What mass of ice, at 0.00 C can be converted to steam, at 100 degrees C, if it absorbs 1.00 x 10 (to the 6th power) Jules of heat energy? How do you find the mass of ice?

To find the mass of ice that can be converted to steam, we need to use the concept of heat transfer and the specific heat capacities of ice and water.

The process of converting ice to steam involves three stages:
1. Raising the temperature of ice from 0°C to 0°C (no change in state)
2. Melting the ice at 0°C
3. Heating the water from 0°C to 100°C and converting it to steam at 100°C

Now, the specific heat capacity of ice is 2.09 J/g°C, and the specific heat capacity of water is 4.18 J/g°C.

Let's break down the heat energy absorbed during each stage:

1. Raising the temperature of ice:
To raise the temperature of the ice from 0°C to 0°C, no phase change occurs, so the heat energy (Q) absorbed can be calculated using the formula:
Q = mass × specific heat capacity × temperature change
Since the temperature change is 0°C, the heat energy absorbed is zero for this stage.

2. Melting the ice:
To convert ice at 0°C to water at 0°C, we use the heat formula:
Q = mass × heat of fusion
The heat of fusion for ice is 333.55 J/g.
So, the heat energy absorbed during melting is 333.55 × mass of ice.

3. Heating the water to steam:
To raise the temperature of the water from 0°C to 100°C and convert it to steam, we use the heat formula:
Q = mass × specific heat capacity × temperature change
Here, the temperature change is 100°C.
So, the heat energy absorbed during this stage is mass of water × 4.18 × 100.

We have the total heat energy absorbed as 1.00 × 10^6 Jules.
So, we can equate the total heat energy to the sum of the heat energies absorbed during each stage:
1.00 × 10^6 = 333.55 × mass of ice + mass of water × 4.18 × 100

Now, we need to find the value of the mass of ice.
To solve for the mass, rearrange the equation and isolate the mass of ice:
mass of ice = (1.00 × 10^6 - mass of water × 4.18 × 100) / 333.55

Plug in the appropriate values and calculate the mass of ice.

[mass ice x heat fusion] + [mass ice x specific heat water x (Tfinal-Tinitial)+ [mass ice x heat vaporization] = 1E6 J.

Solve for mass ice.
Tfinal = 100 C
Tinitial = 0 C
I made a VERY quick estimate and arrived at about 330 grams if I didn't make an error. That's an approximation.