Question

Calculate the amount of heat needed to melt 145.g of solid methanol (CH₃OH) and bring it to a temperature of -15.5C. Be sure your answer has a unit symbol and the correct number of significant digits

Answer 1

We are going to take the values of Molar heat of fusion from text book which is 3.1773 kj/ mole

The specific heat capacity of methanol is 2.53 J / g K

3.1773 KJ heat required to convert 1 mole of methanol solid to melt liquid.

We know, 1 mole of methanol is equivalent to its molar mass which is 32g/mole.

Thus, 32g takes 3.1773 KJ heat to convert into liquid.

145g of methanol will need = 3.1773KJ *145g / 32g = 14.397 KJ

q1 = 14.397 KJ

Now we calculated heat of fusion for 145g of methanol.

Once the solid methanol becomes liquid at -97.6 ⁰C, we need to calculate how much heat will be required to rise its temperature from -97.6 degree to -15.5 degree. Then we add the two heat values and that will be the answer.

Now we gonna use 1St law of thermodynamics.

According to that, the change in internal energy of the system is proportional to change in temperature.

q2 = C ( T2-T1)

Where, C is heat capacity.

T2 = -15.5 C

T1 = -97.6C

We know, heat capacity, C = m * c

Where m is the amount of substance and c is its specific heat capacity.

c = 2.53 J/g (degree)

q2 = mc(T2-T1) = 145g * 2.53 J/ g (degree) * 82.1 degree

= 30118.38 J = 30.11KJ

The total heat is going to required for whole process

Q = q1 + q2 = 14.397 KJ + 30.11 KJ = 44.507 KJ