Exactly 10 mL of water at 25°C was added to a hot iron skillet. All of the water was converted into steam at 100°C. If the mass of the pan was 1.20 kg and the molar heat capacity of iron is 25.19 J/mol∙°C, what was the temperature change of the skillet?

Well, that skillet definitely felt the heat! Now let's calculate the temperature change. To do that, we need to calculate the heat absorbed by the skillet.

First, let's find the moles of water that turned into steam. We know that 1 mole of water is 18.015 g, so 10 mL of water is 10 g. Thus, we have 10 g / 18.015 g/mol = 0.554 mol of water.

Now, let's calculate the heat absorbed by the water using the formula Q = mcΔT, where Q is the heat absorbed, m is the mass, c is the molar heat capacity, and ΔT is the change in temperature.

Q = (0.554 mol) * (25.19 J/mol∙°C) * ΔT

Since the water is converting into steam, it changes from a temperature of 25°C to 100°C, resulting in a ΔT of 100°C - 25°C = 75°C.

Q = (0.554 mol) * (25.19 J/mol∙°C) * 75°C = 1050.37 J

Now, let's find the heat absorbed by the skillet. We'll assume it starts at the same temperature as the water.

Q = mcΔT

1050.37 J = (1.20 kg) * (25.19 J/mol∙°C) * ΔT

Simplifying, we find that the temperature change of the skillet is ΔT = 35.05°C.

So, the skillet can handle the heat like a champ and experienced a temperature change of 35.05°C.

To determine the temperature change of the skillet, we need to calculate the amount of heat absorbed by the iron skillet and use it to find the change in temperature.

1. Calculate the heat absorbed by the skillet:
- The heat absorbed can be determined using the equation:
Q = mcΔT, where Q is the heat absorbed, m is the mass, c is the molar heat capacity, and ΔT is the change in temperature.
- We know that the molar heat capacity of iron (c) is 25.19 J/mol∙°C, and the mass (m) of the skillet is 1.20 kg.
- Since we only want to find the change in temperature (ΔT), we can rearrange the equation as follows:
Q = mcΔT => ΔT = Q / (mc)

2. Calculate the heat absorbed by the water:
- The heat absorbed by the water can be calculated using the formula:
Q = mL, where Q is the heat absorbed, m is the mass, and L is the heat of vaporization.
- We know that the mass of the water is 10 mL, which is equivalent to 10 grams.
- The heat of vaporization for water is approximately 2260 J/g.
- Using the given values, we can calculate the heat absorbed by the water.

3. Calculate the total heat absorbed:
- Since the heat absorbed by the skillet and the water are equal (according to the principle of conservation of energy), we need to calculate the total heat absorbed.

4. Determine the change in temperature:
- Using the total heat absorbed and the molar heat capacity of iron, we can now calculate the change in temperature of the skillet.

Let's perform the calculations step-by-step.

To find the temperature change of the skillet, we need to calculate the heat absorbed by the skillet during the phase change of water to steam.

First, let's determine the heat absorbed by the water to reach its boiling point:

Q1 = mass × specific heat capacity × temperature change
Q1 = 10 g × 4.18 J/g∙°C × (100°C - 25°C)
Q1 = 10 g × 4.18 J/g∙°C × 75°C
Q1 ≈ 3135 J

Next, we need to calculate the heat absorbed during the phase change:

Q2 = mass × heat of vaporization
Q2 = 10 g × 40.7 J/g
Q2 ≈ 407 J

The total heat absorbed by the water is the sum of Q1 and Q2:

Q_total = Q1 + Q2
Q_total = 3135 J + 407 J
Q_total ≈ 3542 J

Now, let's determine the molar heat capacity of the skillet:

Molar heat capacity = heat absorbed / moles
Molar heat capacity = Q_total / (mass / molar mass)
Molar heat capacity = 3542 J / (1200 g / 55.845 g/mol)
Molar heat capacity ≈ 25.81 J/mol∙°C

Finally, we can calculate the temperature change of the skillet:

Temperature change = heat absorbed / (molar heat capacity × moles)
Temperature change = Q_total / (molar heat capacity × (mass / molar mass))
Temperature change = 3542 J / (25.81 J/mol∙°C × (1200 g / 55.845 g/mol))
Temperature change ≈ 5.75°C

Therefore, the temperature change of the skillet is approximately 5.75°C.

[mass H2O x specific heat H2O x (Tfinal-Tinitial)] + [mass H2O x heat vap] + [mass pan x specific heat Fe x delta T] = 0

Substitute and solve for dT. If I didn't goof I get something like 47 C as delta T. The negative sign you get means it is about 47 C LOWER than where it started.
Watch the units.