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What is the \(\mathrm{pH}\) of \(1.0 \mathrm{~L}\) of water to which a. \(1.5 \mathrm{~mL}\) of \(3.0 \mathrm{M} \mathrm{HCl}\) or b. \(1.5 \mathrm{~mL}\) of \(3.0 \mathrm{M} \mathrm{NaOH}\) has been added?

Short Answer

Expert verified
The pH of the HCl solution is 2.35, and the pH of the NaOH solution is 11.65.

Step by step solution

01

Understand the Problem

We are asked to find the pH of water after adding a small volume of either strong acid (HCl) or strong base (NaOH). We'll calculate the change in pH by determining the concentration of hydrogen or hydroxide ions in the new solution.
02

Calculate Initial Moles of HCl or NaOH

First, calculate the number of moles using the formula: moles = concentration \(\times\) volume. For both HCl and NaOH, the volume is 1.5 mL = 0.0015 L and the concentration is 3.0 M. So, moles = 3.0 \(\times\) 0.0015 = 0.0045 moles.
03

Determine Total Volume of Solution

The total volume of the solution after adding 1.5 mL of either HCl or NaOH to 1 L of water becomes: 1000 mL + 1.5 mL = 1001.5 mL = 1.0015 L. This will be used to find the concentration of H鈦 or OH鈦.
04

Calculate Concentration of Ions

For HCl (acid), the H鈦 ion concentration will be the number of moles of HCl divided by the total volume: \[ \text{[H}^+\text{]} = \frac{0.0045}{1.0015} \approx 0.004495 \text{ M} \]. For NaOH (base), the OH鈦 ion concentration is: \[ \text{[OH}^-\text{]} = \frac{0.0045}{1.0015} \approx 0.004495 \text{ M} \].
05

Calculate pH for the Acidic Solution

The pH is calculated using the formula: pH = -log([H鈦篯). For the HCl solution, \( \text{pH} = -\log(0.004495) \approx 2.35 \).
06

Calculate pH for the Basic Solution

To calculate the pH from the OH鈦 concentration, first find the pOH using: pOH = -log([OH鈦籡). For NaOH, \( \text{pOH} = -\log(0.004495) \approx 2.35 \). The pH is then calculated using pH + pOH = 14, so \( \text{pH} = 14 - 2.35 = 11.65 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Acid-Base Reactions
Acid-base reactions are fundamental in chemistry and involve the transfer of hydrogen ions (\(\text{H}^+\) ions) between reactants. When an acid and a base are mixed, they neutralize each other, resulting in the formation of water and a salt. The strength of an acid or base is determined by its ability to donate or accept \(\text{H}^+\) ions. Strong acids, like hydrochloric acid (HCl), completely dissociate in water, increasing the concentration of \(\text{H}^+\) ions in the solution. Similarly, strong bases, such as sodium hydroxide (NaOH), fully dissociate to release hydroxide ions (\(\text{OH}^-\)), which can accept \(\text{H}^+\) ions.
When you add a strong acid to water, the solution's \(\text{H}^+\) ion concentration surges due to the acid鈥檚 dissociation. Conversely, adding a strong base increases the \(\text{OH}^-\) concentration by absorbing \(\text{H}^+\) ions from the water. This dynamic interplay is the crux of acid-base reactions, significantly affecting the solution's pH. Understanding these reactions helps us manipulate the acidity or basicity of solutions in various applications, from laboratory experiments to biological processes in our bodies.
Hydrogen Ion Concentration
Hydrogen ion concentration is crucial in determining a solution鈥檚 acidity. It is denoted as \([\text{H}^+]\) and is expressed in molarity (M). The concept centers around the number of hydrogen ions present in a given volume of solution.
For an acidic solution, understanding \([\text{H}^+]\) is relatively straightforward because acids are \(\text{H}^+\) donors. The higher the \([\text{H}^+]\), the stronger the acidity. In our exercise, adding 1.5 mL of 3.0M HCl increases the \([\text{H}^+]\) due to HCl's full dissociation:
  • The number of moles of \(\text{H}^+\) derived from HCl is calculated using \(0.0045\text{ moles of } \text{HCl}\).
  • Dividing these moles by the new solution volume (1.0015 L), yields \([\text{H}^+] \approx 0.004495\text{ M}\).
Hence, the pH reflects the concentration of these ions.In neutral solutions, like pure water, \([\text{H}^+]\) is \(1 \times 10^{-7}\text{ M}\), and the solution is neither acidic nor basic. Adding substances affects this balance, shifting the pH scale according to the change in \([\text{H}^+]\).
pOH Calculation
The pOH is a measure of the hydroxide ion concentration in a solution. It complements the pH because the two values sum to 14 in aqueous solutions at 25掳C. The equation \(\text{pH} + \text{pOH} = 14\) underlines their relationship.
In our exercise, pOH calculation plays a vital role when dealing with bases. When you add NaOH, a strong base, to water, it dissociates to release \(\text{OH}^-\) ions:
  • The concentration of \([\text{OH}^-]\) is determined by the same method used for acids: dividing the moles of \(\text{OH}^-\) (0.0045 moles) by the total volume (1.0015 L).
  • This gives \([\text{OH}^-] \approx 0.004495 \text{ M}\).
The pOH then uses this concentration:\(\text{pOH} = -\log(0.004495) \approx 2.35\).To find the corresponding pH, subtract the pOH from 14:
  • The result is \(\text{pH} = 14 - 2.35 = 11.65\).
Understanding pOH helps manage the basicity in solutions, confirming that it operates as the opposite of pH. This knowledge assists in precisely manipulating chemical environments.

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