Question

a chemist carefully measures the amount of heat needed to raise the temperature of a 756.0 g sample of a pure substance from 13.7 °c to 20.4 °c. the experiment shows that 9.4 kj of heat are needed. what can the chemist report for the specific heat capacity of the substance? round your answer to 2 significant digits.
□ j·g⁻¹·k⁻¹
□×10⁰

Explanation:

Step1: Recall the formula for specific heat capacity

The formula for heat energy \( q \) is \( q = mc\Delta T \), where \( m \) is mass, \( c \) is specific heat capacity, and \( \Delta T \) is the change in temperature. We need to solve for \( c \), so \( c=\frac{q}{m\Delta T} \).

Step2: Convert units of heat and temperature

First, convert heat from kJ to J: \( q = 9.4\space kJ=9.4\times1000 = 9400\space J \).
Next, calculate the change in temperature \( \Delta T \). Since a change in Celsius is the same as a change in Kelvin, \( \Delta T=20.4^{\circ}C - 13.7^{\circ}C = 6.7\space K \) (or \( 6.7^{\circ}C \)).
The mass \( m = 756.0\space g \).

Step3: Substitute values into the formula

Substitute \( q = 9400\space J \), \( m = 756.0\space g \), and \( \Delta T = 6.7\space K \) into \( c=\frac{q}{m\Delta T} \):
\( c=\frac{9400}{756.0\times6.7} \)

Step4: Calculate the value

First, calculate the denominator: \( 756.0\times6.7 = 5065.2 \)
Then, \( c=\frac{9400}{5065.2}\approx1.8558 \)

Step5: Round to 2 significant digits

Rounding \( 1.8558 \) to 2 significant digits gives \( 1.9 \).

Answer:

\( 1.9\space J\cdot g^{-1}\cdot K^{-1} \)