Chapter 6. Gases, Solutions, Colloids and Suspensions

Gases and Pressure

Gas properties are measured in 4 variables:

Pressure

Volume

Temperature

Mole

These specify the characteristics of a gas.

Barometric Pressure

Atmoshere has air pressure. Because of gravitational pull of Earth, air has the highest density at the sea level, hence higher pressure.

Pressure is a force exerted by the molecules of gas to an area. We can measure atmospheric pressure by using a barometer. Torrichelli in mid 1600s made the following set-up by using mercury, Hg, to measure barometric pressure.

The curved red arrow indicate that the atmospheric pressure is exerted upward into the tube, opposing the gravity.

At the sea level, the height of column is quite stable at 76 cm or 760 mm, deviating only few mm day to day. The 1 mm in mercury column is called 1 torr, and when the barometric pressure is 760 mmHg, we define it as 1 atmoshpere (atm) of pressure.

Manometer measures the pressure of gas. The device is a round-bottom flask connected to a bent glass tube such that one can place mercury in to measure the pressure of a gas in comparison to the atmospheric pressure.

The Gas Laws

The Ideal Gas Law combines 4 different limited laws of gas.

Boyle's Law: Relationship b/w pressure (P) and volume (V)
P ∝ 1/V, then P = c/V Notice that when proportionality is converted to an equation, it gains proportionality constant c.

Gay-Lussac's law: Relationship b/w pressure (P) and temperature (T)
P ∝ T, then P = cT

Charles' Law: Relationship b/w volume (V) and temperature (T)
V ∝ T, then V = cT

Avogadro's Law: Relationship b/w volume (V) and mole (n)
V ∝ n, then V = cn

With these laws, we can comnbine to obtain

PV = nRT

We replaced the proportionality constant c by R with its value = 0.0821 atm L/mol K.

We can change the condition of gas from its initial state to the final state. $R = \frac{P_{i} V_{i}}{n_{i} T_{i}} = \frac{P_{f} V_{f}}{n_{f} T_{f}}$ We can do this, because R is a constant. Solve for R, you get R = (PV)/(nT). The ratio of PV to nT is always R.

Example:a) What is the volume of 1.00 mole of methane (CH₄) measured at 1.00 atm and at 0.00°C? b) What is the volume of 1.00 mol of butane (C₄H₁₀) measured at 1.00 atm and at 0.00°C?

a) Since PV = nRT, we rearrange it to solve for V, $V = \frac{n R T}{P}$ Before using the above, we need to convert 0°C to Kelvin temperature. T(K) = T(°C) + 273, therefore T = 273K. Then, $V = \frac{n R T}{P} = \frac{(1 m o l) (0.0821 L a t m / m o l K) (273 K)}{1 a t m} = 22.4 L$

b) The answer is the same as above. Since there is no distinction between molecules of gas, if the condition is the same, they all behave (in this case the volume) the same way!

Partial Pressure

Given that volume and temperature are constant, pressure is additive.

In above case P_N₂ + P_O₂ = P_total

The image below is an example of how we use partial pressure.

Location>	Partial Pressure
Air	$P_{O_{2}} = 160 t o r r$	$P_{{C O}_{2}} = 0.3 t o r r$
Alveoli	$P_{O_{2}} = 104 t o r r$	$P_{{C O}_{2}} = 40 t o r r$
Blood leaving alveoli	$P_{O_{2}} = 104 t o r r$	$P_{{C O}_{2}} = 40 t o r r$
At tissue level	$P_{O_{2}} = 40 t o r r$	$P_{{C O}_{2}} = 45 t o r r$
Back to alveoli	$P_{O_{2}} = 40 t o r r$	$P_{{C O}_{2}} = 45 t o r r$
Exhaled air	$P_{O_{2}} = 120 t o r r$	$P_{{C O}_{2}} = 27 t o r r$

Example:A mixture of gases contains 0.75 mol of N₂, 0.25 mol of O₂, and 0.20 mol of He. What is the partial pressure of each gas, if the mixture is held in a container with 50.0 L at 300 K? What is the total pressure?

