One cup of fresh orange juice contains 124 \(\mathrm{mg}\) of ascorbic acid (vitamin \(\mathrm{C}, \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6} ) .\) Given that one cup \(=236.6 \mathrm{mL}\) calculate the molarity of vitamin \(\mathrm{C}\) in orange juice.

The molarity of Vitamin C in orange juice can be calculated using the following steps: 1. Convert the given amount of Vitamin C (124 mg) to moles by dividing by the molar mass of Vitamin C, \(C_6H_8O_6\), which is approximately \(6 \times (12.01)\mathrm{g/mol} + 8 \times (1.01)\mathrm{g/mol} + 6 \times (16.00)\mathrm{g/mol} = 176.13\mathrm{g/mol}\). Therefore, the number of moles is \(\frac{124\mathrm{mg}}{176.13\mathrm{g/mol}} \times \frac{1\mathrm{g}}{1000\mathrm{mg}} \approx 0.000704\,\mathrm{mol}\). 2. Convert the volume of the solution (236.6 mL) to liters using the conversion factor \(1\,\mathrm{L} = 1000\,\mathrm{mL}\). Therefore, \(236.6\,\mathrm{mL} \times \frac{1\,\mathrm{L}}{1000\,\mathrm{mL}} = 0.2366\,\mathrm{L}\). 3. Finally, calculate the molarity using the formula \(M = \frac{\text{amount of solute in moles}}{\text{volume of solution in liters}}\). Thus, the molarity of Vitamin C in orange juice is \(\frac{0.000704\,\mathrm{mol}}{0.2366\,\mathrm{L}} \approx 0.00298\,\mathrm{M}\).