Question

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

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

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

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

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%

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

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.

Key concepts

Mole Fraction

Mole fraction is a way to express the concentration of a component in a mixture. It refers to the ratio of the number of moles of one component to the total number of moles in the solution. This measurement provides a dimensionless number, which means it does not have a unit like grams or liters.

In the specific exercise about nickel(II) nitrate, the mole fraction of nickel ions in the solution is calculated by first determining the number of moles for both the solute and the solvent. For nickel(II) nitrate, the number of moles was found to be 0.06676 mol. To find the total moles in the solution, we also considered the moles of water, which was 9.716 mol.

The mole fraction of nickel(II) ions is then calculated as follows:

• The total moles equals 9.78276 mol (sum of moles of nickel(II) nitrate and water).
• Using the formula for mole fraction: \( ext{Mole Fraction of Ni}^{2+} = \frac{0.06676 \text{ mol}}{9.78276 \text{ mol}} \approx 0.006827 \).

Thus, the mole fraction provides insight into the composition of the solution in a very straightforward manner.

Mass Percent

Mass percent is another way to measure concentration, and it indicates the mass of the solute as a percentage of the total mass of the solution. In this exercise, mass percent allows us to understand how much of the solution's weight is attributed to nickel(II) nitrate.

The calculation begins by finding the total mass of the solution, which includes both the mass of the nickel(II) nitrate (12.15 g) and the water (175 g). The total mass came out to be 187.15 g.

Following this, the mass percent can be derived using the following formula:

• Mass percent = \( \frac{\text{mass of Ni(NO}_3{)_2}}{\text{total mass of solution}} \times 100 \)
• Plugging in the values: \( \text{Mass percent} = (\frac{12.15}{187.15}) \times 100 \approx 6.49\% \)

This representation is beneficial in contexts where understanding the proportion of a particular substance in the entire solution is necessary, such as in chemistry labs or industrial applications.

Nickel(II) Nitrate

Nickel(II) nitrate is an inorganic chemical compound with the formula \( ext{Ni(NO}_3 ext{)}_2 \). It features prominently in chemical solutions, acting as the solute in this example.

Understanding the properties of nickel(II) nitrate is important for various applications. It is typically used in electroplating, as a precursor to nickel catalysts, or in chemical synthesis.

For any calculations involving nickel(II) nitrate, knowing its molar mass is crucial. In the exercise, it was calculated to be 182.03 g/mol, derived from the constituent elements:

• Nickel (Ni) has a molar mass of 58.69 g/mol.
• Nitrogen (N) has a molar mass of 14.01 g/mol.
• Oxygen (O) has a molar mass of 16.00 g/mol.

By combining these, the molar mass helps in determining both the number of moles of the compound present in the solution and subsequently, other concentration units like mass percent and mole fraction.