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Q1.28:
Calculate the mass percentage of aspirin ((C_{9}H_{8}O_{4})) in acetonitrile ((CH_{3}CN)) when 6.5 g of (C_{9}H_{8}O_{4}) is dissolved in 450 g of (CH_{3}CN).

Solution :

Step 1: Identifying Given Variables

To determine the mass percentage of the solute in the solution, we identify the following components from the problem statement:

  • Mass of solute (aspirin, $C_9H_8O_4$): $m_{solute} = 6.5\text{ g}$
  • Mass of solvent (acetonitrile, $CH_3CN$): $m_{solvent} = 450\text{ g}$

Step 2: Calculating Total Mass of the Solution

The total mass of the solution ($m_{solution}$) is defined as the sum of the mass of the solute and the mass of the solvent [Per the principle of additive mass in non-reacting mixtures]:

$m_{solution} = m_{solute} + m_{solvent}$

$m_{solution} = 6.5\text{ g} + 450\text{ g} = 456.5\text{ g}$

Step 3: Defining the Mass Percentage Formula

The mass percentage ($\text{w/w}\%$) of a component is defined as the mass of that component divided by the total mass of the solution, multiplied by $100$ [Standard Definition of Mass Percent]:

$\text{Mass Percentage} = \left( \frac{\text{mass of solute}}{\text{total mass of solution}} \right) \times 100$

Step 4: Algebraic Substitution and Execution

Substituting the values obtained in Step 1 and Step 2 into the formula:

$\text{Mass Percentage} = \left( \frac{6.5\text{ g}}{456.5\text{ g}} \right) \times 100$

Calculating the quotient:

$\frac{6.5}{456.5} \approx 0.01423877$

Multiplying by $100$ to express as a percentage:

$0.01423877 \times 100 = 1.423877\%$

Step 5: Significant Figures Adjustment

Given that the mass of the solute ($6.5\text{ g}$) contains two significant figures, we round the final result to two significant figures to maintain numerical precision standards [Per the Rules of Significant Figures in division].

$1.423877\% \approx 1.4\%$

Visual Representation of Composition

Aspirin (1.4%) Acetonitrile (98.6%)

Final Solution: The mass percentage of aspirin in the acetonitrile solution is 1.4%.


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