University:
Boston University
Course:
CAS CH 214 | Organic Chemistry with Qualitative Analysis
Academic year:

2023
Views:

326

Pages:

8
Author:

Carina Watson

TP How many distinguishable ways can 5 water molecules and 2 ink molecules be arranged? 0% 0% 0% 0% 0% 1. 2. 3. 4. 5. 14 21 240 5040 None of these Spontaneous change: How far? • The essence of change • Counting particle dispersal • Practice with particle dispersal The essence of change Why does a drop of ink in water disperse? Why do salt water and fresh water mix? 1 The essence of change A gas fills its container all complexity is an illusion ... things happen simply because they can happen and because they are statistically most likely to happen.” Michael Munowitz, "Principles of Chemistry," W. W. Norton, 2000 A gas fills its container A gas fills its container 2 A gas fills its container A gas fills its container Gas all on left of container A gas fills its container Pressure in a gas is uniform moveable barrier Gas evenly distributed throughout container P proportional to n/V (“lattice gas”) P higher on the right 3 Pressure in a gas is uniform moveable barrier P proportional to n/V (“lattice gas”) P the same on the left and right Gases mix evenly permeable barrier One gas on left, another on right Osmotic pressure across semipermeable membrane Gases mix evenly permeable barrier Equal amounts throughout Pressure equal (n/V) on both sides of membrane, but solute (light grey) cannot pass across membrane to left 4 Osmotic pressure across semipermeable membrane Osmotic pressure across semipermeable membrane Solvent passes across membrane to right making pressure higher (n/V) on right Osmotic pressure across semipermeable membrane Blind chance & dumb luck Everything—absolutely everything—that happens, happens solely because of blind chance and dumb luck. To quantify this … 1. Learn to count the ways 2. Search for greatest number of ways 5 Counting distinguishable (unique) arrange Counting distinguishable unique arrangements Say we have three girls and four boys. The goal: The number of distinguishable arrangements of j identical objects of one kind and k identical objects of another kind is … ! , ! ! What is the probability of calling them into line in the order ? For example 3 ink molecules and 4 water molecules can be uniquely arranged in 3, 4 ! ! ! 35 ways Counting distinguishable (unique) arrange Counting distinguishable (unique) arrange Say we have three girls and four boys. Say we have three girls and four boys. What is the probability of calling them into line in the order ? For each particular arrangement, say about? 3! 4! , how many ways can it come 144 6 Counting distinguishable (unique) arrange Counting distinguishable (unique) arrange Say we have three girls and four boys. Say we have three girls and four boys. If we ignore whether a child is boy or girl, what is the total number of arrangements? This means the total number of arrangements can be expressed as the number, W, of distinguishable arrangements times the number of ways a particular distinguishable arrangement can come about, 7 6 5 4 3 2 1 7! 5040 7! 5040 W 3! 4! W 144 Therefore, the number of distinguishable arrangements is W 7! / 3! 4! 5040/144 35 Counting distinguishable (unique) arrange Practice with particle dispersal More generally, say we have j objects of one kind say, girls and k objects of another kind say, boys . See page 3 of http://quantum.bu.edu/courses/ch102‐spring‐2017/notes/SecondLaw.pdf The number of unique arrangements of objects of one kind and another kind is W j, k j k !/ j! objects of k! 7 TP How many distinguishable ways can 3 water molecules and 2 ink molecules be arranged? 20% 20% 20% 20% 20% 1. 2. 3. 4. 5. 8 10 12 120 None of these Quiz How many distinguishable ways can 2 ink molecules be arranged among 12 water molecules? 0% 0% 0% 0% 0% 1. 2. 3. 4. 5. 36 240 455 720 None of these TP How many distinguishable ways can 5 water molecules and 2 ink molecules be arranged? 0% 0% 0% 0% 0% 1. 2. 3. 4. 5. 14 21 240 5040 None of these The more water, the more ways ink disperses 2 ink particles in water 8