Question

a sample of quartz, which has a specific heat capacity of 0.730 j·g⁻¹·°c⁻¹, is put into a calorimeter (see sketch at right) that contains 250.0 g of water. the quartz sample starts off at 92.7 °c and the temperature of the water starts off at 20.0 °c. when the temperature of the water stops changing its 22.9 °c. the pressure remains constant at 1 atm.
calculate the mass of the quartz sample. be sure your answer is rounded to 2 significant digits.

Explanation:

Step1: Define heat transfer balance

Heat lost by quartz = Heat gained by water: $m_q c_q \Delta T_q = m_w c_w \Delta T_w$

Step2: List known values

$c_q=0.730\ Jg^{-1}^\circ C^{-1}$, $m_w=250.0\ g$, $c_w=4.184\ Jg^{-1}^\circ C^{-1}$, $\Delta T_q=92.7-22.9=69.8^\circ C$, $\Delta T_w=22.9-20.0=2.9^\circ C$

Step3: Solve for $m_q$

$m_q=\frac{m_w c_w \Delta T_w}{c_q \Delta T_q}=\frac{250.0 \times 4.184 \times 2.9}{0.730 \times 69.8}$

Step4: Calculate and round

$m_q=\frac{250.0 \times 4.184 \times 2.9}{0.730 \times 69.8}≈\frac{3034.6}{51.054}≈59.4≈59\ g$

Answer:

59 g