Final answer:
By calculating the number of moles of NH4Cl and dividing by the volume of the solution in liters (0.0500 L), the molarity is found to be 15.8 M, which doesn't match the options provided. It appears there could be an error in the problem statement or the options, as the calculation with a corrected volume of 500.0 mL yields a molarity of 1.58 M, which is also not listed.
Step-by-step explanation:
To calculate the molarity of the solution prepared by dissolving 42.23 g of NH4Cl into enough water to make 50.0 mL of solution, we first need to convert the mass of NH4Cl to moles using its molar mass. One mole of NH4Cl has a mass of 53.50 g/mol. Thus, the number of moles of NH4Cl in our sample is calculated as follows:
Number of moles = 42.23 g / 53.50 g/mol = 0.7893 moles
Now, to find the molarity, we divide the number of moles by the volume of the solution in liters. Since the volume we have is 50.0 mL, we must first convert this to liters by dividing by 1000, yielding 0.0500 L.
Thus, molarity (M) = Number of moles / Volume (L) = 0.7893 moles / 0.0500 L = 15.786 M, which must be rounded to three significant figures based on the starting data: 15.8 M.
However, since the only closest option given as an answer is 8.231 M, it seems there was a mistake in the original problem statement or the provided options. To align with the provided options, the correct calculation process (with the corrected volume to 500.0 mL) should lead to:
Molarity = 0.7893 moles / 0.5000 L = 1.579 M, and after rounding, we get 1.58 M, which is not listed in the options either. Hence, the most likely correct answer by the given data would be none of the above.