Lesson 4 Thermal Energy
Completion requirements
Calculating Heat of Fusion and Heat of Vaporization
The amount of thermal energy being released or absorbed by a phase change can be calculated using a simple formula.
Using the quantity of thermal energy that was added and the number of moles of the substance, you can calculate the heat of fusion or the heat of vaporization of a substance.
D4.16 Ice undergoing fusion
«math»
«msub mathcolor=¨#FFFFFF¨»
«mi mathcolor=¨#FFFFFF¨»H«/mi»
«mrow»
«mi»f«/mi»
«mi»u«/mi»
«mi»s«/mi»
«/mrow»
«/msub»
«mo mathcolor=¨#FFFFFF¨»=«/mo»
«mfrac mathcolor=¨#FFFFFF¨»
«mi»Q«/mi»
«mi»n«/mi»
«/mfrac»
«/math»
Hfus = heat of fusion in kJ/mol (This can also be Hvap depending on if you are calculating the heat of fusion or heat of vaporization.)
Q = quantity of thermal energy added in kJ (This is the same Q as seen in the specific heat capacity formula, however, it uses a different unit.)
n = the amount of the substance in mol
Hfus = heat of fusion in kJ/mol (This can also be Hvap depending on if you are calculating the heat of fusion or heat of vaporization.)
Q = quantity of thermal energy added in kJ (This is the same Q as seen in the specific heat capacity formula, however, it uses a different unit.)
n = the amount of the substance in mol
You can use this formula to determine
- the heat of fusion or the heat of vaporization
- the quantity of thermal energy added
- the amount of the substance used
Let’s try some examples. Each example has a video to go with it. To play the video, click on the play icon next to the example.
Digging Deeper
D4.17 Ice floating in a drink
Normally, a solid object is denser than a liquid one. That is not the case with water: Ice is actually less dense than water, which is why ice floats in our drinks instead of sinking. Go to the following link to learn more about the density of ice.
Learn More
Examples
When 45.0 kJ of thermal energy is added to 7.49 mol of water, the ice melts. What is the heat of fusion of water?
https://adlc.wistia.com/medias/m7elgyguzs
Step 1: List the variables.
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«msub»«mi»H«/mi»«mrow»«mi»f«/mi»«mi»u«/mi»«mi»s«/mi»«/mrow»«/msub»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»?«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»Q«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»45«/mn»«mo».«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»n«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»7«/mn»«mo».«/mo»«mn»49«/mn»«mo»§#160;«/mo»«mi»mol«/mi»«/mtd»«/mtr»«/mtable»«/math»
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«msub»«mi»H«/mi»«mrow»«mi»f«/mi»«mi»u«/mi»«mi»s«/mi»«/mrow»«/msub»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»?«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»Q«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»45«/mn»«mo».«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»n«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»7«/mn»«mo».«/mo»«mn»49«/mn»«mo»§#160;«/mo»«mi»mol«/mi»«/mtd»«/mtr»«/mtable»«/math»
Step 2: Substitute the values into the formula.
«math» «msub» «mi»H«/mi» «mrow» «mi»f«/mi» «mi»u«/mi» «mi»s«/mi» «/mrow» «/msub» «mo»=«/mo» «mfrac» «mi»Q«/mi» «mi»n«/mi» «/mfrac» «mspace linebreak=¨newline¨»«/mspace» «msub» «mi»H«/mi» «mrow» «mi»f«/mi» «mi»u«/mi» «mi»s«/mi» «/mrow» «/msub» «mo»=«/mo» «mfrac» «mrow» «mn»45«/mn» «mo».«/mo» «mn»0«/mn» «mo»§#160;«/mo» «mi»kJ«/mi» «/mrow» «mrow» «mn»7«/mn» «mo».«/mo» «mn»49«/mn» «mo»§#160;«/mo» «mi»mol«/mi» «/mrow» «/mfrac» «/math»
«math» «msub» «mi»H«/mi» «mrow» «mi»f«/mi» «mi»u«/mi» «mi»s«/mi» «/mrow» «/msub» «mo»=«/mo» «mfrac» «mi»Q«/mi» «mi»n«/mi» «/mfrac» «mspace linebreak=¨newline¨»«/mspace» «msub» «mi»H«/mi» «mrow» «mi»f«/mi» «mi»u«/mi» «mi»s«/mi» «/mrow» «/msub» «mo»=«/mo» «mfrac» «mrow» «mn»45«/mn» «mo».«/mo» «mn»0«/mn» «mo»§#160;«/mo» «mi»kJ«/mi» «/mrow» «mrow» «mn»7«/mn» «mo».«/mo» «mn»49«/mn» «mo»§#160;«/mo» «mi»mol«/mi» «/mrow» «/mfrac» «/math»
Step 3: Calculate the answer.
