When a 5.10-g sample of solid sodium hydroxide dissolves in 100.0 g of water in a coffee-cup calorimeter (Figure 5.18), the temperature rises from 20.5 to 33.2 °C. a. Calculate the quantity of heat (in kJ) released in the reaction.

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Identify the mass of the solution, which is the sum of the mass of sodium hydroxide and the mass of water. Here, it is 5.10 g + 100.0 g.

Use the specific heat capacity of water, which is approximately 4.18 J/g°C, to calculate the heat absorbed by the solution. The formula to use is: \( q = m \cdot c \cdot \Delta T \), where \( m \) is the mass of the solution, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.

Calculate the change in temperature, \( \Delta T \), by subtracting the initial temperature from the final temperature: \( 33.2 \text{°C} - 20.5 \text{°C} \).

Substitute the values into the formula to find \( q \), the heat absorbed by the solution. Remember to convert the result from joules to kilojoules by dividing by 1000.

Since the heat is released by the reaction, the value of \( q \) will be negative, indicating an exothermic process. Report the heat released in kilojoules.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or substance to another due to a temperature difference. In this context, when sodium hydroxide dissolves in water, it releases heat, causing the temperature of the water to rise. Understanding how heat is transferred is crucial for calculating the total heat released during the dissolution process.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. For water, this value is typically 4.18 J/g°C. This concept is essential for calculating the heat absorbed by the water when sodium hydroxide dissolves, as it allows us to relate the temperature change to the amount of heat transferred.

Calorimetry

Calorimetry is the science of measuring the heat of chemical reactions or physical changes. In this scenario, a coffee-cup calorimeter is used to measure the heat released when sodium hydroxide dissolves in water. By applying the principles of calorimetry, we can determine the heat change based on the mass of the water, its specific heat capacity, and the observed temperature change.

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When a 5.10-g sample of solid sodium hydroxide dissolves in 100.0 g of water in a coffee-cup calorimeter (Figure 5.18), the temperature rises from 20.5 to 33.2 °C. b. Using your result from part (a), calculate ΔH (in kJ/mol NaOH) for the solution process. Assume that the specific heat of the solution is the same as that of pure water.

Textbook Question

(b) Is this process endothermic or exothermic?

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