Question

Baking soda (sodium hydrogen carbonate, \(\mathrm{NaHCO}_{3}\) ) is often used to neutralize spills of acids on the benchtop in the laboratory. What mass of \(\mathrm{NaHCO}_{3}\) would be needed to neutralize a spill consisting of \(25.2 \mathrm{~mL}\) of \(6.01 \mathrm{M}\) hydrochloric acid solution?

Short answer

Hence, \(12.7~\mathrm{g}\) of sodium hydrogen carbonate (NaHCO3) is needed to neutralize the spill consisting of \(25.2~\mathrm{mL}\) of \(6.01\mathrm{M}\) hydrochloric acid solution.

Step-by-step solution

Find moles of HCl in the spill

Calculate the moles of HCl present in the spill. To do this, multiply the volume of the spill (in liters) by the molarity of the HCl solution: Moles of HCl = volume (L) × molarity (M) Note that 25.2 mL equals 0.0252 L Moles of HCl = \(0.0252~\mathrm{L} \times 6.01~\mathrm{M}\) Moles of HCl = \(0.1514~\mathrm{mol}\)

Use stoichiometry to find moles of NaHCO3

Next, we need to find the moles of NaHCO3 needed to neutralize the HCl in the spill. The balanced chemical equation for this neutralization reaction is: HCl + NaHCO3 → NaCl + CO2 + H2O From the balanced equation, we can see that 1 mole of HCl reacts with 1 mole of NaHCO3. So, the moles of NaHCO3 needed is equal to the moles of HCl. Moles of NaHCO3 needed = \(0.1514~\mathrm{mol}\)

Convert moles of NaHCO3 to mass

Finally, calculate the mass of NaHCO3 required. Use the molar mass of NaHCO3, which is: Molar mass of NaHCO3 = 23.0 (Na) + 1.0 (H) + 12.0 (C) + 16.0 × 3 (O) = 84.0 g/mol Mass of NaHCO3 needed = moles of NaHCO3 × molar mass of NaHCO3 Mass of NaHCO3 needed = \(0.1514~\mathrm{mol} \times 84.0~\mathrm{g/mol}\) Mass of NaHCO3 needed = \(12.7~\mathrm{g}\) Hence, \(12.7~\mathrm{g}\) of sodium hydrogen carbonate (NaHCO3) is needed to neutralize the spill consisting of \(25.2~\mathrm{mL}\) of \(6.01\mathrm{M}\) hydrochloric acid solution.

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves calculating the quantitative relationships between reactants and products in a chemical reaction. In the case of neutralization reactions like the one between hydrochloric acid (HCl) and sodium hydrogen carbonate (\(\text{NaHCO}_3\)), stoichiometry helps us determine how much of each reactant is needed to fully react without excess.
The balanced chemical equation given is: \[\text{HCl} + \text{NaHCO}_3 \rightarrow \text{NaCl} + \text{CO}_2 + \text{H}_2\text{O}\]From this equation, you can see that one mole of HCl reacts with one mole of \(\text{NaHCO}_3\). This one-to-one ratio tells us that the moles of HCl in the acid spill equal the moles of \(\text{NaHCO}_3\) needed for neutralization.

• Start by calculating the moles of HCl using its molarity and volume.
• Then use stoichiometry to find the moles of \(\text{NaHCO}_3\) needed.
• This relationship assures that the entire amount of acid is reacted and neutralized.

Molarity

Molarity refers to the concentration of a solution expressed in moles of solute per liter of solution. It's a crucial concept when dealing with neutralization reactions because it allows you to calculate the exact amount of a substance in a given volume of solution.
In this exercise, the molarity of the hydrochloric acid (HCl) is given as 6.01 M, which means there are 6.01 moles of HCl per liter of solution.
To find the moles of HCl in the spill, you would multiply the molarity (6.01 M) by the volume of the solution in liters (0.0252 L): \[\text{Moles of HCl} = 6.01 \times 0.0252 = 0.1514 \text{ moles}\]
This calculation is key in determining how much sodium hydrogen carbonate is needed for the neutralization.

Molar Mass

Molar mass is the mass of one mole of a given substance and is expressed in grams per mole (g/mol). It's a fundamental concept used to convert between the mass of a substance and the amount of substance (in moles).
In the exercise, you need the molar mass of sodium hydrogen carbonate (\(\text{NaHCO}_3\)), which is calculated by adding up the atomic masses of each element present in the compound:

• Sodium (Na): 23.0 g/mol
• Hydrogen (H): 1.0 g/mol
• Carbon (C): 12.0 g/mol
• Oxygen (O): 16.0 g/mol, multiplied by 3 because there are three oxygen atoms

Adding these together gives the molar mass of \(\text{NaHCO}_3\) as 84.0 g/mol.
Once you know the moles of \(\text{NaHCO}_3\), you calculate the mass needed for neutralization by multiplying the moles by the molar mass: \[\text{Mass of NaHCO}_3 = 0.1514 \text{ mol} \times 84.0 \text{ g/mol} = 12.7 \text{ g}\]

Chemical Equation

A chemical equation summarizes a chemical reaction by showing the reactants and products, and their quantities, in a concise form. It's a script for chemists showing how substances transform.
In this exercise, the chemical equation that describes the neutralization of hydrochloric acid with sodium hydrogen carbonate is: \[\text{HCl} + \text{NaHCO}_3 \rightarrow \text{NaCl} + \text{CO}_2 + \text{H}_2\text{O}\]
This balanced equation indicates that one molecule of hydrochloric acid reacts with one molecule of sodium hydrogen carbonate to produce one molecule each of sodium chloride, carbon dioxide, and water.
The stoichiometric coefficients (numbers in front of the molecules) tell us the ratios in which the substances react. In this equation, all coefficients are implied to be one, showing a simple 1:1 molar ratio between the reactants and products. This is critical in calculations as it directly affects the stoichiometric conversions you'll perform to determine the amount of reactants and products involved.