Problem 118 - General Chemistry

Question

Sodium hydrogen carbonate (baking soda) starts to decompose to sodium carbonate (soda ash) at about \(50^{\circ} \mathrm{C}\). What is this temperature in degrees Fahrenheit?

Step-by-Step Solution

Answer

The temperature in Fahrenheit is \(122^{\circ}F\).

Step 1: Understand the temperature conversion formula

To convert a temperature from degrees Celsius to degrees Fahrenheit, we use the formula: \[ F = C \times \frac{9}{5} + 32 \]where \(F\) is the temperature in Fahrenheit and \(C\) is the temperature in Celsius.

Step 2: Substitute the given Celsius temperature into the formula

We have the temperature \(C = 50^{\circ}C\). Substitute \(50\) into the conversion formula:\[ F = 50 \times \frac{9}{5} + 32 \]

Step 3: Calculate the conversion

First, calculate \(50 \times \frac{9}{5}\):\[ 50 \times \frac{9}{5} = 90 \]Then, add \(32\) to \(90\):\[ F = 90 + 32 = 122 \]

Step 4: Verify the result

Re-evaluate the calculations to ensure there are no errors. The computation was:\[ F = 50 \times \frac{9}{5} + 32 = 90 + 32 = 122 \]The calculations confirm it is correct.

Key Concepts

Decomposition of Sodium Hydrogen Carbonate

The decomposition of sodium hydrogen carbonate, commonly known as baking soda, is an important chemical process. When heated, sodium hydrogen carbonate breaks down into three other compounds: sodium carbonate, water, and carbon dioxide. The reaction can be summarized by the following equation:
\[ 2 ext{NaHCO}_3 (s) \rightarrow ext{Na}_2 ext{CO}_3 (s) + ext{H}_2 ext{O} (l) + ext{CO}_2 (g) \]
This decomposition starts at around \(50^{\circ} \text{C}\), which is relatively low compared to other decomposing reactions. During baking, this reaction is crucial because the release of carbon dioxide gas causes doughs and batters to rise, resulting in soft and fluffy baked goods. The remainder is soda ash, which has various uses including in glass and detergent manufacturing. Understanding this chemical breakdown is vital in both industrial applications and everyday cooking.

Converting Celsius to Fahrenheit

Converting temperatures from Celsius to Fahrenheit is a common need, especially in scientific and culinary contexts. The formula to perform this conversion is:
\[ F = C \times \frac{9}{5} + 32 \]
Here, \(F\) represents the temperature in Fahrenheit, while \(C\) represents the temperature in Celsius. Let's break down each part of the formula:

• The fraction \(\frac{9}{5}\) is used to convert the degree differences, as Fahrenheit has smaller degree intervals compared to Celsius.
• The addition of \(32\) is necessary because the Fahrenheit scale sets \(32^{\circ}F\) as the freezing point of water, compared to \(0^{\circ}C\) in Celsius.

This formula is straightforward and only requires basic arithmetic, making it easy to calculate by hand or by using a calculator.

Calculating Temperatures

Understanding temperature calculations is an essential skill in both daily life and scientific work. To demonstrate calculating temperatures, let's use the conversion of \(50^{\circ} \text{C}\) to Fahrenheit as an example.
Start with the temperature conversion formula mentioned before:
\[ F = C \times \frac{9}{5} + 32 \]Inserting the value \(C = 50\):

• Multiply \(50 \times \frac{9}{5}\) to get \(90\).
• Then add \(32\) to the result, leading to \(F = 122\).

Thus, \(50^{\circ} \text{C}\) converts to \(122^{\circ} \text{F}\). Double-checking calculations helps catch any arithmetic errors, ensuring precision, especially where exact temperatures are critical, such as in baking or chemical processes.