«math» «msub» «mi»H«/mi» «mrow» «mi»f«/mi» «mi»u«/mi» «mi»s«/mi» «/mrow» «/msub» «mo»=«/mo» «mfrac» «mrow» «mn»45«/mn» «mo».«/mo» «mn»0«/mn» «mo»§#160;«/mo» «mi»kJ«/mi» «/mrow» «mrow» «mn»7«/mn» «mo».«/mo» «mn»49«/mn» «mo»§#160;«/mo» «mi»mol«/mi» «/mrow» «/mfrac» «mspace linebreak=¨newline¨»«/mspace» «msub» «mi»H«/mi» «mrow» «mi»f«/mi» «mi»u«/mi» «mi»s«/mi» «/mrow» «/msub» «mo»=«/mo» «mn»6«/mn» «mo».«/mo» «mn»008«/mn» «mo»§#160;«/mo» «mi»kJ«/mi» «mo»/«/mo» «mi»mol«/mi» «/math»
The heat of fusion needs to be rounded to three significant digits, as three digits is the smallest number of digits found in the question.
Hfus = 6.01 kJ/mol
The heat of fusion of water is 6.01 kJ/mol.
«math» «msub» «mi»H«/mi» «mrow» «mi»f«/mi» «mi»u«/mi» «mi»s«/mi» «/mrow» «/msub» «mo»=«/mo» «mfrac» «mrow» «mn»45«/mn» «mo».«/mo» «mn»0«/mn» «mo»§#160;«/mo» «mi»kJ«/mi» «/mrow» «mrow» «mn»7«/mn» «mo».«/mo» «mn»49«/mn» «mo»§#160;«/mo» «mi»mol«/mi» «/mrow» «/mfrac» «mspace linebreak=¨newline¨»«/mspace» «msub» «mi»H«/mi» «mrow» «mi»f«/mi» «mi»u«/mi» «mi»s«/mi» «/mrow» «/msub» «mo»=«/mo» «mn»6«/mn» «mo».«/mo» «mn»008«/mn» «mo»§#160;«/mo» «mi»kJ«/mi» «mo»/«/mo» «mi»mol«/mi» «/math»
The heat of fusion needs to be rounded to three significant digits, as three digits is the smallest number of digits found in the question.
Hfus = 6.01 kJ/mol
The heat of fusion of water is 6.01 kJ/mol.
A pot containing 100.0 g of water is left outside on a hot day. The sun provides 225.65 kJ of thermal energy, which causes the water to evaporate. What is the heat of vaporization of the water?
https://adlc.wistia.com/medias/62lxxu5v41
Step 1: List the variables.
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«msub»«mi»H«/mi»«mrow»«mi»v«/mi»«mi»a«/mi»«mi»p«/mi»«/mrow»«/msub»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»?«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»Q«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»225«/mn»«mo».«/mo»«mn»65«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»n«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»?«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»m«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»100«/mn»«mo».«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»g«/mi»«/mtd»«/mtr»«/mtable»«/math»
Note: This question gives you the amount of water in g rather than mol. You will need to convert the mass to mol using the following formula:
«math» «mi»n«/mi» «mo»=«/mo» «mfrac» «mi»m«/mi» «mi»M«/mi» «/mfrac» «/math»
You may recognize this formula from your chemistry unit. For a review on how to use it, click here.
Remember from your chemistry unit that the molar mass or M of water is 18.02 g/mol. For a review on how to calculate molar mass, click here.
