To find the number of moles of SO4^2- in 100 grams of the complex, you need to use the given information and apply the concept of stoichiometry.
1. Start by converting the mass percent of Ni^2+ in the complex to the mass of Ni^2+ in 100 grams of the complex. Since the mass percent of Ni^2+ in the complex is 27.86%, you can calculate the mass of Ni^2+ as follows:
Mass of Ni^2+ = (27.86/100) * 100 grams = 27.86 grams
2. Use the molar mass of Ni^2+ (which you can find on the periodic table) to convert the mass of Ni^2+ to moles. The molar mass of Ni^2+ is 58.69 g/mol.
Moles of Ni^2+ = Mass of Ni^2+ / Molar mass of Ni^2+ = 27.86 grams / 58.69 g/mol = 0.4748 moles
3. Use the molarity of Ni^2+ in the unknown sample to find the volume of the sample required to obtain 0.475 moles of Ni^2+. The equation to use is:
Moles = Molarity * Volume
Rearrange the equation to solve for volume:
Volume = Moles / Molarity = 0.475 moles / 0.0647 M = 7.34 liters (rounding to 3 decimal places)
4. Convert the volume of the sample from liters to milliliters by multiplying by 1000. This is necessary because 1 liter is equal to 1000 milliliters.
Volume = 7.34 liters * 1000 = 7340 milliliters
5. Based on the given information, the complex contains [Ni(en)(H2O)]^2+ * SO4^2- * H2O. The charge of the complex is zero, so the sum of the charges on all individual ions must be zero. The charge on the nickel ion (Ni^2+) is 2+, and both the en ligand and water ligands have a charge of zero. Therefore, the total charge contributed by the SO4^2- ion must be 2- to balance the charge.
6. Since the charge on the SO4^2- ion is 2-, the number of moles of SO4^2- in the complex is equal to the number of moles of Ni^2+ in the complex. Therefore, the number of moles of SO4^2- in 100 grams of the complex is also 0.4748 moles.
To calculate the mass percent of SO4^2- in the complex, use the formula:
Mass percent of SO4^2- = (mass of SO4^2- / mass of the complex) * 100%
Since you have already calculated the moles of SO4^2- and the molar mass of SO4^2-, you can calculate the mass of SO4^2- as follows:
Mass of SO4^2- = Moles of SO4^2- * Molar mass of SO4^2- = 0.4748 moles * (32.06 g/mol + 4 * 16.00 g/mol) = 22.25 grams (rounded to 2 decimal places)
Finally, calculate the mass percent of SO4^2-:
Mass percent of SO4^2- = (22.25 grams / 100 grams) * 100% = 22.25%
Therefore, there are 0.4748 moles of SO4^2- in 100 grams of the complex, and the mass percent of SO4^2- in the complex is approximately 22.25%.