Calculate Molar Specific Heat of Substance: 284J, 22.0°C to 39.5°C

[G-reg]

Homework Statement

A certain substance has a mass per mole of 55 g/mol. When 284 J is added as heat to a 32.0 g sample of this material, its temperature rises from 22.0°C to 39.5°C

And I know that the specific heat of this substance is 507.14 J/[kg(K)]

Homework Equations

Q = mc[tex]\Delta[/tex]T

The Attempt at a Solution

55 g/mol * (1/32g) = 1.71875mol

284J/[(1.71875mol)/(39.5-22)] = 9.44 J/[mol(K)]

however..this is wrong and now I'm not sure where to go..help pleeeease!

 

[rock.freak667]

Homework Statement

A certain substance has a mass per mole of 55 g/mol. When 284 J is added as heat to a 32.0 g sample of this material, its temperature rises from 22.0°C to 39.5°C

And I know that the specific heat of this substance is 507.14 J/[kg(K)]

I assume you used the information to find that.

[tex]c= 507.14 \frac{J}{kgK}[/tex]


for the substance, 1 mol has how much mass in kg?

 

[kerimek]

The molar specific heat of a substance, also known as its molar heat capacity, is defined as the amount of heat required to raise the temperature of one mole of the substance by one degree Kelvin (or Celsius). It is calculated by dividing the heat added (Q) by the change in temperature (ΔT) and the number of moles (n) of the substance:

C = Q/(nΔT)

In this case, we know that the heat added (Q) is 284 J, the change in temperature (ΔT) is (39.5-22) = 17.5°C (or 17.5 K), and the number of moles (n) is 1.71875 mol (as calculated in your attempt at a solution). Plugging these values into the equation, we get:

C = (284 J)/[(1.71875 mol)(17.5 K)] = 9.44 J/[mol(K)]

This is the correct molar specific heat of the substance. However, you have incorrectly converted the units in your calculation. The specific heat you have calculated is in J/molK, not J/kgK. To convert to J/kgK, you would need to divide by the molar mass (55 g/mol) and multiply by the mass of the sample (32.0 g):

9.44 J/[mol(K)] * (32.0 g)/(55 g/mol) = 5.47 J/[kg(K)]

This is the specific heat of the substance in J/kgK, which is equivalent to 507.14 J/[kg(K)] as given in the problem statement.

In summary, your calculation for the molar specific heat was correct, but you just needed to be careful with your units when converting to the specific heat in J/kgK. I hope this helps clarify the solution for you.