Question

The number of \(\mathrm{H}^{+}\) ions present in \(1 \mathrm{~cm}^{3}\) of a solution whose \(\mathrm{pH}\) is 10 is: (a) \(10^{-10}\) (b) \(10^{-13}\) (c) \(6.02 \times 10^{10}\) (d) \(6.02 \times 10^{13}\)

Short answer

The number of \(\mathrm{H}^+\) ions is \(6.02 \times 10^{10}\).

Step-by-step solution

Understanding pH Definition

The pH of a solution is a measure of its acidity or basicity. It is defined as the negative logarithm of the hydrogen ion concentration: \( \text{pH} = - \log[\text{H}^+] \). In this problem, the pH is given as 10.

Calculating hydrogen ion concentration

Using the definition of pH, we can calculate the concentration of \( \mathrm{H}^+ \) ions as follows: \( [\mathrm{H}^+] = 10^{-\text{pH}} = 10^{-10} \text{ moles per liter} \).

Converting volume from cubic centimeters to liters

Since the concentration is given in moles per liter, we need to convert the volume from cubic centimeters to liters. There are 1000 cubic centimeters in a liter, so \( 1 \text{ cm}^3 = 10^{-3} \text{ liters} \).

Calculating total number of \(\mathrm{H}^+\) ions

Now, we calculate the number of \(\mathrm{H}^+\) ions. Multiply the concentration \( 10^{-10} \text{ moles/liter} \) by the volume in liters \( 10^{-3} \text{ liters} \), to get \( 10^{-13} \text{ moles} \). Then, use Avogadro’s number \( 6.02 \times 10^{23} \) to find the actual number of ions: \[ \text{Number of ions} = 10^{-13} \text{ moles} \times 6.02 \times 10^{23} \text{ ions/mole} = 6.02 \times 10^{10} \text{ ions} \].

Key concepts

pH calculation

The pH value of a solution is a simple way to express how acidic or basic it is. We can determine the acidity by using the formula: \( \text{pH} = - \log[\text{H}^+] \). Here, \([\text{H}^+]\) represents the concentration of hydrogen ions in the solution. For example, if a solution has a pH of 10, it indicates that the solution is quite basic. The negative logarithmic scale means that lower pH corresponds to higher acidity. To find the hydrogen ion concentration, you can rearrange the pH formula: - \([\text{H}^+] = 10^{-\text{pH}}\)Thus, for a pH of 10, the hydrogen ion concentration is \(10^{-10} \text{ moles/liter}\). This mathematically defines how we can convert the pH to a tangible concentration measure.

hydrogen ion concentration

Hydrogen ion concentration \([\text{H}^+]\) is a crucial factor in evaluating the acidity of a solution. The concentration is typically expressed in moles per liter, indicating how many moles of hydrogen ions are present in one liter of the solution.Given that pH can be expressed as \([\text{H}^+] = 10^{-\text{pH}}\), it offers a straightforward way to calculate \([\text{H}^+]\) when the pH is known. For instance, given a solution with a pH of 10, we find:- The hydrogen ion concentration is \(10^{-10} \text{ moles/liter}\).By understanding the hydrogen ion concentration, we gain insight into the solution's chemical properties, allowing us to predict reactions and behaviors effectively.

Avogadro's number

Avogadro's number is a fundamental constant in chemistry, represented as \(6.02 \times 10^{23}\). It defines the number of molecules or atoms in one mole of a substance, providing a bridge between the microscopic world of atoms and the macroscopic world we observe.Using Avogadro's number, you can convert the moles of a substance into actual numbers of particles, such as ions or molecules. For example, in a pH exercise, after calculating the hydrogen ion concentration in moles, Avogadro's number helps find the actual number of ions.Here's how it's applied: - Compute the moles of \(\text{H}^+\) ions for the given volume.- Use Avogadro's number to find the number of ions: Multiply moles by \(6.02 \times 10^{23}\).In summary, Avogadro's number is key to translating between moles and particles, which is pivotal in understanding and predicting chemical behaviors.