The question asks us to determine the concentration of a Gallic acid solution in ethanol in parts per million (ppm), given the mass of the solute and the volume of the solution.

Understanding Parts Per Million (ppm)

Parts per million (ppm) is a way of expressing very dilute concentrations of substances. It represents the number of parts of solute per million parts of the solution. For solutions, especially dilute aqueous solutions, ppm is often interpreted in different ways depending on whether it's mass/mass (w/w), mass/volume (w/v), or volume/volume (v/v).

In this case, the concentration is given as weight per volume (w/v), with the mass of Gallic acid in mg and the volume of ethanol in mL. A common interpretation for ppm (w/v) for dilute solutions is:

• 1 ppm is equivalent to 1 milligram of solute per litre of solution (1 mg/L).
• Alternatively, 1 ppm can be considered 1 microgram of solute per millilitre of solution (1 µg/mL), since 1 mg = 1000 µg and 1 L = 1000 mL.

We will use the first definition (1 ppm = 1 mg/L) as it involves a direct conversion of the given units.

Calculating Gallic Acid Concentration in ppm

We are given:

• Mass of Gallic acid = 0.05 mg
• Volume of ethanol solution = 250 mL

First, let's convert the volume from millilitres (mL) to litres (L), as the standard unit for volume in the mg/L definition of ppm is litres. There are 1000 mL in 1 L.

Volume in L = Volume in mL ÷ 1000

Volume in L = \( \frac{250 \text{ mL}}{1000 \text{ mL/L}} = 0.250 \text{ L} \)

Now, we can calculate the concentration in milligrams per litre (mg/L).

Concentration (mg/L) = \( \frac{\text{Mass of solute (mg)}}{\text{Volume of solution (L)}} \)

Concentration (mg/L) = \( \frac{0.05 \text{ mg}}{0.250 \text{ L}} \)

Let's perform the division:

\( \frac{0.05}{0.250} = \frac{50}{250} = \frac{5}{25} = \frac{1}{5} = 0.2 \)

So, the concentration is 0.2 mg/L.

As established, 1 mg/L is equivalent to 1 ppm. Therefore, a concentration of 0.2 mg/L is equivalent to 0.2 ppm.

The concentration of the Gallic acid solution in ppm is 0.2 ppm.