Unit 7 Chemical Quantities

mole - amount of pure substance that contains as many particles (atoms or molecules) as there are atoms in exactly 12 g of 12C isotope or the gram atomic mass of Carbon.  Particles are
		atoms for elements = gram atomic mass
		molecules for molecular compounds = gram molecular mass
		formula units for ionic compounds = gram formula mass
Molar mass = mass of 1 mol of an element

One mole of any gas at Standard Temperature and Pressure has a volume of 22.4 liters; STP is 1 atmospheric pressure and 0oC or 273K.
One mole contains Avogadro’s number of particles = 6.022 x 1023	or 602 sextillion.

CHANGING MASS TO NUMBER OF MOLES

If you find the mass of a sample of glucose (C6H12O6) to be 90.0 g, how many moles of glucose do you have?

We find the Molar mass of glucose the same way as we would find its molecular mass. We look up the masses of each atom on the periodic table, multiply by the number of atoms present and add the total.

	Carbon 	= 12.0 g  x   6 atoms 	=  72.0 g
	Hydrogen 	= 1.0 g    x 12 atoms 	=   12.0 g
	Oxygen 	= 16.0 g  x   6 atoms 	=   96.0 g
		molar mass of C6H12O6 	=  180.0 g  or 1.80 x 102 g

Now use the formula:

Given:  The mass of the sample is 90.0 g  and the molar mass of the substance is 180 g/mol.

Answer:  0.5 moles C6H12O6 

CHANGING NUMBER OF MOLES TO MASS

A certain laboratory procedure requires the use of 0.100 moles of magnesium.  How many grams of magnesium would you mass out on the balance?  

From the periodic table we get the molar mass of magnesium as 24.3 g. 

Given: The number of moles of the substance = 0.100 mol
	     molar mass of the substance = 24.3 g/mol

Answer = 2.43 g of magnesium

CHANGING NUMBER OF MOLES TO NUMBER OF  PARTICLES
One mole is always Avogadro's number, 6.02 x 1023 , so multiply the number of moles by Avogadro's number.

How many molecules of carbon dioxide are found in 2.50 moles of CO2 ?

Use this formula:

Given:  Number of moles = 2.50 mol

Answer = 1.51 x 1024 molecules of CO2   

CHANGING NUMBER OF PARTICLES TO NUMBER OF MOLES

How many moles of O2 are represented by 7.45 x 1024 molecules of O2? 
Given:  The total number of particles = 7.45 x 1024 molecules of O2

Answer = 12.4 moles of O2

CHANGING NUMBER OF PARTICLES TO MASS
This is a two-step problem.  The first step is to change the number of particles to number of moles, the second step is to change the number of moles into mass.

What would be the mass of 3.75 x 1021 atoms of iron?

First, change the number of atoms to moles:

Answer to step one = 6.23 x 10-3 moles of iron.

Next, change number of moles to mass using the equation:

Final Answer:  Mass of the iron = 0.348 g

CHANGING MASS TO A NUMBER OF PARTICLES
This is a two-step operation.  First we would change the mass to number of moles.  Then we would change number of moles to number of particles.

How many water molecules would be found in a 54.0 gram sample of water?
First, convert the mass of water to moles, i.e. find the molar mass of 54.0g of H2O:

Next, change the number of moles H2O to number of particles H2O.

Answer = 1.81 x 1024 molecules of water.

Molar volume- volume of 1 mole of a gas at STP is 22.4L. Density (in g/L) can also be used to convert volume to mass.

 CONVERTING MOLES OF A GAS TO VOLUME
What is the volume, in liters, of 0.60 mol SO2 gas at STP in significant figures?

Given:  0.60 mol SO2 and 1 mole of gas at STP = 22.4 liters

Answer= Volume of Sulfur Dioxide is 13 liters (in 2 significant figures).
	
CONVERTING DENSITY OF A GAS TO MASS
The density of a gaseous compound containing carbon and oxygen is 1.964g/L at STP.  What is the molar mass of this gas in significant figures?

Given: density of gas is 1.964g/L and 1 mole of gas @STP =22.4 L

Answer= molar mass is 43.99 g/mol in 4 significant figures

CONVERTING MASS OF A GAS TO DENSITY
What is the density of O2 gas at STP in significant figures?

Given: 1 mol O2 and 1 mole of gas at STP = 22.4 liters

Answer = Density of O2 is 1.43 g/L (in 3 significant figures).

Percent Composition and 

Chemical Formulas

Percent composition- percent by mass of each element in a compound.
Empirical formula- lowest whole number (mole) ratio of elements (atoms) in a compound.
	CO2 is a molecular and empirical formula
	C1H2O1 is an empirical formula for glucose, C6H12O6
Molecular formula- actual number of elements (atoms) in a compound.

Example 1: An 8.20g piece of magnesium combines completely with 5.40g of oxygen to form a compound.  What is the percent composition of this compound? 
Given: 8.20g Mg and 5.40g O and total mass is 13.60g

Answer: This compound contains 60.3% magnesium and 39.7% oxygen.

Example 2: Calculate the mass of carbon in 82g of propane (C3H8)

Given:  82g of propane, and the molar mass of propane is 44g.

Answer: For 82g of propane, there is 67.1g of carbon.   Because

Example 3: What is the empirical formula of a compound that is 25.9% nitrogen and 74.1% oxygen?

Convert to moles and find smallest whole-number (mole) ratio of atoms for each element.

The empirical formula must be smallest whole number (mole) ratio.  
Take the mole ratio and divide the largest number by the smallest to reduce it.

The empirical formula would be
 N1O2.50

but that formula is not made up of only whole numbers.  The formula must be the smallest whole number ratio, so the formula is doubled to make
N2O5

Another Example problem:
What is the molecular formula of methyl butanoate if the molecular weight is 102 grams and it contains 31.4% oxygen, 58.8% carbon, and 9.8% hydrogen?
Step 1: Convert to moles.

		31.4g O		1 mole O
		————   X ————   = 1.9625 mol O
				   	16 g O

		58.8g C		1 mole C
		————   X ————   = 4.9 mol C
				   	12 g C

		9.8 g H		1 mole H
		————   X ————   = 9.8 mol H
				   	1 g H

Step 2: Use the mole ratios for each element.
	   4.9				  9.8		 			1.9625
	 ———   = 2.49 C		———   = 4.99 H 		———   = 1 O
	 1.9625				1.9625	 			1.9625

Step 3: Find whole numbers for the formula.

For every molecule of methyl butanoate, there are 5 hydrogens, 2.5 carbons and one oxygen or C2.49H4.99O1

But we need whole numbers in the subscripts.  Multiplying by 2 will do that:

	C2.49 becomes C5 		H4.99 becomes H10		O1 becomes O2
	
Molecular Weight of C5H10O2 is:

C	5 x 12g = 60g		H	10 x 1g = 10g		O	2 x 16g = 32g

	Total 	= 	102 g/mol   which is the correct molecular weight.