«math»«mi»n«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»100«/mn»«mo».«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»g«/mi»«/mrow»«mrow»«mn»18«/mn»«mo».«/mo»«mn»02«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»g«/mi»«mo»/«/mo»«mi»mol«/mi»«/mrow»«/mfrac»«mspace linebreak=¨newline¨»«/mspace»«mi»n«/mi»«mo»=«/mo»«mn»5«/mn»«mo».«/mo»«mn»549«/mn»«mo»§#160;«/mo»«mn»389«/mn»«mo»§#160;«/mo»«mn»567«/mn»«mo»§#160;«/mo»«mi»mol«/mi»«/math»
Do not round this number when calculating heat of vaporization.
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«msub»«mi»H«/mi»«mrow»«mi»v«/mi»«mi»a«/mi»«mi»p«/mi»«/mrow»«/msub»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»?«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»Q«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»225«/mn»«mo».«/mo»«mn»65«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»n«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»?«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»m«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»100«/mn»«mo».«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»g«/mi»«/mtd»«/mtr»«/mtable»«/math»
Note: This question gives you the amount of water in g rather than mol. You will need to convert the mass to mol using the following formula:
«math» «mi»n«/mi» «mo»=«/mo» «mfrac» «mi»m«/mi» «mi»M«/mi» «/mfrac» «/math»
You may recognize this formula from your chemistry unit. For a review on how to use it, click here.
Remember from your chemistry unit that the molar mass or M of water is 18.02 g/mol. For a review on how to calculate molar mass, click here.
«math»«mi»n«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»100«/mn»«mo».«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»g«/mi»«/mrow»«mrow»«mn»18«/mn»«mo».«/mo»«mn»02«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»g«/mi»«mo»/«/mo»«mi»mol«/mi»«/mrow»«/mfrac»«mspace linebreak=¨newline¨»«/mspace»«mi»n«/mi»«mo»=«/mo»«mn»5«/mn»«mo».«/mo»«mn»549«/mn»«mo»§#160;«/mo»«mn»389«/mn»«mo»§#160;«/mo»«mn»567«/mn»«mo»§#160;«/mo»«mi»mol«/mi»«/math»
Do not round this number when calculating heat of vaporization.
Step 2: Substitute the values into the formula.
«math» «msub» «mi»H«/mi» «mrow» «mi»v«/mi» «mi»a«/mi» «mi»p«/mi» «/mrow» «/msub» «mo»=«/mo» «mfrac» «mi»Q«/mi» «mi»n«/mi» «/mfrac» «mspace linebreak=¨newline¨»«/mspace» «msub» «mi»H«/mi» «mrow» «mi»v«/mi» «mi»a«/mi» «mi»p«/mi» «/mrow» «/msub» «mo»=«/mo» «mfrac» «mrow» «mn»225«/mn» «mo».«/mo» «mn»65«/mn» «mo»§#160;«/mo» «mi»kJ«/mi» «/mrow» «mrow» «mn»5«/mn» «mo».«/mo» «mn»549«/mn» «mo»§#160;«/mo» «mn»389«/mn» «mo»§#160;«/mo» «mn»567«/mn» «mo»§#160;«/mo» «mi»mol«/mi» «/mrow» «/mfrac» «/math»
«math» «msub» «mi»H«/mi» «mrow» «mi»v«/mi» «mi»a«/mi» «mi»p«/mi» «/mrow» «/msub» «mo»=«/mo» «mfrac» «mi»Q«/mi» «mi»n«/mi» «/mfrac» «mspace linebreak=¨newline¨»«/mspace» «msub» «mi»H«/mi» «mrow» «mi»v«/mi» «mi»a«/mi» «mi»p«/mi» «/mrow» «/msub» «mo»=«/mo» «mfrac» «mrow» «mn»225«/mn» «mo».«/mo» «mn»65«/mn» «mo»§#160;«/mo» «mi»kJ«/mi» «/mrow» «mrow» «mn»5«/mn» «mo».«/mo» «mn»549«/mn» «mo»§#160;«/mo» «mn»389«/mn» «mo»§#160;«/mo» «mn»567«/mn» «mo»§#160;«/mo» «mi»mol«/mi» «/mrow» «/mfrac» «/math»
Step 3: Calculate the answer.
