Calculate the energy that must be removed to convert substance X from a gas at 115°C to a solid -50.7°C. Assume X has a molar mass of 75.0 g/mol.

Specific heat capacities
ΔHvap 20. kJ/mol C(s) 3.0 J/g · °C
ΔHfus 5.0 kJ/mol C(l) 2.5 J/g · °C
bp 75°C C(g) 1.0 J/g · °C
mp −15°C

If you can go step by step so I can understand how this is done That would be great! Thanks

See below.

To calculate the energy that must be removed to convert substance X from a gas at 115°C to a solid -50.7°C, we need to break down the energy changes during the phase transitions.

The first step is to calculate the energy required to cool substance X from a gas at 115°C to its boiling point (bp) at 75°C. We can use the equation:

Energy1 = mass × specific heat capacity (C(g)) × temperature change

The temperature change is given by:

ΔT1 = bp - initial temperature
= 75°C - 115°C
= -40°C

To convert the temperature change from Celsius to Kelvin, add 273.15:
ΔT1 = -40°C + 273.15
= 233.15 K

Substitute the values into the equation:
Energy1 = mass × C(g) × ΔT1

The molar mass of substance X is given as 75.0 g/mol. Assuming 1 mole of substance X:
Energy1 = 75.0 g × 1.0 J/g · °C × 233.15 K

Next, we calculate the energy required to condense substance X from a gas to a liquid. We use the equation:

Energy2 = moles × ΔHvap

The moles of substance X can be calculated using the molar mass:
Moles = mass ÷ molar mass
= 75.0 g ÷ 75.0 g/mol

Substitute the value into the equation:
Energy2 = (75.0 g ÷ 75.0 g/mol) × 20. kJ/mol
= 20.0 kJ

Now, we calculate the energy required to cool the liquid substance X from its boiling point at 75°C to its melting point (mp) at -15°C. We use the same equation as in the first step:

Energy3 = mass × C(l) × ΔT3

The temperature change is given by:

ΔT3 = mp - bp
= -15°C - 75°C
= -90°C

Convert the temperature change from Celsius to Kelvin:
ΔT3 = -90°C + 273.15
= 183.15 K

Substitute the values into the equation:
Energy3 = mass × C(l) × ΔT3

Finally, we calculate the energy required to freeze substance X from a liquid to a solid. We use the equation:

Energy4 = moles × ΔHfus

Substitute the value into the equation:
Energy4 = (75.0 g ÷ 75.0 g/mol) × 5.0 kJ/mol
= 5.0 kJ

To find the total energy removed, we sum up all the energies:
Total energy = Energy1 + Energy2 + Energy3 + Energy4

Calculate the value to obtain the desired answer.