the heat of fusion for thallium is 21 J/g, and its heat of vaporization is 795 J/g. Thallium's melting point is 304 degrees celsius, and its boiling point is 1457 degrees celsius. The specific heat of liquid thallium is 0.13 J/g degrees celsius. How much heat is needed to change 236 g of solid thallium at 304 degrees celsius to vapor at 1457 degrees celsius and 1 atm?

q1 = heat to melt Tl at 306 C.

q1 = mass x heat fusion.

q2 = heat to move Tl from 306 C to 1457 C.
q2 = mass x specific heat liquid Tl x delta T.

q3 = heat to vaporize Tl
q3 = mass x heat vaporization.

Total Q = q1 + q2 + q3.

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To find the total amount of heat needed to change 236 g of solid thallium at 304 degrees Celsius to vapor at 1457 degrees Celsius, we need to consider the following steps:

1. Heating the thallium from its melting point to its boiling point.
2. Melting the thallium (solid to liquid) at its melting point.
3. Heating the thallium from its melting point to the initial temperature.
4. Heating the thallium from its initial temperature to its boiling point.
5. Vaporizing the thallium (liquid to vapor) at its boiling point.
6. Heating the thallium vapor from its boiling point to the final temperature.

Let's calculate the heat needed for each step:

Step 1: Heating the thallium from its melting point to its boiling point.
The heat needed to raise the temperature of 236 g of solid thallium from its melting point (304 degrees Celsius) to its boiling point (1457 degrees Celsius) can be calculated using the formula:
q = m * c * ΔT
where q is the heat, m is the mass, c is the specific heat, and ΔT is the change in temperature.
Using the specific heat of liquid thallium (0.13 J/g degrees Celsius):
q1 = 236 g * 0.13 J/g degrees Celsius * (1457 - 304) degrees Celsius

Step 2: Melting the thallium (solid to liquid) at its melting point.
The heat needed to melt 236 g of solid thallium at its melting point can be calculated using the formula:
q = m * ΔHfusion
where q is the heat, m is the mass, and ΔHfusion is the heat of fusion.
q2 = 236 g * 21 J/g

Step 3: Heating the thallium from its melting point to the initial temperature.
The heat needed to raise the temperature of 236 g of liquid thallium from its melting point (304 degrees Celsius) to the initial temperature can be calculated using the formula q = m * c * ΔT.
Using the specific heat of liquid thallium (0.13 J/g degrees Celsius):
q3 = 236 g * 0.13 J/g degrees Celsius * (1457 - 304) degrees Celsius

Step 4: Heating the thallium from its initial temperature to its boiling point.
The heat needed to raise the temperature of 236 g of liquid thallium from its initial temperature to its boiling point can be calculated using the formula q = m * c * ΔT.
Using the specific heat of liquid thallium (0.13 J/g degrees Celsius):
q4 = 236 g * 0.13 J/g degrees Celsius * (1457 - 304) degrees Celsius

Step 5: Vaporizing the thallium (liquid to vapor) at its boiling point.
The heat needed to vaporize 236 g of liquid thallium at its boiling point can be calculated using the formula:
q = m * ΔHvaporization
where q is the heat, m is the mass, and ΔHvaporization is the heat of vaporization.
q5 = 236 g * 795 J/g

Step 6: Heating the thallium vapor from its boiling point to the final temperature.
The heat needed to raise the temperature of 236 g of thallium vapor from its boiling point to the final temperature can be calculated using the formula q = m * c * ΔT.
Using the specific heat of liquid thallium (0.13 J/g degrees Celsius):
q6 = 236 g * 0.13 J/g degrees Celsius * (1457 - 304) degrees Celsius

Finally, we can calculate the total heat needed to change 236 g of solid thallium at 304 degrees Celsius to vapor at 1457 degrees Celsius:
Total heat = q1 + q2 + q3 + q4 + q5 + q6

To calculate the total heat needed to change 236 g of solid thallium at 304 degrees Celsius to vapor at 1457 degrees Celsius and 1 atm, we need to consider three steps:

1. Heating solid thallium from its initial temperature (304 degrees Celsius) to its melting point (304 degrees Celsius).
2. Melting the thallium at its melting point (304 degrees Celsius).
3. Heating the liquid thallium from its melting point (304 degrees Celsius) to its boiling point (1457 degrees Celsius) and then vaporizing it at its boiling point (1457 degrees Celsius).

Let's break down the calculations for each step:

1. Heating solid thallium:
Using the specific heat capacity formula (Q = m * c * ΔT), where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature, we can calculate the heat energy required to heat the solid thallium to its melting point.
Q1 = m1 * c1 * ΔT1
Q1 = 236 g * 0.13 J/g degrees Celsius * (304 degrees Celsius - 304 degrees Celsius)
Q1 = 0 J

2. Melting the thallium:
The heat energy needed to melt solid thallium is given by multiplying the mass (m2) by the heat of fusion (ΔHf).
Q2 = m2 * ΔHf
Q2 = 236 g * 21 J/g
Q2 = 4,956 J

3. Heating and vaporizing liquid thallium:
To calculate the heat energy required to heat and vaporize the liquid thallium, we need to consider two separate steps again:
- Heating the liquid thallium from its melting point (304 degrees Celsius) to its boiling point (1457 degrees Celsius)
- Vaporizing the liquid thallium at its boiling point (1457 degrees Celsius).

a. Heating liquid thallium:
Using the specific heat capacity formula again, we can calculate the heat energy required to heat the liquid thallium.
Q3a = m3 * c3 * ΔT3a
Q3a = 236 g * 0.13 J/g degrees Celsius * (1457 degrees Celsius - 304 degrees Celsius)
Q3a = 33,854 J

b. Vaporizing liquid thallium:
The heat energy needed to vaporize liquid thallium is given by multiplying the mass (m3) by the heat of vaporization (ΔHv).
Q3b = m3 * ΔHv
Q3b = 236 g * 795 J/g
Q3b = 187,620 J

Finally, the total heat energy required is the sum of the individual heat energies calculated in each step.
Total Q = Q1 + Q2 + Q3a + Q3b
Total Q = 0 J + 4,956 J + 33,854 J + 187,620 J
Total Q = 226,430 J

Therefore, 236 g of solid thallium at 304 degrees Celsius needs 226,430 J of heat to change to vapor at 1457 degrees Celsius and 1 atm.