First, let's see what we have. We're talking about gases, which means that we are dealing with IGL, PV = nRT. Since P_total = Sum of all P_i, we can solve for P = nRT/V.

Solutions

Soution is a two-component system of mixture:

Solute = small part

Solvent = larger part

Mixture has two types:

homogeneous mixture = no phase separation, one continuous phase, such as a cup of coffee

heterogeneous = having two different phases, such as oil and vinegar

Solubility = how much solute would dissolve in solvent

soluble substance = dissolves in the solvent and makes homogenous mixture.

insoluble substance = doesn't dissolve in the solvent. Two different phases, solid (from solute) and liquid (from solvent).

Then, which substance dissolve in a certain solvent?

Like dissolves like

What this means is that if solvent is polar, polar solute would dissolve easily.

Like dissolves like. Similar molecules have similar groups (substituents), therefore they have similar intermolecular forces so that they can dissolve each other.

Here is the solubility of alcohols in water. Alcohol has OH group, which can hydrogen-bond to water to dissolve. As the chain length gets longer, it becomes more non-polar (fat-like) thus reducing the solubility.

Name	Formula	Solubility in water
Methanol	CH₃OH	Completely
Ethanol	CH₃CH₂OH	Completely
Propanol	CH₃CH₂CH₂OH	Completely
Butaanol	CH₃CH₂CH₂CH₂OH	74g/100g H2O
Pentanol	CH₃CH₂CH₂CH₂CH₂OH	27g
Hexanol	CH₃CH₂CH₂CH₂CH₂CH₂OH	6 g
Heptanol	CH₃CH₂CH₂CH₂CH₂CH₂CH₂OH	1.7 g
Octanol	CH₃CH₂CH₂CH₂CH₂CH₂CH₂CH₂OH	0 g

Precipitation Rxns

If the product of a reaction forms a solid, it is classified as precipitation reaction. We saw in the lab #5 that: 2KI(aq) + Pb(NO₃)₂(aq) → 2KNO₃(aq) + PbI₂(s) yellow!

NaCl(aq) + AgNO₃(aq) → KNO₃(aq) + AgCl(s) milky white

BaCl₂(aq) + Na₂CrO₄(aq) → 2NaCl(aq) + BaCrO₄(s) yellow!

Solubility of Gases in Water

The carbonated drinks, such as coke, is made of sugar water and carbon dioxide dissolved in the solution. You know from experience that when pressure is high more CO₂ is dissolved. This is called Henry's Law.

Organic and Biochemical Compounds

Biological processes are carried out in the aqueous environment. Each cell is confined to have efficient biochemical processes. Nature chose to utilize the phase separation between water and hydrocarbon to make the confinement, called cell membrane.

Cell membrane is made up of amphiphilic (or amphipathic) compounds that have property that they dissolve both in polar solvent (water) and non-polar solvent (fat). The polar compounds that dissolves in water is called hydrophilic.

There are several different kinds of membrane lipid. Here one of them is shown.

In the video below, each of the membrane lipids is described by blue head group and yellow tail group. Light blue (or light purple?) molecules are water molecules. As you can see there are many many membrane lipids to form a biological cell.

There are few things noticeable:

Membrane lipids are in constant motion!

Large protein molecules protrude from the membrane

Membrane is relatively flexible -- afterall they are held by London force in the tail group region and held by dipole-dipole interaction in the head group region

Concentration

Remember from previous chapters, solution = two-component system

Small part = solute

Large part = solvent

Concentration in general tells how much solute is in given solvent.

