Questions: A chemist carefully measures the amount of heat needed to raise the temperature of a 339.0 mg sample of a pure substance from -8.1°C to 1.4°C. The experiment shows that 1.4 J of heat are needed. What can the chemist report for the specific heat capacity of the substance? Be sure your answer has the correct number of significant digits.

Solution Steps

The mass of the sample is given as 339.0 mg. To convert this to grams, we use the conversion factor \(1 \, \text{g} = 1000 \, \text{mg}\).

\[ \text{Mass in grams} = \frac{339.0 \, \text{mg}}{1000} = 0.3390 \, \text{g} \]

The temperature change (\(\Delta T\)) is the final temperature minus the initial temperature. The temperatures are given in degrees Celsius, which can be used directly since the specific heat capacity is in terms of \(\text{K}^{-1}\) and the size of the degree is the same in both Celsius and Kelvin.

\[ \Delta T = 1.4^{\circ} \text{C} - (-8.1^{\circ} \text{C}) = 1.4 + 8.1 = 9.5 \, \text{C} \]

The specific heat capacity (\(c\)) is calculated using the formula:

\[ q = mc\Delta T \]

where \(q\) is the heat added (1.4 J), \(m\) is the mass in grams (0.3390 g), and \(\Delta T\) is the temperature change (9.5 K).

Rearranging for \(c\):

\[ c = \frac{q}{m \Delta T} = \frac{1.4 \, \text{J}}{0.3390 \, \text{g} \times 9.5 \, \text{K}} \]

Calculating \(c\):

\[ c = \frac{1.4}{0.3390 \times 9.5} = \frac{1.4}{3.2205} \approx 0.4345 \, \text{J} \cdot \text{g}^{-1} \cdot \text{K}^{-1} \]

Final Answer