Problem 83 - Chemistry The Central Science In Si Units

Question

Some sulfuric acid is spilled on a lab bench. You can neutralize the acid by sprinkling sodium bicarbonate on it and then mopping up the resulting solution. The sodium bicarbonate reacts with sulfuric acid according to: $$ \begin{aligned} 2 \mathrm{NaHCO}_{3}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+& \\ 2 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{CO}_{2}(g) \end{aligned} $$ Sodium bicarbonate is added until the fizzing due to the formation of \(\mathrm{CO}_{2}(g)\) stops. If \(27 \mathrm{~mL}\) of \(6.0 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) was spilled, what is the minimum mass of \(\mathrm{NaHCO}_{3}\), that must be added to the spill to neutralize the acid?

Step-by-Step Solution

Answer

27.2 grams of \(\mathrm{NaHCO}_3\) is needed to neutralize the spill.

Step 1: Understanding the Reaction

In the given reaction, sodium bicarbonate \((\mathrm{NaHCO}_3)\) reacts with sulfuric acid \((\mathrm{H}_2\mathrm{SO}_4)\) to form sodium sulfate \((\mathrm{Na}_2\mathrm{SO}_4)\), water \((\mathrm{H}_2\mathrm{O})\), and carbon dioxide \((\mathrm{CO}_2)\) gas. The reaction stops when fizzing ends, indicating all acid has reacted.

Step 2: Calculate Moles of Sulfuric Acid

First, calculate the number of moles of sulfuric acid. Use the formula: \[ \text{Moles of } \mathrm{H}_2\mathrm{SO}_4 = \text{Volume (L)} \times \text{Molarity (M)} \] Convert 27 mL to liters:\[ 27 \text{ mL} = 0.027 \text{ L} \]Now calculate the moles:\[ \text{Moles of } \mathrm{H}_2\mathrm{SO}_4 = 0.027 \text{ L} \times 6.0 \text{ M} = 0.162 \text{ moles} \]

Step 3: Use the Balanced Equation to Find Moles of Sodium Bicarbonate

From the balanced equation, 2 moles of sodium bicarbonate \((\mathrm{NaHCO}_3)\) are required per mole of sulfuric acid. Thus, the moles of sodium bicarbonate needed are:\[ 0.162 \text{ moles of } \mathrm{H}_2\mathrm{SO}_4 \times 2 = 0.324 \text{ moles of } \mathrm{NaHCO}_3 \]

Step 4: Calculate Mass of Sodium Bicarbonate

Find the molar mass of sodium bicarbonate \((\mathrm{NaHCO}_3)\):\[ \text{Molar mass of } \mathrm{NaHCO}_3 = 23.0 (\text{Na}) + 1.0 (\text{H}) + 12.0 (\text{C}) + 3 \times 16.0 (\text{O}) = 84.0 \text{ g/mol} \]Calculate the mass of sodium bicarbonate needed:\[ \text{Mass} = 0.324 \text{ moles} \times 84.0 \text{ g/mol} = 27.216 \text{ grams} \]

Step 5: Conclusion

Based on the calculations, the minimum mass of sodium bicarbonate required to neutralize the spill is approximately 27.2 grams.

Key Concepts

Stoichiometry

Stoichiometry is a key concept in chemistry that involves calculating the quantitative relationships between the reactants and products in a chemical reaction. It's like a recipe that tells you how much of each ingredient is needed to make your dish, or in this case, how many moles of a reactant are required to completely react with another.

In our exercise, stoichiometry is used to determine how much sodium bicarbonate (\(\mathrm{NaHCO}_3\)) is needed to neutralize a certain amount of sulfuric acid (\(\mathrm{H}_2\mathrm{SO}_4\)). By looking at the balanced chemical equation, we see the relation:

• 2 moles of \(\mathrm{NaHCO}_3\) react with 1 mole of \(\mathrm{H}_2\mathrm{SO}_4\)

This means that for every mole of sulfuric acid, twice as many moles of sodium bicarbonate are needed. Stoichiometry helps us calculate these amounts accurately using the mole ratio derived from the balanced equation.

Without understanding stoichiometry, we'd have no guided method for knowing precise amounts, making many chemical processes unpredictable and unmanageable.

Chemical Reaction Balancing

Balancing chemical reactions is essential because it ensures that the same amount of each element is present in both the reactants and the products of a reaction. It follows the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction.

In the given reaction, \(2 \mathrm{NaHCO}_3(s)+\mathrm{H}_2 \mathrm{SO}_4(aq) \rightarrow \mathrm{Na}_2 \mathrm{SO}_4(aq)+2 \mathrm{H}_2 \mathrm{O}(l)+2 \mathrm{CO}_2(g)\), everything is balanced:

• 2 sodium (Na) on each side
• 2 hydrogen (H) from the bicarbonate and 2 from the sulfuric acid, making 4 hydrogens, which are present as 2 \(\mathrm{H}_2\mathrm{O}\)
• 2 carbons (C) in each \(\mathrm{CO}_2\) molecule
• 6 oxygens from bicarbonate, sulfuric acid, and the produced carbon dioxide and water, aligned properly on both sides

Balancing is crucial because incorrect ratios can lead to incomplete reactions or unexpected products. It ensures every atom is accounted for, making the reaction not only predictable but replicable in various applications.

Molarity

Molarity (M), often symbolized as \(\text{M}\), is a measurement of the concentration of a solution. Specifically, it refers to the number of moles of solute per liter of solution (mol/L).

In our problem, molarity is used to determine how many moles of sulfuric acid were present in the 27 mL spill:

• The given molarity of sulfuric acid is \(6.0 \text{ M}\)
• Convert 27 mL into liters by dividing by 1000, getting 0.027 L
• The moles of sulfuric acid are calculated as \(0.027 \text{ L} \times 6.0 \text{ M} = 0.162 \text{ moles}\)

Understanding molarity allows us to relate concentrations to quantities required for reactions. Without it, determining how much sodium bicarbonate was needed to neutralize the spill would have been impossible. Molarity thus connects the volume of a solution with its constituent particles, offering insight into its reactivity and strength.