Problem 1 - Chemistry and Chemical Reactivity

Question

Suppose you dissolve \(2.56 \mathrm{g}\) of succinic acid, \(\mathrm{C}_{2} \mathrm{H}_{4}\left(\mathrm{CO}_{2} \mathrm{H}\right)_{2},\) in \(500 .\) mL of water. Assuming that the density of water is \(1.00 \mathrm{g} / \mathrm{cm}^{3},\) calculate the molality, mole fraction, and weight percent of acid in the solution.

Step-by-Step Solution

Answer

Molality is 0.04336 mol/kg, mole fraction is 0.00078, and weight percent is 0.509%.

Step 1: Calculate the Moles of Succinic Acid

First, determine the molar mass of succinic acid, \( \text{C}_2\text{H}_4(\text{CO}_2\text{H})_2 \), by calculating as follows: \( 2(12.01) + 4(1.01) + 4(16.00) + 2(1.01) = 118.09 \) g/mol. Next, find the moles of succinic acid by dividing the mass by the molar mass: \( \frac{2.56 \, \text{g}}{118.09 \, \text{g/mol}} = 0.02168 \, \text{mol} \).

Step 2: Calculate Molality of the Solution

The definition of molality (\( m \)) is moles of solute per kilogram of solvent. Since the solvent (water) has a mass of \( 500 \text{ mL} \times 1.00 \text{ g/mL} = 500 \text{ g} = 0.500 \text{ kg} \), the molality is calculated as: \( \frac{0.02168 \, \text{mol}}{0.500 \, \text{kg}} = 0.04336 \, \text{mol/kg} \).

Step 3: Calculate Mole Fraction of Succinic Acid

First, calculate the moles of water: \( \frac{500 \, \text{g}}{18.015 \, \text{g/mol}} = 27.76 \, \text{mol} \). The mole fraction formula is \( X = \frac{\text{moles of solute}}{\text{moles of solute} + \text{moles of solvent}} \). Thus, \( X = \frac{0.02168}{0.02168 + 27.76} = 0.00078 \).

Step 4: Determine the Weight Percent of Succinic Acid

Weight percent (\( \%w/w \)) is found using \( \frac{\text{mass of solute}}{\text{total mass of solution}} \times 100 \% \). The total mass of solution is \( 2.56 \, \text{g} + 500 \, \text{g} = 502.56 \, \text{g} \). Thus, the weight percent is \( \frac{2.56}{502.56} \times 100 = 0.509 \% \).

Key Concepts

Understanding Molality

Molality is a way to express the concentration of a solution. It's particularly useful in situations where temperature changes occur. Molality is defined as the number of moles of solute per kilogram of solvent. Unlike molarity, which can be affected by temperature (since volume can expand or contract), molality remains constant.

For example, consider you dissolve succinic acid in water. To find the molality, you first need the moles of the solute (here, succinic acid). You then divide this by the mass of the solvent in kilograms.

• Benefits of Molality: It's not affected by temperature fluctuations.
• Usage: Common in colligative properties like boiling point elevation or freezing point depression.

Exploring Mole Fraction

Mole fraction is another way of expressing concentration. It's a ratio of the number of moles of a component to the total number of moles in the solution. The mole fraction is dimensionless, meaning it has no units. When calculating mole fraction, it's important to account for both the solute and the solvent. For instance, in our succinic acid solution, the mole fraction involves calculating the moles of succinic acid and water. By dividing the moles of succinic acid by the total moles, we get its mole fraction.

• Insightfulness: Helps in understanding the ratio of components.
• Use Case: Fundamental in thermodynamic calculations.

The Simplicity of Weight Percent

Weight percent is a straightforward method to describe how much of a solute is present in a certain mass of a solution. It is expressed as a percentage and calculated by the formula: \[ \text{Weight percent} = \left(\frac{\text{mass of solute}}{\text{total mass of solution}} \right) \times 100 \% \]In our example with succinic acid, by dividing its mass by the total mass of the solution and then multiplying by 100, we obtain the weight percent. This method is intuitive because it relates the mass directly, making it easy to interpret in everyday scenarios.

• Advantages: Easy to measure and understand.
• Common Use: Labels on consumer products like "sugar solution" or "bleach percentage."