Calculate the amount of heat, in kJ, needed to convert 30.0 g of ice at -5.2 oC to liquid water at 58 oC.
Specific heat of ice = 2.10 J/(g oC); heat of fusion of ice = 334 J/g; Specific heat of water = 4.18 J/(g oC)
q1 = heat needed to warm ice at -5.2 C to zero.
q1 = mass ice x specific heat ice x (Tfinal-Tinitial) where Tf is zero and Ti is -5.2.
q2 = heat needed to change phase from solid ice at zero to liquid water at zero.
q2 = mass ice x heat fusion
q3 = heat needed to warm liquid H2O at zero C to 58 c.
q3 = mass liquid water x specific heat liq water x (Tf - Ti)
Total q = q1 + q2 + q3.
To calculate the amount of heat needed to convert ice at -5.2 oC to liquid water at 58 oC, we need to consider the following steps:
Step 1: Calculate the heat required to raise the temperature of the ice from -5.2 oC to 0 oC.
The formula to calculate the heat required is:
q1 = mass × specific heat of ice × change in temperature
q1 = m × c1 × (T1 - T2)
where,
q1 = heat required,
m = mass of ice,
c1 = specific heat of ice,
T1 = final temperature (0 oC),
T2 = initial temperature (-5.2 oC).
Substituting the given values:
q1 = 30.0 g × 2.10 J/(g oC) × (0 oC - (-5.2 oC))
Step 2: Calculate the heat required to melt the ice at 0 oC.
The formula to calculate the heat required is:
q2 = mass × heat of fusion of ice
q2 = m × Hf
where,
q2 = heat required,
m = mass of ice,
Hf = heat of fusion of ice.
Substituting the given values:
q2 = 30.0 g × 334 J/g
Step 3: Calculate the heat required to raise the temperature of the water from 0 oC to 58 oC.
The formula to calculate the heat required is:
q3 = mass × specific heat of water × change in temperature
q3 = m × c2 × (T3 - T1)
where,
q3 = heat required,
m = mass of water,
c2 = specific heat of water,
T3 = final temperature (58 oC),
T1 = initial temperature (0 oC).
Substituting the given values:
q3 = 30.0 g × 4.18 J/(g oC) × (58 oC - 0 oC)
Step 4: Calculate the total heat required.
The total heat required is the sum of q1, q2, and q3.
Total heat required = q1 + q2 + q3
Now, you can substitute the values and calculate the total heat required in kJ.