Question

Determine the \(\mathrm{H}_{3} \mathrm{O}^{+}\)concentration in the following solutions. Identify each solution as acidic, basic, or neutral. (a) orange juice, \(\mathrm{pH}=3.50\) (b) lye, \(4.0 \%\) sodium hydroxide, \(\mathrm{pH}=14.00\) (c) saliva, \(\mathrm{pH}=7.00\)

Short answer

The concentration of H3O+ in orange juice is 3.16 x 10^-4 M and is an acidic solution, the concentration of H3O+ in lye is 1.0 x 10^-14 M and is a basic solution, and the concentration of H3O+ in saliva is 1.0 x 10^-7 M and is a neutral solution.

Step-by-step solution

Recall the formula for pH

The pH of a solution is calculated using the formula: pH = -log[H3O+]. Where H3O+ is the hydronium ion concentration. Therefore, to get the concentrations of H3O+ in solutions, the formula has to be rearranged as: [H3O+] = 10^(-pH).

Calculate the concentration of H3O+ in orange juice

The pH of the orange juice is given as 3.50. Apply the formula, [H3O+] = 10^(-3.50) which equals to 3.16 x 10^-4 M.

Identify the solution

Since the pH of orange juice is less than 7, it is considered an acidic solution.

Calculate the concentration of H3O+ in lye

The pH of the lye is given as 14.00. Apply the formula, [H3O+] = 10^(-14.00) which equals to 1.0 x 10^-14 M.

Identify the solution

Since the pH of lye is greater than 7, it is considered a basic solution.

Calculate the concentration of H3O+ in saliva

The pH of the saliva is given as 7.00. Apply the formula, [H3O+] = 10^(-7.00) which equals to 1.0 x 10^-7 M.

Identify the solution

Since the pH of saliva is 7, it is considered a neutral solution.

Key concepts

pH scale

The pH scale is an essential concept in chemistry that measures the acidity or basicity of a solution. It is a logarithmic scale ranging from 0 to 14, where a pH value of 7 is considered neutral, values below 7 are acidic, and values above 7 are basic or alkaline.

The pH scale is directly related to the concentration of hydronium ions \(\mathrm{H}_3\mathrm{O}^+\) in a solution. Each unit change in the pH value represents a tenfold change in the hydronium ion concentration. In other words, a solution with a pH of 6 is ten times more acidic than a solution with a pH of 7.

Understanding the pH value of a substance can predict its corrosive behavior, its suitability for plant growth, or even its edibility. Products we use daily, such as cleaning agents, foods, and personal care items, often have their effectiveness and safety determined by their pH levels.

Hydronium Ion Concentration

The concentration of hydronium ions \(\mathrm{H}_3\mathrm{O}^+\) determines the acidity of a solution. It's quantified in moles per liter \(M\). The relationship between pH and hydronium ion concentration is given by the formula \(\mathrm{pH} = -\log[\mathrm{H}_3\mathrm{O}^+]\).

To find the hydronium ion concentration from a known pH, one would use the inverse logarithmic operation: \[\mathrm{[H}_3\mathrm{O}^+] = 10^{-\mathrm{pH}}\]. This means that for a pH of 3.50, as in the case of the orange juice from the exercise, the hydronium concentration would be \(3.16 \times 10^{-4} M\), indicating a highly acidic environment.

A better understanding of this concept allows chemists to calculate the precise levels of acidity in substances, which is crucial in industries like pharmaceuticals and agriculture where pH balance is key for product effectiveness and safety.

Acidic and Basic Solutions

Solutions can be classified as acidic, basic (alkaline), or neutral based on their pH values. Acidic solutions have a pH less than 7 and higher concentrations of hydronium ions. In contrast, basic solutions have a pH greater than 7 and lower concentrations of hydronium ions but higher concentrations of hydroxide ions \(\mathrm{OH}^-\).

For example, from the exercise, orange juice with a pH of 3.50 is acidic. Lye, with its high pH of 14, is highly basic, often used in cleaning products and requires careful handling. Saliva, with a pH of approximately 7, is neutral, making it neither harmful nor corrosive, thus safe within the human body.

Knowing whether a solution is acidic or basic is vital in various applications. For instance, maintaining the correct pH is vital for aquatic life in a fish tank, for the action of enzymes in biological systems, or for the quality of soil in agriculture. Acid-base indicators, pH metering devices, and universal indicator papers are tools used to measure the pH level and help in identifying the nature of solutions.