times \frac{5}{9} \]\[ C = 215 \times \frac{5}{9} \]\[ C = 119.44 \approx 119.4 \ °\text{C} \]

- Converting Celsius to Kelvin

Next, we convert Celsius to Kelvin using the formula:\[ K = C + 273.15 \]Substitute the calculated Celsius value, 119.4:\[ K = 119.4 + 273.15 \]\[ K = 392.55 \]

Key concepts

Fahrenheit to Celsius conversion

To convert temperatures from Fahrenheit (°F) to Celsius (°C), we use a specific formula. This formula is: \[ C = (F - 32) \times \frac{5}{9} \]First, subtract 32 from the Fahrenheit temperature.Then, multiply the result by \( \frac{5}{9} \). For example, to convert 247°F to Celsius: \[ C = (247 - 32) \times \frac{5}{9} = 215 \times \frac{5}{9} = 119.44 \]So, 247°F is approximately 119.4°C. This simple but effective calculation is fundamental when working in both everyday situations and specific scientific experiments involving temperature conversion.

Celsius to Kelvin conversion

Converting Celsius (°C) to Kelvin (K) is straightforward. The formula used is: \[ K = C + 273.15 \]This equation involves adding 273.15 to the Celsius temperature. Kelvin is often used in scientific contexts because it starts at absolute zero, the theoretical point where molecular motion stops.Using our previous result from the Fahrenheit to Celsius conversion (119.4°C): \[ K = 119.4 + 273.15 = 392.55 \]Thus, 119.4°C is equal to 392.55 K. Scientists and chemists favor the Kelvin scale because it avoids negative numbers and makes calculations more straightforward.

Temperature measurement in chemistry

Temperature is crucial in chemistry as it influences reaction rates, equilibrium states, and physical properties of substances. Many chemical processes are temperature-sensitive, meaning they only occur at specific temperatures.Standard temperature scales in chemistry include Celsius, Kelvin, and sometimes Fahrenheit (for external applications). Each substance has unique temperature-specific behaviors, making accurate temperature measurement essential.Understanding how to convert between temperature scales ensures that experiments and recipes can be accurately replicated and shared globally.

Thermometer usage in chemistry lab

Thermometers are indispensable tools in any chemistry lab. They measure the temperature of substances involved in reactions, ensuring conditions are maintained as required.Different types of thermometers are used, including:

• Mercury thermometers
• Digital thermometers
• Thermocouples

When using a thermometer:

• Always ensure it’s calibrated and suitable for the temperature range you need.
• Immobilize the thermometer in the substance, ensuring it's not touching the container’s bottom or walls, as this can give inaccurate readings.
• Record the temperature once it stabilizes.

Accurate temperature measurement helps control and predict the outcomes of chemical reactions, ensuring safety and consistency in the lab.