«math»«msub»«mi»H«/mi»«mrow»«mi»v«/mi»«mi»a«/mi»«mi»p«/mi»«/mrow»«/msub»«mo»=«/mo»«mfrac»«mrow»«mn»225«/mn»«mo».«/mo»«mn»65«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«/mrow»«mrow»«mn»5«/mn»«mo».«/mo»«mn»549«/mn»«mo»§#160;«/mo»«mn»389«/mn»«mo»§#160;«/mo»«mn»567«/mn»«mo»§#160;«/mo»«mi»mol«/mi»«/mrow»«/mfrac»«mspace linebreak=¨newline¨»«/mspace»«msub»«mi»H«/mi»«mrow»«mi»v«/mi»«mi»a«/mi»«mi»p«/mi»«/mrow»«/msub»«mo»=«/mo»«mn»40«/mn»«mo».«/mo»«mn»662«/mn»«mo»§#160;«/mo»«mn»13«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«mo»/«/mo»«mi»mol«/mi»«/math»
The heat of vaporization needs to be rounded to four significant digits, as four digits is the smallest number of digits found in the question.
Hvap=40.66 kJ/mol
The heat of vaporization of water is 40.66 kJ/mol.
«math»«msub»«mi»H«/mi»«mrow»«mi»v«/mi»«mi»a«/mi»«mi»p«/mi»«/mrow»«/msub»«mo»=«/mo»«mfrac»«mrow»«mn»225«/mn»«mo».«/mo»«mn»65«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«/mrow»«mrow»«mn»5«/mn»«mo».«/mo»«mn»549«/mn»«mo»§#160;«/mo»«mn»389«/mn»«mo»§#160;«/mo»«mn»567«/mn»«mo»§#160;«/mo»«mi»mol«/mi»«/mrow»«/mfrac»«mspace linebreak=¨newline¨»«/mspace»«msub»«mi»H«/mi»«mrow»«mi»v«/mi»«mi»a«/mi»«mi»p«/mi»«/mrow»«/msub»«mo»=«/mo»«mn»40«/mn»«mo».«/mo»«mn»662«/mn»«mo»§#160;«/mo»«mn»13«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«mo»/«/mo»«mi»mol«/mi»«/math»
The heat of vaporization needs to be rounded to four significant digits, as four digits is the smallest number of digits found in the question.
Hvap=40.66 kJ/mol
The heat of vaporization of water is 40.66 kJ/mol.
D4.18 Nugget of gold
A jewellery maker wants to melt some gold to make a ring. If he has 0.38 mol of gold and he knows gold has a heat of fusion of 13.2 kJ/mol, how much thermal energy must he add?
https://adlc.wistia.com/medias/t1yrk8sh9r
Step 1: List the variables.
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«msub»«mi»H«/mi»«mrow»«mi»f«/mi»«mi»u«/mi»«mi»s«/mi»«/mrow»«/msub»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»13«/mn»«mo».«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«mo»/«/mo»«mi»mol«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»Q«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»?«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»n«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»0«/mn»«mo».«/mo»«mn»38«/mn»«mo»§#160;«/mo»«mi»mol«/mi»«/mtd»«/mtr»«/mtable»«/math»
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«msub»«mi»H«/mi»«mrow»«mi»f«/mi»«mi»u«/mi»«mi»s«/mi»«/mrow»«/msub»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»13«/mn»«mo».«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«mo»/«/mo»«mi»mol«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»Q«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»?«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»n«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»0«/mn»«mo».«/mo»«mn»38«/mn»«mo»§#160;«/mo»«mi»mol«/mi»«/mtd»«/mtr»«/mtable»«/math»
Step 2: Rearrange the formula.
