Problem 107 - Chemistry The Molecular Science

Question

Dimethylglyoxime (DMG) reacts with nickel(II) ion in aqueous solution to form a bright red compound. However, DMG is insoluble in water. To get it into aqueous solution where it can encounter \(\mathrm{Ni}^{2+}\) ions, it must first be dissolved in a suitable solvent, such as ethanol. Suppose you dissolve \(45.0 \mathrm{~g} \mathrm{DMG}\left(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{~N}_{2} \mathrm{O}_{2}\right)\) in \(500 . \mathrm{mL}\) ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} ;\right.\) density \(\left.=0.7893 \mathrm{~g} / \mathrm{mL}\right) .\) Determine the molality and weight percent of DMG in this solution.

Step-by-Step Solution

Answer

Molality is 0.9815 mol/kg and weight percent is 10.24%.

Step 1: Convert Ethanol Volume to Mass

To find the total mass of the solvent (ethanol), use its volume and density. Given volume, \( V = 500 \, \text{mL} \) and density, \( \rho = 0.7893 \, \text{g/mL} \), mass \( m_{\text{ethanol}} = V \times \rho = 500 \, \text{mL} \times 0.7893 \, \text{g/mL} = 394.65 \, \text{g} \).

Step 2: Calculate Moles of DMG

Determine the moles of DMG using its molar mass. The formula for DMG is \( \text{C}_4\text{H}_8\text{N}_2\text{O}_2 \). Calculate the molar mass: \(4 \times 12.01 + 8 \times 1.01 + 2 \times 14.01 + 2 \times 16.00 = 116.12 \, \text{g/mol} \). Then, find moles using \( 45.0 \, \text{g} \) of DMG: \( \frac{45.0}{116.12} = 0.3873 \, \text{mol} \).

Step 3: Determine Molality of DMG

Molality (\( m \)) is defined as moles of solute per kilogram of solvent. Using the mass of ethanol calculated previously, \( 394.65 \, \text{g} = 0.39465 \, \text{kg} \), calculate molality: \( m = \frac{0.3873 \, \text{mol}}{0.39465 \, \text{kg}} = 0.9815 \, \text{mol/kg} \).

Step 4: Calculate Weight Percent of DMG

Weight percent is the mass of the solute divided by the total mass of the solution, multiplied by 100. The total mass of the solution is \( 45.0 \, \text{g} + 394.65 \, \text{g} = 439.65 \, \text{g} \). The weight percent is \( \frac{45.0}{439.65} \times 100 \approx 10.24\% \).

Key Concepts

Molality

Molality is a way of expressing the concentration of a solution. It tells us how many moles of a solute are present per kilogram of solvent. One of the key advantages of using molality is that it doesn't change with temperature, unlike volume-based measurements like molarity. This is because mass remains constant regardless of temperature fluctuations.
To calculate molality, you first need to know two things: the number of moles of solute and the mass of the solvent in kilograms. In a problem like the one given, we find the molality of DMG in an ethanol solution by using the formula:

• Number of moles of DMG = 0.3873 mol (calculated from the given mass and molar mass).
• Mass of ethanol = 0.39465 kg (converted from grams using the density).

The molality is then calculated by the formula: \( m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \). Hence, \( m = \frac{0.3873}{0.39465} = 0.9815 \, \text{mol/kg} \). This gives the concentration of DMG in the ethanol solution, showing that there are about 0.9815 moles of DMG per kilogram of ethanol.

Weight Percent

Weight percent, sometimes called mass percent, is another method to express concentration. It indicates what fraction of the total solution is made up by the solute, expressed as a percentage.
To calculate the weight percent, you divide the mass of the solute by the total mass of the entire solution and then multiply by 100. The steps are simple and involve:

• Mass of DMG, the solute = 45.0 g.
• Total mass of the solution = Mass of DMG + Mass of ethanol = 45.0 g + 394.65 g = 439.65 g.

The weight percent is calculated as follows: \( \text{Weight Percent} = \frac{\text{mass of solute}}{\text{total mass of solution}} \times 100 \). For our example, this is \( \frac{45.0}{439.65} \times 100 \approx 10.24\% \). This means the solution consists of approximately 10.24% DMG by mass, indicating the concentration of DMG within the ethanol solution.

Ethanol as Solvent

Ethanol often serves as a solvent due to its unique properties. It's a common choice in both laboratory and industrial applications because it is good at dissolving a wide range of substances.
Ethanol exhibits several characteristics that make it suitable as a solvent:

• **Miscibility with Water**: Ethanol can mix well with water, which is advantageous in reactions involving aqueous solutions.
• **Polarity**: As a polar solvent, ethanol can dissolve many ionic and polar substances, which includes organic compounds like DMG.
• **Volatility**: It has a relatively low boiling point, allowing for easy removal from solutions if needed by simple heating.

In the context of the problem, DMG is insoluble in water; hence, ethanol is used to dissolve it before reacting with nickel(II) ions. This allows DMG to be present in an aqueous solution indirectly, as ethanol helps bridge the solubility gap. Understanding why ethanol is chosen as a solvent highlights its versatility and effectiveness in solving solubility issues in chemical reactions.