Question

a chemist carefully measures the amount of heat needed to raise the temperature of a 132.0 g sample of a pure substance from -0.1 °c to 13.3 °c. the experiment shows that 416. 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.

Explanation:

Step1: Recall the formula for specific heat capacity

The formula for specific heat capacity \( c \) is \( q = mc\Delta T \), so \( c=\frac{q}{m\Delta T} \). Here, \( q = 416\space J \), \( m = 132.0\space g \), and we need to find \( \Delta T \).

Step2: Calculate the temperature change \( \Delta T \)

The initial temperature \( T_1=- 0.1^{\circ}C \) and the final temperature \( T_2 = 13.3^{\circ}C \). So \( \Delta T=T_2 - T_1=13.3^{\circ}C-(- 0.1^{\circ}C)=13.4^{\circ}C \). Since a change in Celsius is the same as a change in Kelvin, \( \Delta T = 13.4\space K \).

Step3: Substitute values into the formula for \( c \)

Substitute \( q = 416\space J \), \( m = 132.0\space g \), and \( \Delta T = 13.4\space K \) into \( c=\frac{q}{m\Delta T} \). So \( c=\frac{416}{132.0\times13.4} \).
First, calculate the denominator: \( 132.0\times13.4 = 132.0\times13+132.0\times0.4=1716 + 52.8 = 1768.8 \).
Then, calculate the value of \( c \): \( c=\frac{416}{1768.8}\approx0.235\space J\cdot g^{-1}\cdot K^{-1} \) (we check significant figures: \( q \) has 3 significant figures, \( m \) has 4, \( \Delta T \) has 3, so the result should have 3 significant figures).

Answer:

\( 0.235\space J\cdot g^{-1}\cdot K^{-1} \)