Problem 83 - Chemistry: The Central Science in SI Units, Global Edition

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 \(6.0 \mathrm{MH}_{2} \mathrm{SO}_{4}\) 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

The minimum mass of NaHCO3 required for neutralizing the acid spill can be calculated using the following steps: 1. Calculate moles of H2SO4 spilled: \(Moles\: of\: H_{2}SO_{4} = 0.027 L \times 6.0 M = 0.162\: moles\) 2. Calculate moles of NaHCO3 required: \(Moles\: of\: NaHCO_{3} = 2 \times Moles\: of\: H_{2}SO_{4} = 2 \times 0.162\: moles = 0.324\: moles\) 3. Convert moles of NaHCO3 to grams: \(Mass\: of\: NaHCO_{3} = 0.324\: moles \times 84 \frac{g}{mol} = 27.216 g\) Therefore, the minimum mass of NaHCO3 required to neutralize the acid spill is 27.216 g.

Step 1: Find moles of sulfuric acid (H2SO4) spilled on the bench

To calculate the moles of H2SO4, we need to multiply the volume of the spilled acid (27 mL) by its concentration (6.0 M): Moles of H2SO4 = Volume × Concentration First, convert the volume of H2SO4 from mL to L: 27 mL = 0.027 L Now, multiply the volume (in L) by the concentration: Moles of H2SO4: \(= 0.027 L \times 6.0 M\)

Step 2: Use stoichiometry to find moles of sodium bicarbonate (NaHCO3) required

The balanced equation shows the stoichiometric ratio between the reactants: \(2 \mathrm{NaHCO}_{3}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{CO}_{2}(g)\) As per the equation, 2 moles of NaHCO3 are required to neutralize 1 mole of H2SO4. So we can find the amount of NaHCO3 required: Moles of NaHCO3 = 2 × Moles of H2SO4

Step 3: Convert moles of sodium bicarbonate (NaHCO3) to grams

To find the mass of NaHCO3, we need to multiply the number of moles of NaHCO3 with its molar mass. The molar mass of NaHCO3 = 23 (Na) + 1 (H) + 12 (C) + 16 x 3 (O) = 84 g/mol Mass of NaHCO3 = Moles of NaHCO3 × Molar Mass of NaHCO3 Calculate the minimum mass of NaHCO3 required for neutralizing the acid spill.

Key Concepts

Neutralization Reaction

A neutralization reaction is a chemical process where an acid and a base react to produce water and a salt. It's a fundamental concept in chemistry with everyday applications, such as antacids neutralizing stomach acid or cleaning up acid spills, like in this exercise.
In a neutralization reaction involving sulfuric acid (a strong acid) and sodium bicarbonate (a weak base), the acid donates protons (H⁺ ions) to the bicarbonate, leading to the formation of water (H₂O) and carbon dioxide (CO₂) gas. This is why you observe fizzing during such a reaction, as CO₂ is released.
**Key Characteristics of Neutralization Reactions:**

• Acid + Base → Salt + Water
• Usually exothermic, releasing heat
• Frequently produces gases if bicarbonates or carbonates are involved

In this exercise, the equation 2 NaHCO₃ + H₂SO₄ → Na₂SO₄ + 2 H₂O + 2 CO₂, shows the neutralization of sulfuric acid by sodium bicarbonate. It illustrates a perfect 2:1 ratio, meaning you'll need 2 moles of NaHCO₃ for every mole of H₂SO₄ spilled, highlighting the importance of stoichiometry in predicting the outcome.

Molar Mass

Molar mass is a key concept in chemistry that indicates the mass of one mole of a substance, measured in grams per mole (g/mol). It's calculated by summing the atomic masses of all atoms in a molecule.
For sodium bicarbonate (NaHCO₃), the molar mass is determined by adding:

• Sodium (Na): 23 g/mol
• Hydrogen (H): 1 g/mol
• Carbon (C): 12 g/mol
• Oxygen (O): 16 g/mol (since there are three oxygen atoms, it's 16 × 3 = 48 g/mol)

Summing these gives a molar mass of 84 g/mol for NaHCO₃. Understanding molar mass is crucial because it connects the measured mass of a substance to the number of particles or moles, allowing for precise chemical calculations.
In the context of the exercise, after determining the moles of sodium bicarbonate required to neutralize the sulfuric acid, you multiply these moles by 84 g/mol to find the required mass of NaHCO₃ for the reaction.

Sulfuric Acid

Sulfuric acid (H₂SO₄) is a highly corrosive strong acid known for its wide industrial applications and laboratory use. As a diprotic acid, it can donate two protons per molecule, facilitating neutralization reactions with bases like sodium bicarbonate.
**Properties of Sulfuric Acid:**

• Clear, colorless, and viscous
• Strong acid with a high affinity to donate protons (H⁺ ions)
• Capable of reacting violently with bases and metals

In this exercise, the spilled 27 mL of 6.0 M sulfuric acid needs to be neutralized. Understanding its concentration is vital as it tells us how many moles of the acid are present.
The concentration 6.0 M suggests there are 6 moles of H₂SO₄ in every liter of solution. Therefore, to find out how much sodium bicarbonate we need, we calculate the moles of H₂SO₄ (by converting volume to liters and multiplying by the molarity) and then apply the stoichiometric ratio from the balanced chemical equation to determine the amount of NaHCO₃ needed.