Question

Calculate the total energy required to change 22 g of ice at -20 degrees Celsius, to water, with a temperature of 50 degrees Celsius. The heat capacity of ice is 2.03 J/g-C, the heat capacity of water is 4.184 J/g-C, and the molar heat of fusion for ice is 6.02 kJ/mol.

Answer 1

Total energy required is J 138883.36 or 138.88336 KJ

Step-by-step explanation:

The total energy required to change 22 g of ice at -20°C, to water, with a temperature of 50°C is:

`\sf Q = Q_1 + Q_2 + Q_3`

where:

• 
  `\sf Q_1` is the energy required to melt the ice.
• 
  `\sf Q_2` is the energy required to raise the temperature of the water from -20°C to 0°C
• 
  `\sf Q_3` is the energy required to raise the temperature of the water from 0°C to 50°C

The energy required to melt the ice is:

`\sf Q_1 = m \cdot L_f`

where:

• m is the mass of the ice (22 g)
• 
  `\sf L_f` is the latent heat of fusion for ice (6.02 kJ/mol)

Now,

`\sf Q_1 = 22 * 6.02 * 10^3 = 132440 J`

The energy required to raise the temperature of the water from -20°C to 0°C is:

`\sf Q_2 = m \cdot c_p \cdot \Delta T`

where:

• 
  `\sf c_p` is the heat capacity of water (4.184 J/g-C)
• 
  `\sf \Delta T` is the change in temperature (0 - 20 = 20°C)

`\sf Q_2 = 22 * 4.184 *20 = 1840.96 J`

The energy required to raise the temperature of the water from 0°C to 50°C is:

`\sf Q_3 = m \cdot c_p \cdot \Delta T`

where:

• 
  `\sf c_p` is the heat capacity of water (4.184 J/g-C)
• 
  `\sf \Delta T` is the change in temperature (0 - 50 = 50°C)

`\sf Q_3 = 22 \cdot 4.184 \cdot 50 = 4602.4 J`

Therefore, the total energy required is:

`\sf Q = 132440+1840.96+4602.4`

Q=138883.36

So, the answer is Total energy required is 138883.36 J or 138.88336 KJ