Chemistry: 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.

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Calculate the amount of heat needed to melt 160. g - id16013784678, naiomireyes74p2aybs

Ответ:

KitKat22Rose9

18.07.2021

Chemistry

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

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:

$q=n\times \Delta H_{(f)}$ ......(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:

$q=n\times C_{l}\times (T_2-T_1)$ ......(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:

$\text{Moles of octane }=\frac{160.g}{114.23g/mol}=1.40 mol$

For process 1:

We are given:

$n=1.40mol\\\Delta H_{fusion}=20.740 kJ/mol$

Putting values in equation (i), we get:

$q_1=1.40mol\times 20.470kJ/mol\\\\q_1=28.658kJ$

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:

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

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

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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.

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