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Chapter 10: Problem 1

A solution is prepared by dissolving \(12.15 \mathrm{~g}\) of nickel(II) nitrate in \(175 \mathrm{~mL}\) of water \((d=1.00 \mathrm{~g} / \mathrm{mL})\). Calculate (a) the mass percent of nickel(II) nitrate in the solution. (b) the mole fraction of nickel(II) ions in the solution.

Short Answer

Expert verified
Answer: (a) The mass percent of nickel(II) nitrate in the solution is 6.49%. (b) The mole fraction of nickel(II) ions in the solution is 0.006827.

Step by step solution

01

Determine the molar mass of nickel(II) nitrate (Ni(NO3)2) and the number of moles of Ni(NO3)2 in the solution

First, we’ll need to find the molar mass of Ni(NO3)2, which can be calculated by adding the molar mass of each element: Ni = 58.69 g/mol N = 14.01 g/mol O = 16.00 g/mol Molar mass of Ni(NO3)2 = 58.69 + 2 * (14.01 + 3 * 16.00) = 182.03 g/mol Now, we will find the number of moles of nickel(II) nitrate in the solution: moles = mass / molar mass moles = 12.15 g / 182.03 g/mol = 0.06676 mol
02

Calculate the total mass of the solution

To calculate the total mass of the solution, we'll need to determine the mass of 175 mL of water: mass_water = volume * density = 175 mL * 1.00 g/mL = 175 g Now we can find the total mass of the solution by adding the masses of nickel(II) nitrate and water: mass_solution = mass_Ni(NO3)2 + mass_water = 12.15 g + 175 g = 187.15 g
03

Calculate the mass percent of nickel(II) nitrate in the solution

The mass percent is the mass of the solute (nickel(II) nitrate) divided by the total mass of the solution, multiplied by 100: mass percent = (mass_Ni(NO3)2 / mass_solution) * 100 = (12.15 g / 187.15 g) * 100 = 6.49%
04

Calculate the number of moles of nickel(II) ions (Ni2+) in the solution

In each mole of Ni(NO3)2, there is one mole of Ni2+ ions. Therefore, the number of moles of Ni2+ ions is equal to the number of moles of Ni(NO3)2: moles_Ni2+ = moles_Ni(NO3)2 = 0.06676 mol
05

Calculate the mole fraction of nickel(II) ions in the solution

We will now calculate the total number of moles in the solution by adding the moles of Ni(NO3)2 and water: moles_water = mass_water / molar_mass_water = 175 g / 18.015 g/mol = 9.716 mol total_moles = moles_Ni(NO3)2 + moles_water = 0.06676 mol + 9.716 mol = 9.78276 mol Finally, we can determine the mole fraction of nickel(II) ions in the solution: mole_fraction_Ni2+ = moles_Ni2+ / total_moles = 0.06676 mol / 9.78276 mol = 0.006827 So, the results are as follows: (a) The mass percent of nickel(II) nitrate in the solution is 6.49%. (b) The mole fraction of nickel(II) ions in the solution is 0.006827.

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