Question

Calculate the amount of heat needed to melt 160. g of solid octane (C8H18 ) and bring it to a temperature of 99.2 degrees c. Round your answer to 3 significant digits. Also, be sure your answer contains a unit symbol.

Answer 1

Answer: The amount of heat needed to melt the given amount of octane is 84.6 kJ

Step-by-step explanation:

We know:

Boiling point of Octane =
`125.6^oC`

Few processes involved are:

(1):
`C_8H_(18) (s) (-57^oC, 219K) \rightleftharpoons C_8H_(18)(s) (-57^oC, 219K`

(2):
`C_8H_(18)(l) (-57^oC, 219K) \rightleftharpoons C_8H_(18)(l) (99.2^oC,372.2K)`

Calculating the heat absorbed for the process having same temperature:

`q=n* \Delta H_((f))` ......(i)

where,

q is the amount of heat absorbed, n is the moles of sample and
`\Delta H_((f))` is the enthalpy of fusion

Calculating the heat released for the process having different temperature:

`q=n* C_(l)* (T_2-T_1)` ......(ii)

where,

n = moles of sample

`C_(l)` = specific heat of liquid

`T_2\text{ and }T_1` are final and initial temperatures respectively

The number of moles is defined as the ratio of the mass of a substance to its molar mass.

The equation used is:

`\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}` ......(3)

Given mass of octane = 160. g

Molar mass of octane = 114.23 g/mol

Plugging values in equation 3:

`\text{Moles of octane }=(160.g)/(114.23g/mol)=1.40 mol`

• For process 1:

We are given:

`n=1.40mol\\\Delta H_(fusion)=20.740 kJ/mol`

Putting values in equation (i), we get:

`q_1=1.40mol* 20.470kJ/mol\\\\q_1=28.658kJ`

• For process 2:

We are given:

`n=1.40mol\\C=255.68J/mol^oC\\T_2=99.2^oC\\T_1=-57^oC`

Putting values in equation (ii), we get:

`q_2=1.40mol* 255.68J/mol^oC* (99.2-(-57))\\\\q_2=55912.10J=55.912kJ`

Calculating the total amount of heat released:

`Q=q_1+q_2`

`Q=[(28.658)+(55.912)]kJ=84.6kJ`

Hence, the amount of heat needed to melt the given amount of octane is 84.6 kJ