a) The molar heat capacity is 25.130 joules per gram per Kelvin.
b) The <em>final</em> temperature of the sample is 21.004 °C.
<h3>Procedure - Determination of the molar heat capacity and the final sensible temperature</h3><h3 /><h3>a) Molar heat capacity of the sample</h3><h3 />
Dimensionally speaking, we can find the molar heat capacity (
), in joules per mol-Celsius, in terms of specific heat of iron (
), in joules per kilogram-Celsius:
(1)
Where
is the molar mass of iron, in grams per mole.
Please notice that
.
If we know that
and
, then the molar heat capacity:
![\bar c = \left(0.45\,\frac{J}{g\cdot ^{\circ}C} \right)\cdot \left(55.845\,\frac{g}{mol} \right)](https://tex.z-dn.net/?f=%5Cbar%20c%20%3D%20%5Cleft%280.45%5C%2C%5Cfrac%7BJ%7D%7Bg%5Ccdot%20%5E%7B%5Ccirc%7DC%7D%20%5Cright%29%5Ccdot%20%5Cleft%2855.845%5C%2C%5Cfrac%7Bg%7D%7Bmol%7D%20%5Cright%29)
![\bar c = 25.130\,\frac{J}{g\cdot ^{\circ}C}](https://tex.z-dn.net/?f=%5Cbar%20c%20%3D%2025.130%5C%2C%5Cfrac%7BJ%7D%7Bg%5Ccdot%20%5E%7B%5Ccirc%7DC%7D)
The molar heat capacity is 25.130 joules per gram per Kelvin. ![\blacksquare](https://tex.z-dn.net/?f=%5Cblacksquare)
<h3>b) Final temperature of the sample</h3><h3 />
The <em>final</em> temperature (
), in degrees Celsius, is determined by definition of sensible heat (
), in joules:
(2)
Where:
- Initial temperature, in degrees Celsius.
- Molar amount, in moles.
If we know that
,
,
and
, then the final temperature of the sample is:
![T_{f} = 12.2\,^{\circ}C + \frac{1239\,J}{(5.6\,mol)\cdot \left(25.130\,\frac{J}{g\cdot ^{\circ}C} \right)}](https://tex.z-dn.net/?f=T_%7Bf%7D%20%3D%2012.2%5C%2C%5E%7B%5Ccirc%7DC%20%2B%20%5Cfrac%7B1239%5C%2CJ%7D%7B%285.6%5C%2Cmol%29%5Ccdot%20%5Cleft%2825.130%5C%2C%5Cfrac%7BJ%7D%7Bg%5Ccdot%20%5E%7B%5Ccirc%7DC%7D%20%5Cright%29%7D)
![T_{f} = 21.004\,^{\circ}C](https://tex.z-dn.net/?f=T_%7Bf%7D%20%3D%2021.004%5C%2C%5E%7B%5Ccirc%7DC)
The <em>final</em> temperature of the sample is 21.004 °C. ![\blacksquare](https://tex.z-dn.net/?f=%5Cblacksquare)
To learn more on specific heat capacity, we kindly invite to check this verified question: brainly.com/question/2530523