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Dr. Ahmed Faiq Al-Alawy
Chapter 2
Moles, Density and Concentration
2.1 The Mole
In the SI system a mole is composed of 6.022 x 10^23 ( Avogadro’s number ) molecules. To convert the number of moles to mass and the mass to moles, we make use of the molecular weight
Mole Molecular Weight(MW)Mass
Thus, the calculations you carry out are
and Mass in g = (MW) (g mol) Mass in lb = (MW) (lb mol) For example
The atomic weight of an element is the mass of an atom based on the scale that assigns a mass of exactly 12 to the carbon isotope 12 C. A compound is composed of more than one atom, and the molecular weight of the compound is nothing more than the sum of the weights of atoms of which it is composed. Example 2. What is the molecular weight of the following cell of a superconductor material? (The figure represents one cell of a larger structure.)
Dr. Ahmed Faiq Al-Alawy
Solution
The molecular weight of the cell is 1764.3 g/g mol. Example 2. If a bucket holds 2.00 lb of NaOH (MW=40), how many a) Pound moles of NaOH does it contain? b) Gram moles of NaOH does it contain? Solution
Example 2. How many pounds of NaOH (MW=40) are in 7.50 g mol of NaOH? Solution
2.2 Density
Density is the ratio of mass per unit volume, as for example, kg/m^3 or lb/ft^3. Density has both a numerical value and units. Specific volume is the inverse of density, such as cm^3 /g or ft^3 /lb.
For example , given that the density of n-propyl alcohol is 0.804 g/cm^3 , what would be the volume of 90.0 g of the alcohol? The calculation is
Dr. Ahmed Faiq Al-Alawy
Example 2. If a 70% (by weight) solution of glycerol has a specific gravity of 1.184 at 15°C, what is the density of the solution in (a) g/cm^3? (b) lbm/ft^3? and (c) kg/m^3? Solution (a) (1.184 g glycerol/ cm^3 )/(1 g water/ cm^3 ) * (1 g water/ cm^3 ) = 1.184 g solution/cm^3. (b) (1.184 lb glycerol/ft^3 )/(1 lb water/ft^3 ) * (62.4 lb water/ft^3 ) = 73.9 lb solution/ft^3. (c) (1.184 kg glycerol/m^3 )/(1 kg water/m^3 ) * (1000 kg water/m^3 ) = 1.184 * l0^3 kg solution/m^3.
The specific gravity of petroleum products is often reported in terms of a hydrometer scale called °API. The equation for the API scale is
The volume and therefore the density of petroleum products vary with temperature , and the petroleum industry has established 60 °F as the standard temperature for volume and API gravity. Example 2. In the production of a drug having a molecular weight of 192, the exit stream from the reactor flows at a rate of 10.5 L/min. The drug concentration is 41.2% (in water), and the specific gravity of the solution is 1.024. Calculate the concentration of the drug (in kg/L) in the exit stream, and the flow rate of the drug in kg mol/min. Solution Take 1 kg of the exit solution as a basis for convenience. Basis: 1 kg solution
Dr. Ahmed Faiq Al-Alawy
To get the flow rate, take a different basis, namely 1 minute. Basis: 1 min = 10.5 L solution
2.4 Flow Rate
For continuous processes the flow rate of a process stream is the rate at which material is transported through a pipe. The mass flow rate ( m ) of a process stream is the mass ( m ) transported through a line per unit time ( t ).
The volumetric flow rate (F) of a process stream is the volume (V) transported through a line per unit time.
The molar flow (n) rate of a process stream is the number of moles ( n ) of a substance transported through a line per unit time.
2.5 Mole Fraction and Mass (Weight) Fraction
Mole fraction is simply the number of moles of a particular compound in a mixture or solution divided by the total number of moles in the mixture or solution. This definition holds for gases , liquids , and solids. Similarly, the mass (weight) fraction is nothing more than the mass (weight) of the compound divided by the total mass (weight) of all of the compounds in the mixture or solution. Mathematically, these ideas can be expressed as
Mole percent and mass (weight) percent are the respective fractions times 100. Example 2. An industrial-strength drain cleaner contains 5 kg of water and 5 kg of NaOH. What are the mass (weight) fractions and mole fractions of each component in the drain cleaner container?
Dr. Ahmed Faiq Al-Alawy
2.7 Concentration
Concentration generally refers to the quantity of some substance per unit volume. a. Mass per unit volume (lb of solute/ft^3 of solution, g of solute/L, lb of solute/barrel, kg of solute/m^3 ). b. Moles per unit volume (lb mol of solute/ft^3 of solution, g mol of solute/L, g mol of solute/cm^3 ). c. Parts per million ( ppm ); parts per billion ( ppb ), a method of expressing the concentration of extremely dilute solutions; ppm is equivalent to a mass (weight) fraction for solids and liquids because the total amount of material is of a much higher order of magnitude than the amount of solute; it is a mole fraction for gases. d. Parts per million by volume (ppmv) and parts per billion by volume (ppbv) e. Other methods of expressing concentration with which you may be familiar are molarity (g mol/L), molality (mole solute/kg solvent), and normality (equivalents/L). Example 2. The current OSHA 8-hour limit for HCN (MW = 27.03) in air is 10.0 ppm. A lethal dose of HCN in air is (from the Merck Index) 300 mg/kg of air at room temperature. How many mg HCN/kg air is 10.0 ppm? What fraction of the lethal dose is 10.0 ppm? Solution Basis: 1 kg mol of the air/HCN mixture
Example 2. A solution of HNO 3 in water has a specific gravity of 1.10 at 25°C. The concentration of the HNO 3 is 15 g/L of solution. What is the a. Mole fraction of HNO 3 in the solution?