«math» «msub» «mi»H«/mi» «mrow» «mi»f«/mi» «mi»u«/mi» «mi»s«/mi» «/mrow» «/msub» «mo»=«/mo» «mfrac» «mi»Q«/mi» «mi»n«/mi» «/mfrac» «/math»
We need to isolate Q. To do this, we need to move n to the other side of the formula. Since it is being divided, we use multiplication to move it to the other side.
Q = Hfusn
If you struggle with rearranging formulas, please contact your teacher for help. This is an important skill that will be used in all of your future math and science courses!
«math» «msub» «mi»H«/mi» «mrow» «mi»f«/mi» «mi»u«/mi» «mi»s«/mi» «/mrow» «/msub» «mo»=«/mo» «mfrac» «mi»Q«/mi» «mi»n«/mi» «/mfrac» «/math»
We need to isolate Q. To do this, we need to move n to the other side of the formula. Since it is being divided, we use multiplication to move it to the other side.
Q = Hfusn
If you struggle with rearranging formulas, please contact your teacher for help. This is an important skill that will be used in all of your future math and science courses!
Step 3: Substitute the values into the formula.
Q = Hfusn
Q = (13.2 kJ/mol)(0.38 mol)
Q = Hfusn
Q = (13.2 kJ/mol)(0.38 mol)
Step 4: Calculate the answer.
Q = (13.2 kJ/mol)(0.38 mol)
Q = 5.016 kJ
This answer needs to be rounded to two significant digits, as two digits is the smallest number of digits in the question. Please note that 0.38 has two digits as the zero in front does not count.
Q = 5.0 kJ
The jewellery maker would need to add 5.0 kJ of energy to melt 0.38 mol of gold.
Q = (13.2 kJ/mol)(0.38 mol)
Q = 5.016 kJ
This answer needs to be rounded to two significant digits, as two digits is the smallest number of digits in the question. Please note that 0.38 has two digits as the zero in front does not count.
Q = 5.0 kJ
The jewellery maker would need to add 5.0 kJ of energy to melt 0.38 mol of gold.
The same jewellery maker decides to make a ring out of silver instead. He already has the 5.0 kJ of thermal energy to add, and he knows silver has a heat of fusion of 11.3 kJ/mol. How many mol of silver can he melt?
https://adlc.wistia.com/medias/pk45ls6cfz
Step 1: List the variables.
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«msub»«mi»H«/mi»«mrow»«mi»f«/mi»«mi»u«/mi»«mi»s«/mi»«/mrow»«/msub»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»11«/mn»«mo».«/mo»«mn»3«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«mo»/«/mo»«mi»mol«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»Q«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»5«/mn»«mo».«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»n«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»?«/mo»«/mtd»«/mtr»«/mtable»«/math»
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«msub»«mi»H«/mi»«mrow»«mi»f«/mi»«mi»u«/mi»«mi»s«/mi»«/mrow»«/msub»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»11«/mn»«mo».«/mo»«mn»3«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«mo»/«/mo»«mi»mol«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»Q«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»5«/mn»«mo».«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»n«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»?«/mo»«/mtd»«/mtr»«/mtable»«/math»
Step 2: Rearrange the formula.
«math» «msub» «mi»H«/mi» «mrow» «mi»f«/mi» «mi»u«/mi» «mi»s«/mi» «/mrow» «/msub» «mo»=«/mo» «mfrac» «mi»Q«/mi» «mi»n«/mi» «/mfrac» «/math»
We need to isolate n. To do this, we need to move n to the other side of the formula, since we cannot isolate a variable on the bottom of a fraction. This means we need to get rid of the fraction. Since it is being divided, we use multiplication to move it to the other side.
Q = Hfusn
Now that we have gotten rid of the fraction, we can move the Hfus to the other side to isolate n. To do this we, need to divide, since Hfus is being multiplied.
«math» «mfrac» «mi»Q«/mi» «msub» «mi»H«/mi» «mrow» «mi»f«/mi» «mi»u«/mi» «mi»s«/mi» «/mrow» «/msub» «/mfrac» «mo»=«/mo» «mi»n«/mi» «/math»
If you struggle with rearranging formulas, please contact your teacher for help. This is an important skill that will be used in all of your future math and science courses!
