# Calculate the amount of heat liberated (in KJ) from 366 g of mercury, when it cools from 77.0...

## Question:

Calculate the amount of heat liberated (in KJ) from {eq}\rm 366\ g {/eq} of mercury, when it cools from {eq}\rm 77.0 ^\circ C {/eq} to {eq}\rm 12.0 ^\circ C {/eq}.

## Heat Transfer:

When heat is transferred to or from a substance translates to a change in temperature. These properties can be related through the heat transfer equation, {eq}\displaystyle q = mc\Delta T {/eq}, where q is the heat transferred, m is the mass of the substance, c is the specific heat, and {eq}\displaystyle \Delta T {/eq} is the respective change in temperature.

Determine the heat, q, liberated from the mercury by applying the heat transfer equation, {eq}\displaystyle q = mc\Delta T {/eq}. We have the mass, m = 366 g, the change in temperature, {eq}\displaystyle \Delta T {/eq} =12.0 - 77.0 = -65.0 {eq}\displaystyle ^\circ {/eq}C, and mercury has a heat capacity of c = 0.140 J/g {eq}\displaystyle ^\circ {/eq}C. We plug in the given to determine the answer.

{eq}\begin{align} \displaystyle q &= mc\Delta T\\ &= 336\ g\times 0.140\ J/g^\circ C\times -65.0 ^\circ C\\ &= -3057.6\ J\\ &\approx\boxed{\rm -3.06\ kJ} \end{align} {/eq} 