How much energy is needed to heat 8.50 g of ice from -30.0 C to 70.0 C?

The heat of fusion of water is 6.01 kJ/mol, and the molar heat capacity is 36.6 J/(mol.K) for ice and 75.3 J/(mol.K) for liquid water.

I got 19.24kJ but it isn't correct!!

You do this in steps.

q1 = energy needed to heat solid ice from -30 C to solid ice at 0 C.
q1 = mass ice x specific heat ice x (Tfinal-Tinitial) where Tf is 0 and Ti is -30 C.

q2 = heat needed to change the phase at zero C from solid ice to liquid water.
q2 = mass ice x heat fusion

q3 = heat needed to raise the T of liquid water at zero C to 70 c.

q3 = mass water x specific heat liquid H2O x (Tfinal-Tinital) = ?

NOTE: Make sure the units are ok. If you intend to use J/mol K for specific heat then you MUST use mass in mols and not grams. My suspicion is this is where you went wrong.

Total is q1 + q2 + q3

Chemistry sucks dog nuts

To calculate the energy required to heat the ice, we need to consider two steps: heating the ice from -30.0°C to 0°C and then melting the ice at 0°C, followed by heating the resulting water from 0°C to 70.0°C.

Step 1: Heating the ice from -30.0°C to 0°C
The heat required for this step can be calculated using the formula:

Q = m × ΔT × C

where:
Q is the heat in joules (J),
m is the mass of the ice in grams (g),
ΔT is the change in temperature in degrees Celsius (°C), and
C is the heat capacity in joules per gram per degree Celsius (J/g°C).

Since the molar heat capacity is given, we can convert it to the heat capacity per gram using the molar mass of water (18.02 g/mol).

For ice:
C_ice = 36.6 J/(mol·K) × (18.02 g/mol) ≈ 658.932 J/(g·K)

Using the formula:
Q1 = m × ΔT1 × C_ice

Q1 = 8.50 g × (0°C - (-30.0°C)) × 658.932 J/(g·K)
= 8.50 g × (30.0°C) × 658.932 J/(g·K)

Step 2: Melting the ice at 0°C
During this step, the heat required is equal to the heat of fusion (ΔH_fusion) multiplied by the mass of the ice.

For water:
ΔH_fusion = 6.01 kJ/mol = 6010 J/mol

Using the formula:
Q2 = m × ΔH_fusion

Q2 = 8.50 g × 6010 J/mol

Step 3: Heating the water from 0°C to 70.0°C
Here, we will use the heat capacity for liquid water.

For liquid water:
C_water = 75.3 J/(mol·K) × (18.02 g/mol) ≈ 1356.906 J/(g·K)

Using the formula:
Q3 = m × ΔT3 × C_water

Q3 = 8.50 g × (70.0°C - 0°C) × 1356.906 J/(g·K)

To find the total heat required, we sum up the heat values for each step:

Total Q = Q1 + Q2 + Q3

Finally, convert the total heat to kJ:

Total Q = (Q1 + Q2 + Q3) / 1000

By following these steps and performing the calculations, you should be able to determine the correct amount of energy required to heat the ice.

To calculate the energy required to heat 8.50 g of ice from -30.0 °C to 70.0 °C, we need to consider several steps:

1. Calculate the energy required to raise the temperature of the ice to its melting point.
2. Calculate the energy required to melt the ice at its melting point.
3. Calculate the energy required to heat the resulting water from the melting point to the final temperature.

Let's go through each step together:

Step 1: Calculate the energy required to raise the temperature of the ice to its melting point.
The molar heat capacity for ice is 36.6 J/(mol.K). We need to convert the mass of ice to moles using its molar mass, which is approximately 18.0 g/mol.

Mass of ice = 8.50 g
Molar mass of ice = 18.0 g/mol

Moles of ice = (mass of ice) / (molar mass)
Moles of ice = 8.50 g / 18.0 g/mol

Next, we need to calculate the temperature change from -30.0 °C to the melting point of ice, which is 0.0 °C.
Temperature change = (melting point - initial temperature)
Temperature change = (0.0 °C - (-30.0 °C))

Now, we can calculate the energy required to raise the temperature of the ice using the formula:
Energy = (moles of ice) × (molar heat capacity) × (temperature change)

Step 2: Calculate the energy required to melt the ice at its melting point.
The heat of fusion (melting) of water is given as 6.01 kJ/mol. We can use this value to calculate the energy required to melt the ice.

Energy to melt ice = (moles of ice) × (heat of fusion)

Step 3: Calculate the energy required to heat the resulting water from the melting point to the final temperature.
We need to calculate the temperature change from the melting point (0.0 °C) to the final temperature (70.0 °C). The molar heat capacity for liquid water is 75.3 J/(mol.K).

Temperature change = (final temperature - melting point)
Temperature change = (70.0 °C - 0.0 °C)

Finally, we can calculate the energy required to heat the water using the formula:
Energy = (moles of water) × (molar heat capacity) × (temperature change)

After calculating these three steps, you can add up the energies from each step to find the total energy required.

I hope this step-by-step explanation helps you correct your answer. If you have any additional questions or need further assistance, feel free to ask!