Question

What volume of \(0.150 \mathrm{M} \mathrm{HNO}_{3}\) solution is needed to exactly neutralize \(35.0 \mathrm{mL}\) of \(0.150 \mathrm{M} \mathrm{NaOH}\) solution?

Short answer

To exactly neutralize the $35.0 \mathrm{mL}$ of $0.150 \mathrm{M}$ $\mathrm{NaOH}$ solution, you would need $35.0 \mathrm{mL}$ of the $0.150 \mathrm{M}$ $\mathrm{HNO}_{3}$ solution.

Step-by-step solution

Identify the Given Values

The exercise provides the molarity of the nitric acid (\(HNO_{3}\)) solution, which is 0.150 M, and the molarity and volume of the sodium hydroxide (\(NaOH\)) solution, which are 0.150 M and 35.0 mL respectively.

Calculate Moles of NaOH

The number of moles of \(NaOH\) in the 35.0 mL of solution can be calculated using the formula: Moles = Molarity x Volume. Since the volume needs to be in liters for this calculation, convert milliliters to liters by dividing it by 1000. So, \(35.0 mL = 0.035 L\). Therefore, moles of \(NaOH = 0.150M * 0.035L = 0.00525\) moles.

Calculate Volume of HNO3 Needed

In a neutralization reaction, the moles of acid needed to neutralize a base equals the moles of the base. Hence, the moles of \(HNO_{3}\) needed are also \(0.00525\) moles. The volume of \(HNO_{3}\) needed can be calculated using the formula: Volume = Moles / Molarity. So, Volume of \(HNO_{3} = 0.00525 moles / 0.150 M = 0.035 L\).

Convert back to mL

Convert the volume of solution from liters back to milliliters by multiplying by 1000. This gives \(35.0 mL\). Therefore, \(35.0 mL\) of \(0.150 M HNO_{3}\) solution is needed to exactly neutralize \(35.0 mL\) of \(0.150 M NaOH\) solution.

Key concepts

Molarity

Molarity is a measure of the concentration of a solute in a solution. It tells you how many moles of a solute are present in one liter of a solution.
To calculate molarity, you use the formula:
\[\text{Molarity (M)} = \frac{\text{Moles of solute}}{\text{Liters of solution}}\]For example, in our exercise, we have a nitric acid solution with a molarity of 0.150 M. This means in one liter of this solution, there are 0.150 moles of nitric acid.
Understanding molarity is crucial because it allows us to predict how solutions will behave in reactions, specifically in terms of proportions.
This can be particularly useful when you need to determine how much of one solution is required to react with a given quantity of another in a neutralization reaction.
For any solution, always convert volume from milliliters to liters by dividing by 1000 to use molarity effectively.

Acid-Base Reaction

An acid-base reaction, also known as a neutralization reaction, occurs when an acid and a base react to form water and a salt.
The classic general form of this reaction is:

• Acid + Base \( \rightarrow \) Salt + Water

In our example, nitric acid (\( \text{HNO}_3 \)) reacts with sodium hydroxide (\( \text{NaOH} \)) to form sodium nitrate (\( \text{NaNO}_3 \)) and water:

• \( \text{HNO}_3 + \text{NaOH} \rightarrow \text{NaNO}_3 + \text{H}_2\text{O} \)

A neutralization reaction is complete when the moles of the acid equal the moles of the base.
In the given problem, this condition means that the amount of nitric acid needed should equal the amount of sodium hydroxide we started with, which tells us how to balance our chemical equation.
Understanding these reactions is key to solving problems where you need to find out how much acid is required to neutralize a base, or vice versa.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It allows us to predict precisely how much of each substance is involved in a reaction.
This is particularly important in neutralization reactions, where you often need to know how much of an acid you need to react with a base to achieve neutralization.

In the given exercise, we used stoichiometry to determine that the moles of nitric acid needed equal the moles of sodium hydroxide present.

• We calculated the moles of sodium hydroxide as 0.00525 moles, considering its molarity and volume.
• Because of the 1:1 mole ratio between \( \text{HNO}_3 \) and \( \text{NaOH} \), we also need 0.00525 moles of nitric acid to complete the reaction.

Once you have the moles, you can find the volume of \( \text{HNO}_3 \) required using the molarity formula:
Volume = \( \frac{\text{Moles}}{\text{Molarity}} \).

Stoichiometry provides the necessary framework to solve chemistry problems, ensuring everything is in perfect balance, much like a delicate dance between the components of the reaction.