part I

MOLE

1 mole = 6.02 x 10²³ things (Avogadro’s number)

If the mass of an element is equal to its atomic mass there is 1 mole of the element.

Example

1. In 16 g of O there is 1 mole of O and 6.02 x 10²³ O atoms

2. In 32g of O there are 2 moles of O and 2 (6.02 x 10²³) O atoms

3. In 4 moles of H there are 4 moles of H and 4 (6.02 x 10²³) O atoms

4. In 18 g of H₂O there are

        1 mole of H₂O therefore 6.02 x 10²³ H₂O molecules

        2 moles of H atoms therefore 2 (6.02 x 10²³) H atoms

        1 mole of O atoms  therefore 6.02 x 10²³ O atoms

5. In 36 g of H₂O there are

        2 mole of H₂O therefore 2 (6.02 x 10²³) H₂O molecules

        4 moles of H atoms therefore 4 (6.02 x 10²³) H atoms

        2 moles of O atoms therefore 2 (6.02 x 10²³) O atoms

COLLIGATIVE PROPERTIES OF SOLUTIONS

The colligative properties depend only on the concentration of the solute and not on the nature of the solute.

Boiling point elevation

For water

K_b (boiling point elevation) = .52 ⁰C/m            

Freezing point depression

For water

K_f (freezing point depression) = 1.86 ⁰C/m

m = molality (moles of solute/kg of solvent)

molality is not temperature dependent because no volume is present in the formula

Molarity is temperature dependent because volume is present in the formula. As T Increases V increases.

Problems:

1) Calculate the molality when 75.0 grams of MgCl₂ is dissolved in 500.0 g of solvent.

2) 49.8 grams of KI is dissolved in 1.00 kg of solvent. What is the molality?

3) What is the molality of a solution made by dissolving 0.1356 g MgSO₄ in 200.0 mL of water?

4) What is the molality of a solution of 6.44 g of Cd(NO₃)₂ in 375.0 g of water?

5) How many grams of Sr(ClO₄)₂ are required to make a 0.30 m aqueous solution using 600 g of water?

6) What is the molality of a 0.123 M HCl(aq) solution? The density of the solvent is 1.030 g/mL.

The formula to use for the two properties above is ΔT = K_b m i                 

ΔT = change in T from the pure solvent boiling or freezing point.

i = van Hoff factor

The van Hoff factor is the number of moles of particles dissolved in the solvent.

Example:

In NaCl(aq) i = 2 because NaCl(aq) --> Na⁺(aq) +Cl^-(aq)

In CaCl₂(aq) i = 3 because CaCl₂ (aq) -->Ca²⁺(aq) + 2 Cl^-(aq)

In C₆H₁₂O₆(aq) i = 1 because C₆H₁₂O₆ (aq) --> C₆H₁₂O₆ (aq)

Problems:

1) Calculate the boiling point of a solution containing 4 moles of (NH₄)₂CO₃(s) dissolved in 500. g of water?

2) Calculate the freezing point of a solution containing 2 moles of Ca(NO₃)(s) dissolved in 2 kg of water?

3) What is the Kb of a solvent, if 3 moles of a sugar are dissolved in 2,500 g of solvent and the change in temperature is 2^oC?

4) Calculate the boiling point of a solution of 0.0222 m glucose, a non-electrolyte in water.

5) What would be the boiling point of a solution when 20. g of Ca₃(PO₄)₂(s) are dissolved in 4 kg of water?

6) Seawater contains 3.5% (by weight) of dissolved NaCl(s). Calculate the normal boiling point of seawater.

7) Calculate the molar mass of sulfur if 35.5 grams of sulfur dissolve in 100.0 grams of CS₂ to produce a solution that has a boiling point of 49.48^oC. The Kb for CS₂ is 2.35^oCand its boiling point is 46.23^oC.

Hint: First, solve for m. Second, calculate the number of moles of solute in the solution. Finally, remember that molar mass is g/mol.

8) Compare the molar mass of sulfur in the periodic table and your answer to question 7.

MOLE FRACTION

X = partial # moles / total amount of moles

Problems

1) What is the mole fraction of O₂ in a mixture of 2 mole O₂ and 3 moles of N₂?

ALLOY

A mixture of pure metals is called an alloy. The melting point of an alloy will be lower than either of the component metals because the new bonds are formed between different atoms which in general results in weaker bonds.

ORGANIC SOLVENTS

Organic solvents are usually nonpolar.

SPECIFIC GRAVITY

Specific gravity of a substance is the density of the substance over the density of water.

Problems

1) A cylinder of plastic is 100 mm long, and 50 mm in diameter. It has a mass of 1 kg. Determine its specific gravity and indicate whether it would float or sink in water. The density of water is 1 g/mL.

2) A piece of unknown material has an intricate shape. It has a mass of 126 g. You submerge it to find it displaces 422 ml of water. What is the specific gravity of the piece?

