Question

The total acidity in water samples can be determined by neutralization with standard sodium hydroxide solution. What is the total concentration of hydrogen ion, \(\mathrm{H}^{+},\) present in a water sample if \(100 . \mathrm{mL}\) of the sample requires \(7.2 \mathrm{~mL}\) of \(2.5 \times 10^{-3} \mathrm{M} \mathrm{NaOH}\) to be neutralized?

Short answer

The total concentration of hydrogen ion (H+) present in the water sample is \(1.8 \times 10^{-4} \mathrm{M}\).

Step-by-step solution

Write the balanced chemical equation for the neutralization reaction

The neutralization reaction between sodium hydroxide (NaOH) and hydrogen ions (H+) can be represented by the following balanced chemical equation: NaOH + H+ → Na+ + H2O In this reaction, one mole of NaOH reacts with one mole of H+ to produce one mole of Na+ and one mole of water.

Calculate the moles of NaOH used in the reaction

The volume of NaOH solution used is 7.2 mL and its concentration is \(2.5 \times 10^{-3} \mathrm{M}\). To find the moles of NaOH, we can use the formula: n = CV. Convert mL to L before calculating: Volume of NaOH = 7.2 mL = 0.0072 L Concentration of NaOH = \(2.5 \times 10^{-3} \mathrm{M}\) Moles of NaOH = (0.0072 L) × \(2.5 \times 10^{-3} \mathrm{M}\) = \(1.8 \times 10^{-5}\) moles

Determine the moles of H+ in the water sample

From the balanced chemical equation, we see that one mole of NaOH reacts with one mole of H+. So, the moles of H+ in the water sample will be equal to the moles of NaOH used in the reaction: Moles of H+ = \(1.8 \times 10^{-5}\) moles

Calculate the concentration of H+ in the water sample

To find the concentration of H+ in the water sample, we can use the formula: C = n/V. The volume of the water sample is 100 mL. Convert to L before calculating: Volume of water sample = 100 mL = 0.1 L Moles of H+ = \(1.8 \times 10^{-5}\) moles Concentration of H+ = \(\frac{1.8 \times 10^{-5} \mathrm{moles}}{0.1 \mathrm{L}}\) = \(1.8 \times 10^{-4} \mathrm{M}\) The total concentration of hydrogen ion (H+) present in the water sample is \(1.8 \times 10^{-4} \mathrm{M}\).

Key concepts

Neutralization Reaction

In the realm of chemistry, a neutralization reaction is an essential process involving the reaction between an acid and a base. This process typically results in the formation of water and salt, which are generally neutral substances. For example, when sodium hydroxide (NaOH), a strong base, reacts with hydrogen ions (\(\text{H}^{+}\)), a common component of acids, water and sodium ions are produced. In a neutralization reaction:

• The acid (providing \(\text{H}^{+}\) ions) and the base (providing hydroxide ions, \(\text{OH}^{-}\)) react to neutralize each other.
• The products are neutral substances such as water and a salt.

In the exercise given, NaOH reacts with the \(\text{H}^{+}\) ions in the water sample. The balanced equation for this reaction is:NaOH + \(\text{H}^{+}\) → \(\text{Na}^{+}\) + \(\text{H}_{2}O\)

Molar Concentration

Molar concentration, also known as molarity, is a way to express the concentration of a solution. It tells us how many moles of a solute are present in one liter of solution. Molarity is an essential dimension in chemistry, particularly in titration experiments like the one in the exercise. It helps you understand how tightly packed solute particles are in the solution. The formula for calculating molarity is:\[C = \frac{n}{V}\]where \(C\) is the molarity, \(n\) is the number of moles of solute, and \(V\)is the volume of solution in liters.In the exercise, the concentration of sodium hydroxide (\(\text{NaOH}\)) solution was given as \(2.5 \times 10^{-3} \text{M}\). By using the given volume of \(7.2 \text{mL}\) or \(0.0072 \text{L}\), the moles of \(\text{NaOH}\) used in the reaction were calculated. This molarity was key to finding out the number of \(\text{H}^{+}\) ions in the water sample.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions. They are like recipes that tell you what ingredients you need and how they react with each other. A chemical equation consists of reactants on the left side, products on the right side, and an arrow pointing from reactants to products.

• Reactants: The starting substances that react with each other, like \(\text{NaOH}\) and \(\text{H}^{+}\) in our exercise.
• Products: The new substances formed as a result of the reaction, such as \(\text{Na}^{+}\) and \(\text{H}_{2}O\).
• Conservation of Mass: Chemical equations must be balanced to ensure the same number of atoms of each element on both sides.

In our exercise, the balanced chemical equation is NaOH + \(\text{H}^{+}\) → \(\text{Na}^{+}\) + \(\text{H}_{2}O\). This means one mole of \(\text{NaOH}\) reacts with one mole of \(\text{H}^{+}\) ions to produce one mole of water and sodium ions.