«math» «msub» «mi»H«/mi» «mrow» «mi»f«/mi» «mi»u«/mi» «mi»s«/mi» «/mrow» «/msub» «mo»=«/mo» «mfrac» «mi»Q«/mi» «mi»n«/mi» «/mfrac» «/math»
We need to isolate n. To do this, we need to move n to the other side of the formula, since we cannot isolate a variable on the bottom of a fraction. This means we need to get rid of the fraction. Since it is being divided, we use multiplication to move it to the other side.
Q = Hfusn
Now that we have gotten rid of the fraction, we can move the Hfus to the other side to isolate n. To do this we, need to divide, since Hfus is being multiplied.
«math» «mfrac» «mi»Q«/mi» «msub» «mi»H«/mi» «mrow» «mi»f«/mi» «mi»u«/mi» «mi»s«/mi» «/mrow» «/msub» «/mfrac» «mo»=«/mo» «mi»n«/mi» «/math»
If you struggle with rearranging formulas, please contact your teacher for help. This is an important skill that will be used in all of your future math and science courses!
Step 3: Substitute the values into the formula.
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mfrac»«mi»Q«/mi»«msub»«mi»H«/mi»«mrow»«mi»f«/mi»«mi»u«/mi»«mi»s«/mi»«/mrow»«/msub»«/mfrac»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»n«/mi»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mn»5«/mn»«mo».«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«/mrow»«mrow»«mn»11«/mn»«mo».«/mo»«mn»3«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«mo»/«/mo»«mi»mol«/mi»«/mrow»«/mfrac»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»n«/mi»«/mtd»«/mtr»«/mtable»«/math»
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mfrac»«mi»Q«/mi»«msub»«mi»H«/mi»«mrow»«mi»f«/mi»«mi»u«/mi»«mi»s«/mi»«/mrow»«/msub»«/mfrac»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»n«/mi»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mn»5«/mn»«mo».«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«/mrow»«mrow»«mn»11«/mn»«mo».«/mo»«mn»3«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«mo»/«/mo»«mi»mol«/mi»«/mrow»«/mfrac»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»n«/mi»«/mtd»«/mtr»«/mtable»«/math»
Step 4: Calculate the answer.
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mfrac»«mrow»«mn»5«/mn»«mo».«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«/mrow»«mrow»«mn»11«/mn»«mo».«/mo»«mn»3«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«mo»/«/mo»«mi»mol«/mi»«/mrow»«/mfrac»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»n«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»n«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»0«/mn»«mo».«/mo»«mn»442«/mn»«mo»§#160;«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mi»mol«/mi»«/mtd»«/mtr»«/mtable»«/math»
This answer needs to be rounded to two significant digits, as two digits is the smallest number of digits found in the question.
n = 0.44 mol
The jewellery maker can melt 0.44 mol of silver with 5.0 kJ of thermal energy.
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mfrac»«mrow»«mn»5«/mn»«mo».«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«/mrow»«mrow»«mn»11«/mn»«mo».«/mo»«mn»3«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«mo»/«/mo»«mi»mol«/mi»«/mrow»«/mfrac»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»n«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»n«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»0«/mn»«mo».«/mo»«mn»442«/mn»«mo»§#160;«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mi»mol«/mi»«/mtd»«/mtr»«/mtable»«/math»
This answer needs to be rounded to two significant digits, as two digits is the smallest number of digits found in the question.
n = 0.44 mol
The jewellery maker can melt 0.44 mol of silver with 5.0 kJ of thermal energy.
Read This
Please read pages 385 to 387 in your Science 10 textbook. Make sure you take notes on your readings to study from later. You should focus on the different calculations you can do with the heat of vaporization and the heat of fusion formulas and how to do them. Please also try the practice questions found on these pages. Remember, if you have any questions or you do not understand something, ask your teacher!
Practice Questions
Complete the following practice questions to check your understanding of the concept you just learned. Make sure you write complete answers to the practice questions in your notes. After you have checked your answers, make corrections to your responses (where necessary) to study from.
- Spring time in Alberta means lots of melting snow and ice, but how much thermal energy does this absorb from the surrounding environment? If 1 500 g of snow (known to have a heat of fusion of 6.01 kJ/mol) melts, how much thermal energy is absorbed?
