What is the percent Na₂CO₃ by mass in a 1.92 molal aqueous solution? A)0.160% B)16.9% C)99.5% D)20.4% E)19.2%

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The percent by mass ($w/w\% $) of a solution can be calculated using the formula: $$ \text{\% by mass} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100\% $$ For a molal solution, molality ($m$) is defined as moles of solute per kilogram of solvent. Given a 1.92 molal solution, we have 1.92 moles of NaCl (sodium chloride) per 1 kg (or 1000 g) of water. The molar mass of NaCl is approximately 58.44 g/mol (Na = 22.99, Cl = 35.45), so the mass of NaCl in this solution is: $$ 1.92 \, \text{mol} \times 58.44 \, \text{g/mol} = 112.2 \, \text{g} $$ The total mass of the solution is the mass of the solute plus the mass of the solvent: $$ 112.2 \, \text{g} (\text{NaCl}) + 1000 \, \text{g} (\text{water}) = 1112.2 \, \text{g} $$ Therefore, the percent by mass of NaCl in the solution is: $$ \frac{112.2 \, \text{g}}{1112.2 \, \text{g}} \times 100\% \approx 10.1\% $$ However, none of the provided options match this calculation. It seems there might have been a mistake in the calculation or interpretation of the question. Given the options and the typical approach to such a problem, the correct answer would be based on the correct application of the formula and the given data. Since my calculation does not match any of the options and assuming there might have been a mistake in my interpretation, let's correct the approach based on the concept:The correct approach involves calculating the mass of the solute and the total mass of the solution correctly, then applying the percent by mass formula. Given the error in matching the options, let's analyze the options provided:- Option A (0.160%) is too low for a 1.92 molal solution of NaCl.- Option B (16.9%) could be considered reasonable if we account for the mass of NaCl and water correctly.- Option C (99.5%) is unrealistic for a solution, as it suggests almost pure solute.- Option D (20.4%) and Option E (19.2%) are also possible percentages but would require specific contexts not provided here.Given the mistake in the initial calculation and explanation, without the correct context or recalculating based on a specific formula directly tied to the options, it's challenging to provide the accurate selection from the given choices. The explanation aimed to demonstrate the calculation process for percent by mass in a solution, but please note the discrepancy in the final answer.

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