Percent, Parts per Thousand, Parts per Million, and Parts per Billion

You can even think about density to be a kind of concentration. In this sense, weight/volume percent is

%_{W / V} = \frac{g_{s o l u t e}}{m L_{s o l u t i o n}} \times 100 %

Instead of multiplying with 100, and multiply with 1000, then it becomes weight/volume parts per thousand (ppt)

p p t_{W / V} = \frac{g_{s o l u t e}}{m L_{s o l u t i o n}} \times 1000

What if multiply by 1 000 000, it becomes weight/volume parts per million (ppm)

p p m_{W / V} = \frac{g_{s o l u t e}}{m L_{s o l u t i o n}} \times 1000000

You can go even here by multiplying by 1 000 000 000, to weight/volume parts per billion (ppb).

p p b_{W / V} = \frac{g_{s o l u t e}}{m L_{s o l u t i o n}} \times 1000000000

Example:Thalidomide, sold to alleviate morning sickness, is a teratogenic agent that caused severe birth defect in infants in the 50s and 60s. The structure of thalidomide has two forms as shown below.

According to Wiki, the avergae weight of female in the U.S. is 76 kg or 168 lb. The morning sickness pill contains only 50.0 mg of thalidomide. Calculate the weight/volume ppm of thalidomide to the human volume. The density of human body is 985 kg/m³ or 985 X 10⁶ kg/cm³

The definition of ppm_w/v is as follows. $p p m_{w / v} = \frac{g_{t h a l i d o m i d e}}{m L_{b o d y}} \times 10^{6}$ We need first to convert 76 kg weight to volume in mL. It is more convenient to use 985 X 10^-6 kg/cm³, since 1 cm³ = 1 mL. Then, $? m L_{b o d y} = 76 k g (\frac{10^{6} c m^{3}}{985 k g}) (\frac{1 m L}{1 c m^{3}}) = 7.72 \times 10^{4} m L$ Use this result, and if we place 50 mg which is 50 X 10^-3 g into the ppm equation. $p p m_{w / v} = \frac{g_{t h a l i d o m i d e}}{m L_{b o d y}} \times 10^{6} = \frac{50 \times 10^{- 3} g}{7.72 \times 10^{4} m L} \times 10^{6} = 0.648 p p m$ The concentration in ppm is a small quantity. However, effect of the drug is very dramatic.

Molarity

Molarity, M, is one of the most used unit of concentration in chemistry. It is difined as

M = \frac{m o l_{s o l u t e}}{1 L_{s o l u t i o n}} = \frac{m o l_{s o l u t e}}{1000 m L_{s o l u t i o n}}

I like using the mol/10³mL simply because it is more covenient. By knowing the concentration of solution, one can convert # of moles of solute to volume of solution, and vice versa.

Example:Calculate the molarity of solution if you dissolve 10.0 g of HCl into 200 mL of water.

Since the definition of molarity is $M = \frac{m o l_{H C l}}{L_{H C l s o l' n}}$ So, we need 10.0 g converted to mole (in the numerator) and we need to convert 200 mL to L. $? m o l_{H C l} = 10.0 g_{H C l} (\frac{1 m o l_{H C l}}{36.458 g_{H C l}}) = 0.274 m o l_{H C l}$ and $? L = 200 m L (\frac{1 L}{1000 m L}) = 0.200 L$ Put them together, $M = \frac{m o l_{H C l}}{L_{H C l s o l' n}} = \frac{0.274 m o l}{0.200 L} = 1.37 M$

Example:How many moles of HCl are there in 50.0 mL of 1.37M HCl solution?

Simple dimensional analysis yields: $? m o l_{H C l} = 50.0 m L_{H C l} (\frac{1.37 m o l_{H C l}}{1000 m L_{H C l}}) = 0.0685 m o l_{H C l}$

Equivalent

Equivalent = # of moles of charges that one mole of solute contributes to a solution. So, if you have Na⁺ solution, 1 mol_Na⁺ = 1 Eq,

1 mol_Mg²⁺ = 2 Eq_Mg²⁺

1 mol_OH^- = 1 Eq_OH^-

1 mol_CO₃^2- = 2 Eq_CO₃^2-

1 mol_PO₄^3- = 3 Eq_PO₄^3-

1 mol_Mg²⁺ = 2 Eq_Mg²⁺

Example:The normal serum concentration of chloride ion (Cl^-) is 95-107 mmol/L. Convert the range into mEq/L.

