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 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.

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.

Concentrations are assumed to be in Molarity unless otherwise specified.

Consider the reaction:

- 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},orr = k [A] [B]

^{2}

This expression is referred to as a

with the sum of various exponents referred to as theRate Law. 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.order of the reactionLooking 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 rater = 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].

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}

r_{1}/r_{2} = (k [A]_{1}^{n})/(k [A]_{2}^{n})

r_{1}/r_{2} = ([A]_{1}/[A]_{2})^{n}

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

ln (r_{1}/r_{2}) = ln ([A]_{1}/[A]_{2})^{n} = n ln ([A]_{1}/[A]_{2})

n = ln (r_{1}/r_{2})/ln ([A]_{1}/[A]_{2})

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

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*© R A Paselk*

*Last modified 18 April 2011*