Question

Sodium bicarbonate \(\left(\mathrm{NaHCO}_{3}\right)\) is called baking soda because, when heated, it releases carbon dioxide gas, which is responsible for the rising of cookies, some doughnuts, and cakes. (a) Calculate the volume (in liters) of \(\mathrm{CO}_{2}\) produced by heating \(5.0 \mathrm{~g}\) of \(\mathrm{NaHCO}_{3}\) at \(180^{\circ} \mathrm{C}\) and 1.3 atm. (b) Ammonium bicarbonate \(\left(\mathrm{NH}_{4} \mathrm{HCO}_{3}\right)\) has also been used for the same purpose. Suggest one advantage and one disadvantage of using \(\mathrm{NH}_{4} \mathrm{HCO}_{3}\) instead of \(\mathrm{NaHCO}_{3}\) for baking.

Short answer

Volume of \( \text{CO}_2 \) is approximately 0.857 L. \( \text{NH}_4\text{HCO}_3 \) advantage: potential improved rise; disadvantage: possible ammonia odor.

Step-by-step solution

Write the balanced chemical equation

When sodium bicarbonate (\( \text{NaHCO}_3 \)) is heated, it decomposes into sodium carbonate (\( \text{Na}_2\text{CO}_3 \)), carbon dioxide (\( \text{CO}_2 \)), and water (\( \text{H}_2\text{O} \)). The balanced chemical equation is: \[ 2 \text{NaHCO}_3 (s) \rightarrow \text{Na}_2\text{CO}_3 (s) + \text{CO}_2 (g) + \text{H}_2\text{O} (g) \]

Molar mass calculation

Calculate the molar mass of \( \text{NaHCO}_3 \): - \( \text{Na} = 22.99 \text{ g/mol} \)- \( \text{H} = 1.01 \text{ g/mol} \)- \( \text{C} = 12.01 \text{ g/mol} \)- \( \text{O} = 3 \times 16.00 \text{ g/mol} = 48.00 \text{ g/mol} \)Adding these, the molar mass of \( \text{NaHCO}_3 \) = 84.01 g/mol.

Calculate moles of NaHCO3

Given mass of \( \text{NaHCO}_3 \) = 5.0 gCalculate the moles of \( \text{NaHCO}_3 \) using its molar mass:\[ \text{Moles of } \text{NaHCO}_3 = \frac{5.0 \text{ g}}{84.01 \text{ g/mol}} \approx 0.0595 \text{ moles} \]

Moles of CO2 produced

According to the balanced equation, 2 moles of \( \text{NaHCO}_3 \) produce 1 mole of \( \text{CO}_2 \).Use stoichiometry to calculate moles of \( \text{CO}_2 \):\[ \text{Moles of } \text{CO}_2 = \frac{0.0595}{2} \approx 0.02975 \text{ moles}\]

Use the Ideal Gas Law

To find the volume of \( \text{CO}_2 \), apply the ideal gas law: \[ PV = nRT \]Given:- Pressure \( P = 1.3 \text{ atm} \)- Moles \( n = 0.02975 \) moles- Gas constant \( R = 0.0821 \text{ L atm/mol K}\)- Temperature \( T = 180^{\circ}C = 453\text{ K} \)Substitute these values:\[ V = \frac{nRT}{P} = \frac{0.02975 \times 0.0821 \times 453}{1.3} \approx 0.857 \text{ L} \]

Consider NH4HCO3 and NaHCO3 in baking

One advantage of using \( \text{NH}_4 \text{HCO}_3 \) is that it already contains both an acid and a base in one compound, which may improve the rise of baked goods. However, a disadvantage is that it can release ammonia, which might impart an undesirable odor or taste if not fully decomposed.

Key concepts

Baking Soda

Baking soda, or sodium bicarbonate (\( \text{NaHCO}_3 \)), is a common ingredient found in many kitchens. It serves multiple purposes, but it's perhaps most famously known for its role in baking. When heated, it undergoes a chemical reaction, decomposing to produce carbon dioxide gas (\( \text{CO}_2 \)). This release of gas is what helps dough and batter rise, making baked goods fluffy and light.
Baking soda is a base, and when it comes into contact with an acid, it reacts to form bubbles of carbon dioxide. This makes it valuable in baking, particularly in recipes that contain acidic ingredients like buttermilk or lemon juice.
One of the benefits of using baking soda is its ability to produce carbon dioxide quickly. However, it must be balanced properly in recipes to prevent a metallic taste.

Gas Laws

Gas laws are fundamental in understanding how gases behave under different conditions of pressure, volume, and temperature. In this exercise, the gas laws help us determine the volume of carbon dioxide (\( \text{CO}_2 \)) produced when baking soda is heated.
Gas laws, such as Boyle's Law, Charles's Law, and Avogadro's Law, describe the behavior of gases. However, the Ideal Gas Law is particularly useful as it combines these principles into a single equation: \( PV = nRT \). This equation relates a gas's pressure (\( P \)), volume (\( V \)), temperature (\( T \)), and the amount in moles (\( n \)) as long as you use the ideal gas constant (\( R \)).
Understanding how these laws work is critical for calculating the change in gas volume when chemical reactions occur, especially in baking where precise quantities of gas can affect the final product.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It is a critical analytical tool in chemistry, allowing us to predict the amounts of products that will form in a reaction or how much reactant will be needed.
When heating baking soda, stoichiometry helps us calculate how much carbon dioxide (\( \text{CO}_2 \)) gas will be released from a given amount of baking soda. By using the balanced chemical equation, we determine how many moles of each substance are involved and apply proportional chemical relationships.
This concept is essential in chemistry because it ensures that reactions are well understood and that materials are used efficiently, which is particularly important in industrial and laboratory settings, as well as in everyday cooking.

Ideal Gas Law

The Ideal Gas Law is a fundamental principle in chemistry that relates the four variables of a gas: pressure (\( P \)), volume (\( V \)), temperature (\( T \)), and amount in moles (\( n \)). It is expressed by the formula: \( PV = nRT \). The constant (\( R \)) is the ideal gas constant with a value of 0.0821 L atm/mol K.
This law assumes that gases behave ideally, meaning that interactions between molecules are negligible and the molecules occupy no volume. While no real gas perfectly fits this model, many gases, like carbon dioxide produced from baking soda, closely follow this law under certain conditions.
In baking, applying the Ideal Gas Law helps determine the quantity of gas produced, as seen in this exercise. Knowing this allows bakers to adjust their recipes to achieve the desired texture and rise in baked goods.