Question

What will be the \(\mathrm{pH}\) of a soft drink if hydrogen ion concentration in sample is \(3.8 \times 10^{-3} \mathrm{M?}\) (a) \(3.8\) (b) \(5.04\) (c) \(2.42\) (d) \(9.2\)

Short answer

The pH of the soft drink is 2.42.

Step-by-step solution

Understanding the pH scale

The pH of a solution is a measure of the acidity or basicity of the solution. It is defined as the negative logarithm to base 10 of the hydrogen ion concentration. The formula to calculate pH is given by pH = -log10[H+], where [H+] is the concentration of hydrogen ions in moles per liter (M).

Using the given hydrogen ion concentration

In this case, the hydrogen ion concentration given for the soft drink is [H+] = 3.8 x 10^-3 M. We will plug this value into the pH formula.

Calculating the pH

Using the formula pH = -log10[H+], we substitute the given value for [H+] to get pH = -log10(3.8 x 10^-3).

Solving the equation

Calculate the logarithm of the hydrogen ion concentration: pH = -log10(3.8 x 10^-3). Using a calculator, we find pH = -(-2.42) = 2.42.

Key concepts

pH scale

The pH scale is a numerical scale used to specify the acidity or basicity of an aqueous solution. It typically ranges from 0 to 14, with 7 being neutral. A pH less than 7 indicates an acidic solution, while a pH greater than 7 indicates a basic (or alkaline) solution. The lower the pH, the higher the acidity, and conversely, the higher the pH, the higher the basicity.

For educational clarity, one can visualize the pH scale as a spectrum with acids on one end, bases on the other, and pure water right in the middle.

hydrogen ion concentration

Hydrogen ion concentration refers to the amount of hydrogen ions present in a solution. It is denoted by [H⁺], measured in moles per liter (M). These ions are actually protons, as a hydrogen atom loses its electron to become a hydrogen ion. In chemistry, the concentration of hydrogen ions in a solution is critical because it determines the solution's pH. A higher concentration of hydrogen ions (lower pH) implies more acidity, while a lower concentration (higher pH) suggests basicity.

When we discuss a soft drink with a hydrogen ion concentration of \(3.8 \times 10^{-3} \mathrm{M}\), we're examining how its acidity relates to that specific concentration.

acidity and basicity

Acidity and basicity are fundamental concepts in chemistry that describe the nature of a solution. Acids are substances that can donate hydrogen ions in an aqueous solution, while bases accept hydrogen ions. Acids tend to taste sour and can corrode metals, whereas bases tend to taste bitter and can feel slippery. The terms acidity and basicity also correlate to the concentration of hydrogen ions: the more hydrogen ions present, the more acidic the solution is.

It's significant to observe here, in the case of the soft drink from our exercise, that its acidic nature is due to the hydrogen ions released in the beverage.

logarithms in chemistry

Logarithms are an essential tool in chemistry, prominently used in the calculation of pH. The logarithmic function allows us to express the wide range of hydrogen ion concentrations in aqueous solutions in a manageable scale, the pH scale. The pH is calculated using the negative logarithm to base 10 of the hydrogen ion concentration (\(-\log[H^{+}]\)).

To compute the pH from a given hydrogen ion concentration, one needs to understand how to operate the logarithmic function. This mathematical concept simplifies the representation of very large or very small numbers, making calculations more practical for chemists and students alike. In the case of our soft drink, the equation \(\text{pH} = -\log(3.8 \times 10^{-3})\) is used to determine its acidity level.