Chemistry/physics-molar heat capacity?

[monarchus]

Chemistry/physics--molar heat capacity?

Homework Statement

When 5.00 J of heat are added to 1.50 g of cobalt, its temperature rises by 3.42 degree celsius. What is the molar heat capacity o cobalt in J mol-1 K-1?

A) 0.710
B) 0.875
C) 2.30
D) 57.4


P.S. if your answer is A, please explain why you want to add 273 to the change of the temperature to make it Kelvin. Wasn't change of temperature is the same no matter it is in the form of degree Celsius or Kelvin?

thank you.

Homework Equations

Q = n x c x T

Q = heat evolved
n = number of moles
c = molar heat capacity
T = change in temperature

The Attempt at a Solution

5 = (1.5 / 58.9 ) x c x 3.42

c = 57.4

 

[Borek]

D is the correct answer. You are right, delta T is the same regardless of whether you use Kelvin or Celsius scale.

 

[Blueshift5]

I would like to first clarify the question and make sure we are using the correct units. The unit for molar heat capacity is J mol^-1 K^-1, so we need to make sure all the values are in the correct units.

In this case, the heat added (Q) is given in Joules (J), the mass (m) is given in grams (g), and the change in temperature (T) is given in degrees Celsius (°C). However, the units for molar heat capacity (c) are in Kelvin (K). This is why we need to convert the change in temperature from degrees Celsius to Kelvin by adding 273.15 (not just 273).

The reason for this is because the Kelvin scale is an absolute temperature scale where 0 K represents the lowest possible temperature (absolute zero). On the other hand, the Celsius scale is a relative temperature scale where 0°C represents the freezing point of water and 100°C represents the boiling point of water. Therefore, we need to use Kelvin in this equation to get the correct value for the molar heat capacity.

Now, to solve for the molar heat capacity, we can rearrange the equation to isolate c:

c = Q / (n x T)

We have all the values except for n (number of moles). To find n, we can use the molar mass of cobalt, which is 58.9 g mol^-1.

n = m / M = 1.50 g / 58.9 g mol^-1 = 0.0255 mol

Substituting all the values into the equation, we get:

c = 5 J / (0.0255 mol x 3.42 K) = 57.4 J mol^-1 K^-1

Therefore, the correct answer is D) 57.4.

In summary, as scientists, we must pay attention to the units used in our calculations and make sure they are consistent to get the correct results. In this case, we needed to convert the change in temperature from degrees Celsius to Kelvin to use the correct units for the molar heat capacity.