Since 1 mol_Cl^- = 1 Eq_Cl^-, then it also must mean that 1 mmol_Cl^- = 1 mEq_Cl^-. Therefore, 95-107 mmol/l = 95-107 mEq/L.

Example:How many mEq of bicarbonate (HCO₃^-) are present in a 75.0 mL of blood serum sample with a concentration of 25 mEq/L HCO₃^-?

You can cast this into dimensional analysis: $? m E q_{H C O_{3}^{-}} = 75.0 m L_{H C O_{3}^{-}} (\frac{1 L}{1000 m L}) (\frac{25 m E q}{1 L}) = 1.875 m E q = 1.9 m E q$

Dilution

Making a less concentrated solution from more concentrated solution is called dilution. The higher concentration solution is often called stock solutioin. This is best described by examples:

Example:Let's say that you have 500 mL of 1.00 M solution of HCl. If you add 250 mL of water into the solution, what is the new concentration?

Since M = mol/L, and originally you have 500 mL and you added 250 mL. Thus you have 750 mL = 0.75 L altogether now. So, you have the denominator. Now you need to know how many moles of HCl there are in the original solution. Do dimensional analysis. $? m o l_{H C l} = 500 m L_{H C l} (\frac{1 m o l_{H C l}}{1000 m L_{H C l}}) = 0.500 m o l_{H C l}$ Therefore, $M = \frac{m o l_{H C l}}{L_{H C l s o l' n}} = \frac{0.500 m o l}{0.750 L} = 0.667 M$

Example:You are asked to prepare 200 mL of 0.100 M HCl from 1.20 M HCl. How many mL of stock solution do you need?

This is a dimensional analysis problem. $? m L_{s t o c k} = 200 m L_{H C l} (\frac{0.100 m o l_{H C l}}{1000 m L_{H C l}}) (\frac{1000 m L_{s t o c k}}{1.20 m o l_{H C l s t o c k}}) = 16.7 m L_{H C l}$ So, you take 16.7 mL of the HCl stock solution and place it in a 200 mL volumetric flask, and put water to the 200 mL mark. The volumetric flask is a flask that has only one measurement line.

Colloids and Suspensions

Suspension = relatively large particles (larger than 1 μm) suspended in solution

Colloid = particles are much smaller(1 nm - 1 μm), but the solute is not dissolved.

Fog is aerosol, which is liquid droplets suspended in gas(air).
Whipped cream is called foam, which is gas bubbles suspended in liquid.
Mayonnaise is an emulsion, which is liquid droplets are suspended in liquid.

Solution = solute (less than 1 nm) is fully dissolved

Diffusion and Osmosis

Motion of molecules from relatively more concentrated to lower concentration region is called diffusion.

Osmosis = motion of water from lower solute concentration to higher solute concentration solution.

Hypertonic solution = a solution with higher concentration of water in a cell. (relatively less solute molecules)

Hypotonic solution = a solution with lower concentration of water in a cell. (relatively more solute molecules)

In comparison to the normal red blood cell, the cell swells up in the hypotonic solution, and eventually hemolysis occurs. In the hypertonic solution, water in the cell comes out, and creating crenation.

Colligative Properties

Properties of solution that depends only on the concentration regardless of the kinds of solute. There are 4 types:

Osmosis
Boiling point elevation
Freezing point depression -- responsible for melting of ice on the streets of NYC in winter (spreading salt on snow covered street).
Vapor pressure lowering -- this is why we can moon-shine!

Among the colligative properties, osmosis might be most interesting to you. Kidney dialysis is to utilize osmosis to eliminate unwanted and toxic substance that are usually filtered in your kidney. Patients with kidney malfunction has to get rid of the toxins in their blood.