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

Question: Calculate the mass percent and mole fraction of nickel(II) nitrate in a solution containing 12.15 g of nickel(II) nitrate and 175 mL of water. Answer: The mass percent of nickel(II) nitrate in the solution is 6.49%, and the mole fraction of nickel(II) ions is 0.00680.

Step-by-step solution

Find the mass of the solute and solvent

To find the mass percent, we first need the mass of nickel(II) nitrate (solute) and the mass of water (solvent). The mass of nickel(II) nitrate is already given as \(12.15 \mathrm{~g}\). The volume of water is given as \(175 \mathrm{~mL}\). To find the mass of water, we will use the formula: Mass = Volume × Density The density of water is given as \(1.00 \mathrm{~g}/\mathrm{mL}\). Therefore, the mass of water is: Mass of water = \(175 \mathrm{~mL} \times 1.00 \mathrm{~g}/\mathrm{mL} = 175 \mathrm{~g}\)

Calculate the mass percent of nickel(II) nitrate

Now that we have the mass of the solute and solvent, we can use the mass percent formula: Mass percent = \(\frac{\text{mass of solute}}{(\text{mass of solute} + \text{mass of solvent})} \times 100\) Mass percent of nickel(II) nitrate = \(\frac{12.15 \mathrm{~g}}{(12.15 \mathrm{~g} + 175 \mathrm{~g})} \times 100 = 6.49 \%\) Therefore, the mass percent of nickel(II) nitrate in the solution is \(6.49 \%\).

Calculate the moles of nickel(II) ions and water

To find the mole fraction, we need to find the moles of nickel(II) ions and moles of water. To find moles, use the formula: Moles = \(\frac{\text{mass}}{\text{molar mass}}\) The molar mass of nickel(II) nitrate (\(\mathrm{Ni(NO_3)_2}\)) is: \(58.69 (\mathrm{Ni}) + 2\left[14.01 (\mathrm{N}) + 3 \times 16.00 (\mathrm{O})\right] = 58.69 + 2 \times 62.01 = 182.71 \mathrm{~g/mol}\) The molar mass of water (\(\mathrm{H_2O}\)) is \(18.02 \mathrm{~g/mol}\). Moles of nickel(II) nitrate = \(\frac{12.15 \mathrm{~g}}{182.71 \mathrm{~g/mol}} = 0.0665 \mathrm{~mol}\) Moles of water = \(\frac{175 \mathrm{~g}}{18.02 \mathrm{~g/mol}} = 9.71 \mathrm{~mol}\)

Calculate the mole fraction of nickel(II) ions

Now that we have the moles of nickel(II) ions and water, we can use the mole fraction formula: Mole fraction = \(\frac{\text{moles of solute}}{(\text{moles of solute} + \text{moles of solvent})}\) Mole fraction of nickel(II) ions = \(\frac{0.0665 \mathrm{~mol}}{(0.0665 \mathrm{~mol} + 9.71 \mathrm{~mol})} = 0.00680\) Therefore, the mole fraction of nickel(II) ions in the solution is \(0.00680\).

Key concepts

Mass Percent Calculation

Understanding the concentration of a solution is a fundamental aspect of chemistry. Mass percent is one of the simplest ways to express solution concentration, defined as the mass of the solute divided by the total mass of the solution, multiplied by 100 to get the percentage.To calculate the mass percent, you need to know both the mass of the solute and the mass of the solvent. In our example, we were given a mass of nickel(II) nitrate (solute), and we calculated the mass of water (solvent) by using the product of its volume and density.
The formula used is:\[\begin{equation}Mass\text{ percent} = \left( \frac{mass\text{ of solute}}{mass\text{ of solute + mass of solvent}} \right) \times 100\end{equation}\]For clarity, if a solution is made by dissolving 12.15g of solute in 175g of solvent, the mass percent would be:\[\begin{equation}Mass\text{ percent of solute} = \left( \frac{12.15}{12.15 + 175} \right) \times 100 = 6.49\%\end{equation}\]This concept is crucial for a range of applications, from calculating drug dosages in medicine to brewing coffee at the perfect strength.

Mole Fraction Calculation

Another way to express the concentration of components in a mixture is through the mole fraction. It is a ratio of the moles of one component to the total moles of all components in the solution.To find the mole fraction, you need the number of moles of each component. Moles are calculated by dividing the mass of a substance by its molar mass. In our exercise, we dealt with nickel(II) nitrate and water. By using their respective molar masses, we derived the number of moles for each.
The formula is quite straightforward:\[\begin{equation}Mole\text{ fraction} = \frac{moles\text{ of component}}{total\text{ moles of all components}}\end{equation}\]For instance, if a solution contains 0.0665 moles of nickel(II) ions and 9.71 moles of water, the mole fraction of nickel(II) ions is:\[\begin{equation}Mole\text{ fraction of nickel(II) ions} = \frac{0.0665}{0.0665 + 9.71} = 0.00680\end{equation}\]Mole fraction is a dimensionless quantity and provides a way to understand the proportion of a particular substance within a mixture without the influence of volume or mass units.

Molarity and Molality

Two additional vital concentration terms in chemistry are molarity and molality. These two measurements, while sounding similar, have distinct differences and are used in different contexts.

Molarity

Molarity, denoted as M, is the number of moles of solute per liter of solution. It is volume-based and therefore changes with temperature as the volume of the solution expands or contracts.The formula for molarity is:\[\begin{equation}Molarity (M) = \frac{moles\text{ of solute}}{liters\text{ of solution}}\end{equation}\]

Molality

Molality, denoted as m, is the number of moles of solute per kilogram of solvent. Unlike molarity, molality is mass-based and does not change with temperature, making it useful for thermodynamic calculations.The formula for molality is:\[\begin{equation}Molality (m) = \frac{moles\text{ of solute}}{kilograms\text{ of solvent}}\end{equation}\]When working with reactions involving significant temperature changes, molality is the preferred unit since it remains constant regardless of the physical state of the solution.

Stoichiometry

Delving into the realm of chemical reactions, stoichiometry comes into play. It involves the calculation of reactants and products in a chemical reaction. It is central to the principle of conservation of mass where matter is neither created nor destroyed.Stoichiometry relies on balanced chemical equations to determine the relationship between the amounts of reactants and products. The coefficients in a balanced equation tell us the ratio of moles of each substance that react or are formed. It's like a recipe in cooking, specifying precisely how much of each ingredient you need.To perform stoichiometric calculations, one must start with a balanced chemical equation, then convert known quantities of substances into moles and use the mole ratios to find the unknown quantities.
For example, if a recipe called for 2 eggs per cake and you wanted to make 3 cakes, you would use stoichiometry to calculate that you need 6 eggs. This same principle applies to chemicals in a reaction, except we are calculating moles instead of counting eggs.