# Colligative properties, cont.

### Osmotic pressure ()

V = nRT; or, dividing both sides by V, = MRT, where M = molarity.

Example: What are the osmotic pressures of 1.00 M sugar and 1 M aluminum chloride solutions at 25°C?

sugar= MRT = (1 mol/L)(0.0821 L*atm/mol*K)(298 K) = 24.5 atm

AlCl3= MRT = (1 mol/L)(4 mol ion/mol)(0.0821 L*atm/mol*K)(298 K) = 97.9 atm

### Colloids

Colloids are defined by particle size = 1.0 nm< colloid < 100 nm (particles in solution are 0.1 - 1.0 nm in diameter, whereas particles > 100 nm dispersed in a fluid are considered to be in suspension.) Colloids generally do not settle out.

• Biomacromolecules are often colloidal (proteins, DNA & RNA)
• particles in inks are sometimes colloidal.

# Chemical Kinetics

Study of rates and mechanisms of reactions. Experimentally, look at rates of reactions, use this information to guess mechanisms

• Rate is a measure of how fast the reaction goes. Can measure how fast a reactant is used up, or how fast a product appears. Use the stoichiometry of the reaction to relate a particular rate to the overall reaction rate.
• A mechanism is a detailed description of the steps leading from reactants to products.

### Concentration Dependence of Reaction Rates

Concentrations are assumed to be in Molarity unless otherwise specified.

Consider the reaction:

A + 2B+ C D + E

• Let's assume that if [A] is doubled while all other concentrations are unchanged, that the rate doubles. We can then say that the rate is proportional to [A]; r [A]
• Let's now assume that if [B] is doubled the rate quadruples, while 3 x [B] gives 9 x rate (again, all other concentrations are unchanged). We can say that the rate is proportional to the square of [B]; r [B]2.
• Finally let's say that if [C] is changed, no effect is seen on the rate; r [C]0 or r = constant.
• We can now combine these expressions to give

r [A] [B]2 [C]0,or

r = k [A] [B]2

This expression is referred to as a Rate Lawwith the sum of various exponents referred to as the order of the reaction. The overall order of this reaction is thus 3rd order - it is first order in A, second order in B, and zero order in C.

Looking at the different reaction orders:

• First Order: For A C, or A + B C + D, etc.
• r = k [A]; & r =-d [A]/dt = d[C]/dt.
• Note that we could measure the rate by measuring the changes in concentrations of any of the species. That is, even though changing [B] won't affect the rate, we could measure the rate change occurring by changing [A] by measuring [B] since the stoichiometry says that for each A lost, one B is also lost!
• Note: if double [A], double rate; triple [A], triple rate.
• Second order: For A C, or A + B C + D, etc. Two cases:

r = k [A][B]

• Note if double [A] or [B] will double rate; if double both [A] and [B] will quadruple rate

r = k [A]2, etc.

• Note if double [A] will quadruple rate, if triple [A] will increase rate nine-fold
• Higher order reactions occur, but are uncommon.
• Zero order: r = k[A]0 = k: Only occurs with catalysts, important in enzyme catalysis. 0 order also only occurs above a minimum [A].

### So how do we determine the order of a reaction?

The experiment is to increase the concentration of a single reactant, and observe the rate. Sometimes the order will be obvious (i.e. double, double = directly proportional = 1st order). If not, then can take the results of two experiments and divide them and do some algebraic manipulations to find the correct order.

Example: Find the order of the reaction given the data below.

 Experiment [A] rate 1 0.0167 3.61 x 10-3 2 0.0569 4.20 x 10-2

r = k [A]n

r1/r2 = (k [A]1n)/(k [A]2n)

r1/r2 = ([A]1/[A]2)n

But we want to find n, so take logs of both sides:

ln (r1/r2) = ln ([A]1/[A]2)n = n ln ([A]1/[A]2)

n = ln (r1/r2)/ln ([A]1/[A]2)

n = ln(0.0361 / 0.420)/ln(0.0167 / 0.0569)) = 2

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