Step 1: List the variables.
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«msub»«mi»H«/mi»«mrow»«mi»f«/mi»«mi»u«/mi»«mi»s«/mi»«/mrow»«/msub»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»6«/mn»«mo».«/mo»«mn»01«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«mo»/«/mo»«mi»mol«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»Q«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»?«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»n«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»?«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»m«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»1«/mn»«mo»§#160;«/mo»«mn»500«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»g«/mi»«/mtd»«/mtr»«/mtable»«/math»
Note: This question gives you the amount of water in g rather than mol. You will need to convert the mass to mol using the following formula:
«math» «mi»n«/mi» «mo»=«/mo» «mfrac» «mi»m«/mi» «mi»M«/mi» «/mfrac» «/math»
You may recognize this formula from your chemistry unit. For a review on how to use it, click here.
Remember from your chemistry unit that the molar mass or M of water is 18.02 g/mol. For a review on how to calculate molar mass, click here.
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mi»n«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mrow»«mn»1«/mn»«mo»§#160;«/mo»«mn»500«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»g«/mi»«/mrow»«mrow»«mn»18«/mn»«mo».«/mo»«mn»02«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»g«/mi»«mo»/«/mo»«mi»mol«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mi»n«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»83«/mn»«mo».«/mo»«mn»240«/mn»«mo»§#160;«/mo»«mn»843«/mn»«mo»§#160;«/mo»«mn»51«/mn»«mo»§#160;«/mo»«mi»mol«/mi»«/mtd»«/mtr»«/mtable»«/math»
Do not round this number when calculating the quantity of thermal energy.
Step 2: Rearrange the formula.
«math» «msub» «mi»H«/mi» «mrow» «mi»f«/mi» «mi»u«/mi» «mi»s«/mi» «/mrow» «/msub» «mo»=«/mo» «mfrac» «mi»Q«/mi» «mi»n«/mi» «/mfrac» «/math»
We need to isolate Q. To do this, we need to move n to the other side of the formula. Since it is being divided, we use multiplication to move it to the other side.
Q = Hfusn
If you struggle with rearranging formulas, please contact your teacher for help. This is an important skill that will be used in all of your future math and science courses!
Step 3: Substitute the values into the formula.
Q = Hfusn
Q = (6.01 kJ/mol)(83.240 843 51 mol)
Step 4: Calculate the answer.
Q = (6.01 kJ/mol)(83.240 843 51 mol)
Q = 500.277 kJ
The heat of vaporization needs to be rounded to three significant digits, as three digits is the smallest number of digits found in the question.
Q = 500 kJ
The amount of thermal energy absorbed is 500 kJ.
- Sylvan lake near Red Deer, Alberta, is a popular summer hang out spot for people of all ages. It can get quite warm in the summer, which causes the water in the lake to evaporate into the atmosphere. During dry years, the level of the lake can drop. If the sun provides 1 500 kJ of thermal energy to be absorbed by the water molecules and the heat of vaporization of water is 40.66 kJ/mol.
- How many mol of water is evaporated?Step 1: List the variables
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«msub»«mi»H«/mi»«mrow»«mi»v«/mi»«mi»a«/mi»«mi»p«/mi»«/mrow»«/msub»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»40«/mn»«mo».«/mo»«mn»66«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«mo»/«/mo»«mi»mol«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»Q«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»1«/mn»«mo»§#160;«/mo»«mn»500«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»n«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»?«/mo»«/mtd»«/mtr»«/mtable»«/math»Step 2: Rearrange the formula.
«math»«msub»«mi»H«/mi»«mrow»«mi»v«/mi»«mi»a«/mi»«mi»p«/mi»«/mrow»«/msub»«mo»=«/mo»«mfrac»«mi»Q«/mi»«mi»n«/mi»«/mfrac»«/math»
We need to isolate n. To do this, we need to move n to the other side of the formula, since we cannot isolate a variable on the bottom of a fraction. This means we need to get rid of the fraction. Since it is being divided, we use multiplication to move it to the other side.
