Some properties of aluminum are summarized in the following list.

normal melting point 658°C
heat of fusion 0.395 kJ/g
normal boiling point 2467°C
heat of vaporization 10.52 kJ/g
specific heat of the solid 0.902 J/g°C

(a) Calculate the quantity of energy required to heat 1.75 mol of aluminum from 17°C to its normal melting point.

(b) Calculate the quantity of energy required to melt 1.37 mol of aluminum at 658°C.

(c) Calculate the amount of energy required to vaporize 1.36 mol of aluminum at 2467°C.

I'm the one who posted the question... this is how I'm doing part A. I'm told it's the wrong answer, but I can't figure out what I'm doing wrong. I'm hesitant on going to parts B and C until I understand part A.

Part A:

Step one: I changed the mols of Al to grams.

13.9mol Al * (26.9815g Al / 1mol Al) = 47.2176g Al

Step two: I plugged the numbers into the Q = s * m * change in T

Q = (0.902 J/g*C)(47.2176g Al) ( 641C)
Q = 27300KJ = 2.73 * 10^4KJ

Again, I'm told I'm wrong here. Any help would be appreciated thanks!

I answered this above but generically.

I don't know where you came up with 13.9 mol Al; however, it must just be a typo because the 47.2 is correct for grams.
The Q step is ok, also; however, the answer is not in kJ.
mass (g) x specific heat (J/g*C) x (T in C) gives Joules.
I think that is the trouble you are having.

To calculate the quantity of energy required for these processes, we can use the following formulas:

(a) The energy required to heat a substance can be calculated using the formula:

Q = m * C * ΔT

Where Q is the quantity of energy in joules, m is the mass in grams, C is the specific heat capacity in J/g°C, and ΔT is the change in temperature in °C.

First, we need to calculate the mass of aluminum for 1.75 mol. The molar mass of aluminum is 26.98 g/mol, so:

Mass of aluminum = 1.75 mol * 26.98 g/mol = 47.1775 g

Now, we can calculate the quantity of energy required to heat this mass of aluminum from 17°C to its normal melting point (658°C):

ΔT = 658°C - 17°C = 641°C

Q = 47.1775 g * 0.902 J/g°C * 641°C = 27178.7 J

(b) The energy required to melt a substance can be calculated using the formula:

Q = m * ΔHfus

Where Q is the quantity of energy in joules, m is the mass in grams, and ΔHfus is the heat of fusion in J/g.

First, we need to calculate the mass of aluminum for 1.37 mol, similarly to (a):

Mass of aluminum = 1.37 mol * 26.98 g/mol = 36.9266 g

Now, we can calculate the quantity of energy required to melt this mass of aluminum at 658°C:

Q = 36.9266 g * 0.395 kJ/g = 14.593 kJ = 14593 J

(c) The energy required to vaporize a substance can be calculated using the formula:

Q = m * ΔHvap

Where Q is the quantity of energy in joules, m is the mass in grams, and ΔHvap is the heat of vaporization in J/g.

First, we need to calculate the mass of aluminum for 1.36 mol, similarly to (a) and (b):

Mass of aluminum = 1.36 mol * 26.98 g/mol = 36.6808 g

Now, we can calculate the quantity of energy required to vaporize this mass of aluminum at 2467°C:

Q = 36.6808 g * 10.52 kJ/g = 385.334 kJ = 385334 J