Use the following table:A solution containing 80. g of NaNO3 in 75 g of H2O at 50 °C is cooled to 20 °C. b. How many grams of solid NaNO3 crystallized after cooling?

Ch.9 Solutions

Timberlake - Chemistry: An Introduction to General, Organic, and Biological Chemistry 13th Edition

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Timberlake 13th Edition

Ch.9 Solutions

문제 28b

9장, 문제 28b

Use the following table:

A solution containing 80. g of NaNO₃ in 75 g of H₂O at 50 °C is cooled to 20 °C.
b. How many grams of solid NaNO₃ crystallized after cooling?

검증된 단계별 안내

Determine the solubility of NaNO₃ at 50 °C and 20 °C using the provided solubility table. The solubility indicates how many grams of NaNO₃ can dissolve in 100 g of H₂O at each temperature.

Calculate the amount of NaNO₃ that can dissolve in 75 g of H₂O at 50 °C. Use the proportion: \( \text{grams of NaNO₃} = \text{solubility at 50 °C} \times \frac{75}{100} \).

Calculate the amount of NaNO₃ that can dissolve in 75 g of H₂O at 20 °C. Use the proportion: \( \text{grams of NaNO₃} = \text{solubility at 20 °C} \times \frac{75}{100} \).

Determine the amount of NaNO₃ that crystallized by subtracting the amount of NaNO₃ that can dissolve at 20 °C from the amount that was dissolved at 50 °C: \( \text{crystallized NaNO₃} = \text{dissolved at 50 °C} - \text{dissolved at 20 °C} \).

Verify that the total amount of NaNO₃ in the solution (80 g) is consistent with the calculated dissolved and crystallized amounts to ensure the solution is accurate.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Solubility

Solubility refers to the maximum amount of a solute that can dissolve in a solvent at a given temperature. In this case, the solubility of NaNO₃ in water at different temperatures is crucial for determining how much of the salt remains dissolved or crystallizes out when the solution is cooled from 50 °C to 20 °C.

Crystallization

Crystallization is the process where dissolved solute comes out of solution and forms solid crystals. This occurs when the solution becomes supersaturated, which can happen when the temperature decreases, leading to a reduction in solubility. Understanding this process is essential for calculating the amount of NaNO₃ that crystallizes upon cooling.

Mass Balance

Mass balance is a principle that states that the mass of the solute before and after a process must be accounted for. In this scenario, it involves calculating the initial mass of NaNO₃, determining how much remains dissolved at the lower temperature, and finding the difference to ascertain the mass that crystallized out of the solution.