Dr. Ahmed Faiq Al-Alawy b. ppm of HNO 3 in the solution? Solution Basis: 1 L of solution
Basis: 100 g solution The mass of water in the solution is: 100 – 1.364 = 98.636 g H 2 O. g MW gmol mol fraction HNO 3 1.364 63.02 0.02164 0. H 2 O 98.636 18.016 5.475 0. Total 5.4966 1
Example 2. Sulfur trioxide (SO 3 ) can be absorbed in sulfuric acid solution to form more concentrated sulfuric acid. If the gas to be absorbed contains 55% SO 3 , 41% N 2 , 3% SO 2 , and 1% O 2 , how many parts per million of O 2 are there in the gas? What is the composition of the gas on a N 2 free basis? Solution
Example 2. To avoid the possibility of explosion in a vessel containing gas having the composition of 40% N 2 , 45% O 2 , and 15% CH 4 , the recommendation is to dilute the gas mixture by adding an equal amount of pure N 2. What is the final mole fraction of each gas? Solution
The basis is 100 moles of initial gas
Dr. Ahmed Faiq Al-Alawy
- A cubic centimeter of mercury has a mass of 13.6 g at Earth’s surface. What is the density of mercury?
- What is the approximate density of water at room temperature in kg/m^3?
- For liquid HCN, a handbook gives: sp. gr. 10°C/4°C = 1.2675. What does this statement mean?
- Answer the following questions true or false: a. The density and specific gravity of mercury are the same. b. Specific gravity is the ratio of two densities. c. If you are given the value of a reference density, you can determine the density of a substance of interest by multiplying by the specific gravity. d. The specific gravity is a dimensionless quantity.
- A mixture is reported as 15% water and 85% ethanol. Should the percentages be deemed to be by mass, mole, or volume?
- Answer the following questions true or false: a) In engineering practice the compositions of liquids and solids are usually denoted in weight (mass) fraction or percent. b) In engineering practice the composition of gases is usually denoted in mole fraction or percent. c) e. A pseudo-average molecular weight can be calculated for a mixture of pure components whether solid, liquid, or gases.
- Do parts per million denote a concentration that is a mole ratio?
- Does the concentration of a component in a mixture depend on the amount of the mixture?
- Pick the correct answer. How many ppm are there in 1 ppb? (a) 1000, (b) 100, (c) 1, (d) 0.1, (e) 0.01, (f) 0.001?
- How many ppb are there in 1 ppm?
- Does 50 ppm represent an increase of five times a value of 10 ppm?
Answers:
- (a) T; (b) T; (c) T
- No
- (a) T; (b) T; (c) T
- 13.6 g/cm^3
- 1000 kg/m^3
Dr. Ahmed Faiq Al-Alawy
- The statement means that the density at 10°C of liquid HCN is 1.2675 times the density of water at 4°C.
- (a) F – the units differ; (b) T; (c) T; (d) F.
- Mass
- (a) T; (b) T; (c) T
- For gases but not for liquids or solids.
- No
- 1000
- No (4 times)
Problems
- Convert the following: a) 120 g mol of NaCl to g. b) 120 g of NaCl to g mol. c) 120 lb mol of NaCl to lb. d) 120 lb of NaCl to lb mol.
- Convert 39.8 kg of NaCl per 100 kg of water to kg mol of NaCl per kg mol of water.
- How many lb mol of NaNO 3 are there in 100 lb?
- The density of a material is 2 kg/m^3. What is its specific volume?
- An empty 10 gal tank weighs 4.5 lb. What is the total weight of the tank plus the water when it is filled with 5 gal of water?
- If you add 50 g of sugar to 500 mL of water, how do you calculate the density of the sugar solution?
- For ethanol, a handbook gives: sp. gr. 60°F = 0.79389. What is the density of ethanol at 60°F?
- The specific gravity of steel is 7.9. What is the volume in cubic feet of a steel ingot weighing 4000 lb?
- The specific gravity of a solution is 0.80 at 70°F. How many cubic feet will be occupied by 100 lb of the solution at 70°F?
- A solution in water contains 1.704 kg of HNO 3 /kg H 2 O, and the solution has a specific gravity of 1.382 at 20°C. What is the mass of HNO 3 in kg per cubic meter of solution at 20°C?
Dr. Ahmed Faiq Al-Alawy
- 0.79389 g/cm^3 (assuming the density of water is also at 60°F)
- 8.11 ft^3
- 2 ft^3
- 870 kg HNO 3 /m^3 solution.
- 132 min
- 0.654 kg mol/hr
- 9
- SO 2
- 14.8 kg
- O 2 0.62; SO 2 0.19; SO 3 0.
- (d)
- 72.17 lb
- (a) C 4 : 0.50, C 5 : 0.30, C 6 : 0.20; (b) C 4 : 0.57, C 5 : 0.28, C 6 : 0.15; (c) C 4 : 57, C 5 : 28, C 6 : 15; (d) 66.4 kg/kg mol
- 12000 mg/L
Supplementary Problems (Chapter Two):
Problem 1
Dr. Ahmed Faiq Al-Alawy
Problem 2
Problem 3
Dr. Ahmed Faiq Al-Alawy
Problem 7
Solution
Problem 6
