Question

After an afternoon party, a small cooler full of ice is dumped onto the hot ground and melts. If the cooler contained 8.00 kg of ice and the temperature of the ground was 42.0°C, calculate the energy that is required to melt all the ice at 0°C. The heat of fusion for water is 80.0 cal/g.

How much heat energy is required to convert 25.9 g of solid iron at 21 °C to liquid iron at 1538 °C? The molar heat of fusion of iron is 13.8 kJ/mol. Iron has a normal melting point of 1538 °C. The specific heat capacity of solid iron is 0.449 J/g·°C

How many grams of ethanol, C2H5OH, can be boiled with 539.8 kJ of heat energy? The molar heat of vaporization of ethanol is 38.6 kJ/mol.

Answer 1

1. we have mass of 8kg or 8000 g

so at first we are converting 8000 g of solid ice into liquid at 0 C .(conversion of solid to liquid without change in temperature )

heat of fusion = 80.0 cal/g

now total heat required = 8000 * 80 =640000 cal

2 . molar mass of iron = 55.845 or 56 g

so no of mole = given mass / molar mass

given mass = 25.9 so mole = 25.9/56 = 0.4625 moles

specific heat of iron = 0.449 J/g C

now at first we have to increase the temperature 21 to 1538 or difference is 1517 K

now heat required = m*c* t , here m is mass, c is specific heat capacity , t is change in temperature

putting the values = 25.9* 0.449 *1517 = 17641.3447 j

now for fusion heat = 13.8kJ/mole * mole of iron

= 13.8*0.4625 = 6.3825kJ or 63825 J

total heat reuired is some of both the heat = 17641.3447 + 63825 =81466.3447 J or 81.35 J

3. total heat =539.8 Kj

heat of vapourisation = 38.6KJ/mole

no of mole = total heat / molar heat = 539.8/38.6=13.984 moles

molar mass of ethanol = 46

so total mass = mole * molecular mass

=46*13.984 = 643.264 g

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