Question

When baking soda (sodium bicarbonate or sodium hydrogen carbonate, \(\mathrm{NaHCO}_{3}\) ) is heated, it releases carbon dioxide gas, which is responsible for the rising of cookies, doughnuts, and bread. (a) Write a balanced equation for the decomposition of the compound (one of the products is \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) ). (b) Calculate the mass of \(\mathrm{NaHCO}_{3}\) required to produce \(20.5 \mathrm{~g}\) of \(\mathrm{CO}_{2}\)

Short answer

78.24 g of NaHCO3 is needed to produce 20.5 g of CO2.

Step-by-step solution

Write the Decomposition Reaction

To find the balanced chemical equation for the decomposition of sodium bicarbonate (\( \mathrm{NaHCO}_{3} \)), we consider the products: sodium carbonate (\( \mathrm{Na}_{2} \mathrm{CO}_{3} \)), water (\( \mathrm{H}_{2} \mathrm{O} \)), and carbon dioxide (\( \mathrm{CO}_{2} \)). The decomposition reaction is: \[ 2 \mathrm{NaHCO}_{3(s)} \rightarrow \mathrm{Na}_{2} \mathrm{CO}_{3(s)} + \mathrm{H}_{2} \mathrm{O}_{(g)} + \mathrm{CO}_{2(g)} \]This equation is balanced with regard to all elements involved.

Calculate Moles of CO2 Produced

Using the formula for moles, \( n = \frac{m}{M} \), where \( m \) is the mass and \( M \) is the molar mass. First, calculate the molar mass of \( \mathrm{CO}_{2} \) which is: \( 12.01 + (2 \times 16.00) = 44.01 \ \mathrm{g/mol} \).Next, calculate the moles of \( \mathrm{CO}_{2} \) produced using its mass:\[ n = \frac{20.5 \ \mathrm{g}}{44.01 \ \mathrm{g/mol}} \approx 0.466 \ \text{mol} \]

Use Stoichiometry to Find Moles of NaHCO3 Needed

According to the balanced equation, 2 moles of \( \mathrm{NaHCO}_{3} \) produce 1 mole of \( \mathrm{CO}_{2} \). Therefore, to find the moles of \( \mathrm{NaHCO}_{3} \) needed to produce 0.466 moles of \( \mathrm{CO}_{2} \):\[ \text{Moles of } \mathrm{NaHCO}_{3} = 2 \times 0.466 = 0.932 \ \text{mol} \]

Calculate Mass of NaHCO3 Required

The molar mass of \( \mathrm{NaHCO}_{3} \) is calculated as: \( 22.99 + 1.01 + 12.01 + (3 \times 16.00) = 84.01 \ \mathrm{g/mol} \). To find the mass required, use:\[ m = n \times M = 0.932 \ \text{mol} \times 84.01 \ \mathrm{g/mol} \approx 78.24 \ \mathrm{g} \]

Key concepts

Balanced Chemical Equation

In chemistry, a balanced chemical equation is a symbolic representation of a chemical reaction in which the number of atoms for each element is equal on both the reactant and product sides. This is crucial because it reflects the law of conservation of mass, which states that matter cannot be created or destroyed in a closed system.

For the decomposition of sodium bicarbonate (\(\text{NaHCO}_3\)), the equation is written as:\[ 2\,\text{NaHCO}_{3(s)} \rightarrow \text{Na}_{2}\text{CO}_{3(s)} + \text{H}_{2}\text{O}_{(g)} + \text{CO}_{2(g)} \]

• Each element is counted on both sides to ensure they match.
• For example, there are 2 sodium (Na) atoms on each side.
• This balance ensures that the reaction properly represents actual chemistry occurring at the atomic level.

The balanced equation helps us understand the precise conversion that occurs during the reaction, which is critical for further calculations, such as stoichiometry and mole calculations.

Stoichiometry

Stoichiometry refers to the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It allows chemists to predict the amounts of substances consumed and produced.

By using the balanced equation for the decomposition of sodium bicarbonate, we establish a proportional relationship between reactants and products:

• The given equation shows that 2 moles of \(\text{NaHCO}_3\) yield 1 mole each of \(\text{Na}_{2}\text{CO}_3\), \(\text{H}_2\text{O}\), and \(\text{CO}_2\).
• This ratio is critical for calculating how much starting material is needed to produce a specific amount of a product.

Stoichiometry thus serves as the foundation for converting measurements in grams to moles, and using ratios from balanced equations to solve problems.

Mole Calculations

Mole calculations in chemistry involve using the concept of the mole to determine the amount of substance needed or produced. A mole is a standard unit of measurement in chemistry, representing Avogadro's number (approximately\(6.022 \times 10^{23}\) atoms, molecules, or ions).

• To calculate how much \(\text{NaHCO}_3\) is required to produce 20.5 grams of \(\text{CO}_2\), the moles of \(\text{CO}_2\) were first calculated.
• Using the formula \( n = \frac{m}{M} \), where \(n\) is the number of moles, \(m\) is mass, and \(M\) is molar mass, we found \(0.466\) moles of \(\text{CO}_2\).
• The balanced equation then indicated that this equates to \(0.932\) moles of \(\text{NaHCO}_3\).
• Finally, by converting these moles back to grams, the required mass of \(\text{NaHCO}_3\) was determined to be approximately 78.24 grams.

Mole calculations are crucial because they provide a method to quantify relationships in chemical reactions, converting between actual masses to moles to facilitate stoichiometric predictions.

Chemical Reactions

Chemical reactions are processes where substances are transformed into different substances. In the decomposition of sodium bicarbonate (\(\text{NaHCO}_3\)), we see a clear example of such a transformation. In this type of reaction:

• Sodium bicarbonate breaks down into sodium carbonate (\(\text{Na}_{2}\text{CO}_3\)), water (\(\text{H}_{2}\text{O}\)), and carbon dioxide (\(\text{CO}_2\)).
• This reaction is temperature-induced, showcasing how energy inputs can drive changes in chemical substances.

The decomposition of \(\text{NaHCO}_3\) is significant in both everyday applications like baking and in teaching fundamental chemistry concepts. It illustrates not only changes in chemical structure but also broader principles like energy dynamics and gas evolution.