Question

Initial mass of ice = 150.89 g
Final mass of ice = 99.69 g
Initial temperature of water = 42 °C
Final temperature of water = 0.4 °C

1. Determine the mass of the ice that has melted.
2. Determine the variation of the water temperature (ΔT).
3. a) Calculate the energy (in J) released by 100 g of water when it cooled by ΔT. The specific heat capacity(c) of water is 4.18 J/(g°C). Use the formula Q = mcΔT and the mass of water.
   b) Convert your answer into kJ.
4. Calculate the energy necessary to melt 1 g of ice (in kJ). Use the mass of ice.
5. Using the results from this experiment, determine how many kJ are required to melt 1 mole of ice.
6. Write the chemical equation for the melting of ice. Don't forget to include the value for the energy term in your equation

please help me solve this

Answer 1

When Ice melts then it absorbs heat form the water. Because melting of ice is an Endothermic process. So the temp of water decreases. Now this amount of heat absorbed by ice (Q) is calculated by the formula-

Q = m * C * ΔT

where Q = amount of heat absorbed

m = mass of the ice melted

C = specific heat capacity of ice

ΔT = change in temperature = Tfinal - Tinitial

a-

Now in the given question,

mass of ice melted = m = 150.89 g - 99.69 g = 51.2‬ g

Spcific heat capacity of ice = 2.03 J/g^oC

Change in temperature = ΔT = 42 °C - 0.4 °C = 41.6‬°C

Now putting these values, the amount of heat absorbed is

Q = m * C * ΔT

= 51.2‬ g * 2.03 J/g^oC * (41.6‬°C)

= 4323.7 J

= 4.3237 kJ

b-

It shows that amount of heat required to melt 51.2 g of ice = 4.3237 kJ

Then amount of heat required to melt 1 kg = 1000 g of ice = 4.3237 kJ * 1000/51.2

= 84.44 kJ

c-

Again if we consider 1 mole of ice, then molar mass of ice = molar mass of water = 18g

Then amount of heat required to melt 18 g of ice = 4.3237 kJ * 18/51.2

= 1.52 kJ

d-

Now if we take

m= 100 g of water, it is cooled by ΔT = 41.6‬°C and specific heat (C) = 4.18 J/(g°C), then amount of heat released is

Q = m * C * ΔT

= 100 g * 4.18 J/g^oC * (-41.6‬°C)

= - 17388 J

= - 17.388 kJ