NETWORK SOLIDS

Network solids are solids where atoms are all covalently bonded to one another therefore, no molecules are present. They are usually hard except for graphite which is used as a lubricant. They have high melting point and low conductivity.

Example

Diamond, graphite and SiO₂

Note: Graphite is soft and has some conductivity

UNIT CELL

The simplest repeating unit in a crystal is called a unit cell. Each unit cell is defined in terms of lattice points (the points in space about which the particles are free to vibrate)

Crystals could be divided into many unit cells categories.

In the simple cubic unit cell there are eight equivalent particles on the eight corners.

In the body-centered cubic unit cell there are eight identical particles on the eight corners but a ninth identical particle is present in the center of the body of the unit cell.

In the face-centered cubic unit cell there are eight identical particles on the eight corners and six more, each located in the centers of the six faces of the unit cell.

part II

IDEAL GAS EQUATION

PV = nRT     

n = moles of gas         

R = universal gas constant (0.08206 L atm/ K mol)

Problems

1.  A sample of H₂(g) has a volume of 8.56L at a T of 0^oC and P of 1.5 atm. How many moles of H₂ are present?

2. How many moles are present in 1.75L of N₂ at STP?

3. Calculate the pressure of 26.94 g of O₃ at 44.8^oC in a 200 mL container.

4. Calculate the volume of 30.0 g of CH₄ at 298K and 1.50 atm.

5. Calculate the total pressure in atm of a mixture of 0.0325 mol of H₂ and 0.0623 mol of O₂, in a 3.25 L flask at 25.0 ^oC. Assume ideal gas behavior.

6. If 200 mL of N₂ at 25^oC and 400 mm Hg, and 200 mL of O₂ at 25^oC and 300 mm Hg are placed in a 700 mL vessel, what is the total pressure of the mixture?

MOLAR VOLUME OF GAS

At  STP 1 mole of any gas occupies a volume of 22.4 L

Use the ideal gas equation to prove it.

PARTIAL PRESSURE FROM MOLE RATIO

In a mixture of gases the partial pressure of any gas is equal the mole ratio of the gas multiplied by the total pressure.

Problems

1. What is the partial pressure of helium in a mixture consisting of 3 moles of helium and 7 moles of oxygen at sea level?

2. Calculate the partial pressure of gas A in a mixture of 1.0 mol of gas A and 2.0 mol of gas B in a 4.0 L container if the total pressure is 2.5 atm. Assume ideal gas behavior.

HYDROGEN BONDING

A strong intermolecular attraction between hydrogen and either F, O, or N

VAPOR PRESSURE OF SOLUTION

A nonvolatile solute added to a solvent lowers the vapor pressure of the solvent.

NORMAL BOILING POINT

Normal = sea level = 1 atm

TRIPLE PHASE DIAGRAM

The triple point is where the three states of matter co-exist in equilibrium.

When pressure increases both the melting and boiling points increase. The exception is when the solid-liquid line is negative in this case only the boiling point increases while the melting point decreases

The slope of the solid-liquid line is negative if the liquid state is denser than the solid states.

UNITS OF PRESSURE

1 atm = 101.3 kPa = 760 mm Hg = 760 torr

MANOMETER

A manometer is an instrument that measures the pressure of gases.

GRAHAM’S LAW OF EFFUSION

Effusion is the passage of a gas through a tiny hole into an evacuated chamber. The rate of transfer is the rate of effusion.

The smallest the mass of a gas is, the faster it will effuse.

r₁ / r₂ = t₂ / t₁ = (MW₂ / MW₁)^1/2

r₁ = rate of effusion of gas 1

r₂ = rate of effusion of gas 2

t₁ = time required for effusion of gas 1

t₂ = time required for effusion of gas 2

MW₁ = molecular weigh of gas 1

MW₂ = molecular weigh of gas 2

Problems

1. At STP, which gas on the periodic table of elements effuse the fastest?

2. At STP, which gas on group 18 effuse the fastest?

3. If 0.50 moles of CO2 effuse in 74.7 seconds, how long will it take for 0.50 mol of He to effuse under identical conditions?

4. A given volume of ozone required 95.2 s to effuse. Under the same conditions, another gas required 66.5 s for the same volume to effuse. What is the molar mass of this gas?

ENTROPY

Entropy is the measure of disorder.

Ex. Entropy increases from solid to liquid to gas

SUBLIMATION

CO₂, I₂, and naphthalene are examples of substances that sublime.

COLLECTION OF GAS

Some gases can be collected through the displacement of water. In this case the vapor pressure above the water is equal to the vapor pressure of the gas collected plus the vapor pressure of the water above the water.

Problems

1. Oxygen is collected over water at 25 ºC and the resulting mixture over the water has a pressure of 760 torr. What is the pressure of oxygen? The vapor pressure of H₂O at 25 ºC is 19.0 torr.

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