Question

A dilute aqueous solution of boric acid, \(\mathrm{H}_{3} \mathrm{BO}_{3},\) is often used as an eyewash. How would you prepare \(500.0 \mathrm{~mL}\) of a \(0.50 \%(\mathrm{~m} / \mathrm{v})\) boric acid solution?

Short answer

Measure 2.5 grams of boric acid and dissolve it in water to make 500 mL solution.

Step-by-step solution

Understand the Meaning of % (m/v)

The notation \(0.50\% (m/v)\) means that there are 0.50 grams of solute (in this case, boric acid) per 100 mL of solution.

Calculate the Required Mass of Boric Acid

Since you need to prepare 500.0 mL of solution, you have to determine how much boric acid this corresponds to. Using the % (m/v) definition, set up the proportion: \(\frac{0.50 \, \text{grams}}{100 \, \text{mL}} = \frac{x \, \text{grams}}{500.0 \, \text{mL}}\).

Solve for x

Cross-multiply and solve for \(x\): \[0.50 \, \text{grams} \times 500.0 \, \text{mL} = 100 \, \text{mL} \times x\] \[x = \frac{0.50 \times 500.0}{100} \] \[x = 2.5 \, \text{grams}\].

Measure and Mix

Measure 2.5 grams of boric acid. Mix it thoroughly in enough water to bring the total volume of the solution up to 500.0 mL.

Key concepts

Percent Concentration

When discussing solutions, percent concentration is an easy way to express how much of a solute is present in a given volume of solution. This type of concentration can be expressed in several ways, such as weight/weight and weight/volume. The particular focus here is mass/volume, represented as ",

Mass/Volume Percentage

Mass/volume percentage, or %(m/v), is a common way of describing the density of a solute within a solution. It tells us how many grams of a solute are present in 100 milliliters (mL) of solution. For example, a solution labeled as 0.50%(m/v) contains 0.50 grams of solute for every 100 mL of the solution.
 However, if the solution volume changes, such as preparing more than or less than 100 mL, we use a simple mathematical conversion to find the new amount of solute needed. For instance, a problem might state you need 500 mL of 0.50%(m/v) solution.  To solve this, adjust the amount of solute proportionally. Cross-multiply to keep the proportions consistent:

•   \,\frac{0.50 \, \text{g}}{100 \, \text{mL}} = \,\frac{x \, \text{g}}{500 \, \text{mL}}
 
• Cross-multiply and solve for \(x\) to get \(x = 2.5 \, \text{g}\).

Using this formula ensures the desired concentration in your new solution volume.

Dilute Solution

A dilute solution is one that contains a relatively small amount of solute compared to the solvent. In practical terms, this means the solute is "watered down". Dilution is often used in processes such as creating medicinal solutions, where a lower concentration is needed for safe use, like an eyewash.
  When handling any dilution, always ensure you accurately measure the solute and solvent. Begin by weighing the correct amount of solute as calculated, dissolve it in solvent, and adjust the volume as needed.   Taking these steps properly ensures safety and efficacy!

Boric Acid Solution

Boric acid is a weak acid that’s widely used for its antiseptic properties. It's commonly found in products like eyewashes, where mild antibacterial action is beneficial. When preparing a boric acid solution for use, particularly for delicate applications like an eyewash, maintaining the right concentration is vital for safety.
  Start with precisely measured amounts of boric acid, dissolving this in a specified volume of water. Use clean, distilled water to avoid introducing contaminants. This ensures that the solution is safe for sensitive applications.   Dilution and adjustment techniques are necessary to keep the solution consistent. Taking these precautions means the solution delivers the intended effects without causing irritation.