Help me solve this problem

Question

The specific heat of solid iron metal at 273.15K and 1 bar pressure is 0.449 J/g*K. How much heat (in units of kJ) is released when 96.01g of Fe(s) cools from 338.5K to 293.9K.

Assume the specific heat is constant over the given temperature range. (Show your steps).

Answer 1

Jenna,

This problem is worked in a similar fashion as if you were given temperature change in ^oC. Remember the relationship

q = m x s x ΔT where q = heat; m = mass; s is the specific heat; and ΔT is the change in temperature.

If you go ahead and plug in the given information (with units) you will see that the units cancel and the result will be the heat calculated in Joules. Then convert Joules to kilojoules kJ.

Here the temperature is given in Kelvin. ΔT in Kelvin is the same numerical value as ΔT in ^oC.

Hope this helps!

q = 96.01 g x 0.449 J/g*K x (338.5 K - 293.9 K) = 1922.6 J = 1.92 kJ (3 sig fig answer)

Answer 2

Hello Jena,

The formula for heat is Q = m*c*ΔT where ΔT = final_temperature - initial_temperature

You'd need to make sure units are consistent: if m is in grams, c in J/g*K, and ΔT in K, then Q will be in Joules, so be sure to divide the answer for Q by 1000 to get it into kiloJoules.

Q = (96.01 g) * (0.449 J/g*K) * (293.9-338.5)K = -1922.64 Joules (Q is negative b/c it's released as the problem indicates)

As mentioned earlier, divide by 1000 to get this answer in kilojoules, and you're all set!