Q = Hvapn
Now that we have gotten rid of the fraction, we can move the Hvap to the other side to isolate n. To do this, we need to divide, since Hvap is being multiplied.
«math»«mfrac»«mi»Q«/mi»«msub»«mi»H«/mi»«mrow»«mi»v«/mi»«mi»a«/mi»«mi»p«/mi»«/mrow»«/msub»«/mfrac»«mo»=«/mo»«mi»n«/mi»«/math»
If you struggle with rearranging formulas, please contact your teacher for help. This is an important skill that will be used in all of your future math and science courses!Step 3: Substitute the values into the formula.
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mfrac»«mi»Q«/mi»«msub»«mi»H«/mi»«mrow»«mi»v«/mi»«mi»a«/mi»«mi»p«/mi»«/mrow»«/msub»«/mfrac»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»n«/mi»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mrow»«mn»1«/mn»«mo»§#160;«/mo»«mn»500«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«/mrow»«mrow»«mn»40«/mn»«mo».«/mo»«mn»66«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«mo»/«/mo»«mi»mol«/mi»«/mrow»«/mfrac»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»n«/mi»«/mtd»«/mtr»«/mtable»«/math»Step 4: Calculate the answer.
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mfrac»«mrow»«mo»§#160;«/mo»«mn»1«/mn»«mo»§#160;«/mo»«mn»500«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«/mrow»«mrow»«mn»40«/mn»«mo».«/mo»«mn»66«/mn»«mo»§#160;«/mo»«mi»kJ«/mi»«mo»/«/mo»«mi»mol«/mi»«/mrow»«/mfrac»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»n«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»n«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»36«/mn»«mo».«/mo»«mn»891«/mn»«mo»§#160;«/mo»«mn»293«/mn»«mo»§#160;«/mo»«mn»65«/mn»«mo»§#160;«/mo»«mi»mol«/mi»«/mtd»«/mtr»«/mtable»«/math»
n = 36.891 293 65 mol
This answer needs to be rounded to four significant digits, as four digits is the smallest number of digits found in the question.
n = 36.89 mol
There will be 36.89 mol of water evaporated from Sylvan Lake. - How many g of water is evaporated?To convert mol to g, you need to use the following formula from the chemistry unit:
«math»«mi»n«/mi»«mo»=«/mo»«mfrac»«mi»m«/mi»«mi»M«/mi»«/mfrac»«/math»Step 1: List the variables.
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mi»n«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»36«/mn»«mo».«/mo»«mn»89«/mn»«mo»§#160;«/mo»«mi»mol«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»m«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»?«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»M«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»18«/mn»«mo».«/mo»«mn»02«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»g«/mi»«mo»/«/mo»«mi»mol«/mi»«/mtd»«/mtr»«/mtable»«/math»Step 2: Rearrange the formula.
«math»«mi»n«/mi»«mo»=«/mo»«mfrac»«mi»m«/mi»«mi»M«/mi»«/mfrac»«/math»
We need to isolate m. To do this, we need to move M to the other side of the formula. Since it is being divided, we use multiplication to move it to the other side.
nM = mStep 3: Substitute the values into the formula.
«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mi»n«/mi»«mi»M«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»m«/mi»«/mtd»«/mtr»«mtr»«mtd»«mrow»«mo»(«/mo»«mn»36«/mn»«mo».«/mo»«mn»89«/mn»«mo»§#160;«/mo»«mi»mol«/mi»«mo»)«/mo»«mo»(«/mo»«mn»18«/mn»«mo».«/mo»«mn»02«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»g«/mi»«mo»/«/mo»«mi»mol«/mi»«mo»)«/mo»«/mrow»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»m«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»m«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»664«/mn»«mo».«/mo»«mn»757«/mn»«mo»§#160;«/mo»«mn»8«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»g«/mi»«/mtd»«/mtr»«/mtable»«/math»
This answer needs to be rounded to four significant digits, as four digits is the smallest number of digits found in the question.
m = 664.8 g
664.8 g of water would evaporate from Sylvan Lake.
- How many mol of water is evaporated?