Question

***S...A 51.5 g sample of quartz is put into a calorimeter (see sketch at right) that contains 250.0 g ofwater. The quartz sample starts off at 89.5 °C and the temperature of the water starts off at21.0 °C. When the temperature of the water stops changing it's 23.4 °C. The pressure remainsconstant at 1 atm.Calculate the specific heat capacity of quartz according to this experiment. Be sure your answer isrounded to 2 significant digits.0g. °CX?thermominsulatedcontainerwatersample.a calon

Answer 1

The specific heat capacity of quartz (to 2 significant digits) according to the experiment is 0.74 J/g⁰C

Step-by-step explanation

Given parameters:

`\begin{gathered} Mass\text{ }ofquartz\text{ }sample,m_q=51.5g \\ \\ Mass\text{ }of\text{ }water,m_w=250.0g \\ \\ Temperature\text{ }of\text{ }the\text{ }quartz\text{ }sample,T_q=89.5^0C \\ \\ Temperature\text{ }of\text{ }the\text{ }water,T_w=21.0^0C \\ \\ Temperature\text{ }of\text{ }the\text{ }mixture,T_(qw)=23.4^0C \\ \\ Specific\text{ }heat\text{ }capacity\text{ }of\text{ }water,c_w=4.186J\text{/}g^0C \end{gathered}`

What to find:

The specific heat capacity of quartz (Cq) according to this experiment.

Step-by-step solution:

The specific heat capacity of quartz (Cq) according to this experiment can be calculated using the formula for heat lost = heat gained.

`\begin{gathered} -Q=+Q \\ \\ -(m_q* c_q*(T_(qw)-T_q))=m_w* c_w*(T_(qw)-T_w) \end{gathered}`

The temperature of the quartz is higher than that of the water, so the quartz will give off energy in form of heat to the water.

Putting the values of the given parameters into the formula above, we have:

`\begin{gathered} -(51.5g* c_q*(23.4^0C-89.5^0C)=250.0g*4.186J\text{/}g^0C*(23.4^0C-21.0^0C) \\ \\ -(51.5g* c_q*-66.1^0C)=1046.5J\text{/}^0C*2.4^0C \\ \\ 3404.15g^0C* c_q=2511.6J \\ \\ Divide\text{ }bothsides\text{ }by\text{ }3404.15g^0C \\ \\ (3404.15g^0C* c_q)/(3404.15g^0C)=(2511.6J)/(3404.15g^0C) \\ \\ c_q=0.737805325\text{ }J\text{/}g^0C \\ \\ The\text{ }answer\text{ }rounded\text{ }to\text{ }2\text{ }significant\text{ }digits\text{ }is: \\ \\ c_q=0.74\text{ }J\text{/}g^0C \end{gathered}`

Thus, the specific heat capacity of quartz (to 2 significant digits) according to the experiment is 0.74 J/g⁰C