A 97.0 mg sample of Red 40 dye was dissolved and diluted to a final volume of 1.50 L with deionized water. What is the concentration of the Red 40 dye solution in ppm?

To calculate the concentration of Red 40 dye in parts per million (ppm), we use the fact that 1 ppm is equivalent to 1 milligram of substance in 1 liter of solution.

The steps for calculating the concentration are as follows:

1. Convert the mass of the Red 40 dye from milligrams to grams, because ppm is based on grams of solute per liters of solution. Make sure the mass and volume are consistent with each other. \( \text{97.0 mg} = \text{97.0} \times 10^{-3} \text{g} \) (since there are 1000 mg in a gram).

2. Use the volume of the solution to determine ppm. The volume given is 1.50 L.

3. Calculate the ppm concentration using the formula: \( \text{ppm} = \frac{\text{mass of solute (g)}}{\text{volume of solution (L)}} \times 10^6 \)

Plugging the values into the formula gives: \( \text{ppm} = \frac{0.097\, \text{g}}{1.50\, \text{L}} \times 10^6 \)

4. Perform the calculation: \( \text{ppm} = \frac{0.097}{1.50} \times 10^6 \) \( \text{ppm} = 0.0647 \times 10^6 \) \( \text{ppm} = 64.7 \text{ ppm} \)

So, the concentration of Red 40 dye in the solution is 64.7 ppm.