- Calculate the moles of NaOH: \(2.0 \text{ mol/L} \times 0.10 \text{ L} = 0.20 \text{ mol}\).
- Identify the 1:1 molar ratio between NaOH and HCl in the neutralization reaction.
- Determine the required moles of HCl, which is \(0.20 \text{ mol}\).
- Convert moles to mass: \(0.20 \text{ mol} \times 36.46 \text{ g/mol} = \boxed{7.292 \text{ g}}\).
Explanation
- Determine Moles of NaOH
To neutralize the sodium hydroxide (NaOH) solution, we must first determine the number of moles of NaOH present. We are given a volume of \(0.10 \text{ L}\) and a molarity of \(2.0 \text{ M}\). The formula to calculate moles is \(\text{moles} = \text{Molarity} \times \text{Volume}\). Thus, the number of moles of NaOH is \(2.0 \text{ mol/L} \times 0.10 \text{ L} = 0.20 \text{ moles}\).
- Determine Stoichiometry of the Reaction
The neutralization reaction between hydrochloric acid (HCl) and sodium hydroxide (NaOH) is given by the equation: \[\text{HCl}(aq) + \text{NaOH}(aq) \rightarrow \text{NaCl}(aq) + \text{H}_2\text{O}(l).\] This balanced equation shows a 1:1 stoichiometric ratio, meaning one mole of HCl is required to neutralize exactly one mole of NaOH. Since we have \(0.20 \text{ moles}\) of NaOH, we require exactly \(0.20 \text{ moles}\) of HCl for complete neutralization.
- Calculate the Mass of HCl Required
Now, we convert the required moles of HCl into grams. The molar mass of HCl is approximately \(36.46 \text{ g/mol}\). Using the formula \(\text{mass} = \text{moles} \times \text{molar mass}\), we calculate the mass of HCl: \[\text{mass}_{\text{HCl}} = 0.20 \text{ mol} \times 36.46 \text{ g/mol} = 7.292 \text{ grams}.\] Therefore, the amount of HCl needed to neutralize the given solution is \(7.292 \text{ grams}\).
Examples
In a chemistry laboratory, chemists often perform titrations to determine the concentration of an unknown solution. For example, if a student has an acidic solution of unknown concentration, they can neutralize it with a known quantity of a base like NaOH to find out how much acid was initially present. This fundamental process of using stoichiometric ratios helps in accurately quantifying substances, which is critical in everything from pharmaceuticals to environmental testing.