How much heat energy, in kilojoules, is required to convert 53.0 g of ice at -18.C to water at 25.0 C ?

q1 = heat to raise T of solid ice from -18 to zero.

q1 = mass ice x specific heat solid ice x (Tfinal-Tinitial) (Watch the sign in Tf-Ti)

q2 = heat to convert solid ice at zero C to liquid water at zero C.
q2 = mass ice x heat fusion.

q3 = heat to raise T of melted ice from zero to 25C.
q3 = mass water x specific heat liquid water x (Tfinal-Tinitial)

To calculate the heat energy required to convert ice at -18°C to water at 25.0°C, you need to consider the following steps:

1. Calculate the heat energy required to raise the temperature of ice from -18°C to 0°C.
2. Calculate the heat energy required to change the ice at 0°C to liquid water at 0°C.
3. Calculate the heat energy required to raise the temperature of the water from 0°C to 25.0°C.

Let's go through each step:

1. Calculating heat energy to raise the temperature of ice from -18°C to 0°C:
The specific heat capacity of ice is approximately 2.09 J/g°C.
The change in temperature is: 0°C - (-18°C) = 18°C.
Therefore, the heat energy (q1) required to raise the temperature of ice from -18°C to 0°C can be calculated using the following formula:
q1 = (mass of ice) x (specific heat capacity of ice) x (change in temperature)
q1 = (53.0 g) x (2.09 J/g°C) x (18°C)
Note: It is important to convert the mass of ice to grams to match the specific heat capacity unit.
After performing the calculation, q1 is obtained in joules.

2. Calculating heat energy to change ice at 0°C to liquid water at 0°C:
The heat of fusion (melting) for ice is 334 J/g.
The mass of ice remains the same as before (53.0 g).
Therefore, the heat energy (q2) required to melt the ice can be calculated using the following formula:
q2 = (mass of ice) x (heat of fusion)
q2 = (53.0 g) x (334 J/g)
After performing the calculation, q2 is obtained in joules.

3. Calculating heat energy to raise the temperature of water from 0°C to 25.0°C:
The specific heat capacity of water is approximately 4.18 J/g°C.
To determine the amount of energy required, we need to consider the final temperature of the water.
The change in temperature is: 25.0°C - 0°C = 25.0°C.
Therefore, the heat energy (q3) required to raise the temperature of water from 0°C to 25.0°C can be calculated using the following formula:
q3 = (mass of water) x (specific heat capacity of water) x (change in temperature)
Since the ice has melted into water, the mass remains the same (53.0 g).
q3 = (53.0 g) x (4.18 J/g°C) x (25.0°C)
After performing the calculation, q3 is obtained in joules.

Now, add up the three amounts of heat energy to get the total heat energy required:
Total heat energy = q1 + q2 + q3

To convert the total heat energy from joules to kilojoules, divide the result by 1000 (1 kilojoule = 1000 joules).

Perform the calculations and you will have the total heat energy required in kilojoules to convert 53.0 g of ice at -18°C to water at 25.0°C.

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