. Construct four MOLS of order 5 .

Name: Problem 42, Chapter 10: Introductory Combinatorics
Uploaded: 2021-03-19T00:37:27-08:00
Duration: 12 min 49 s
Channel: Dr. Satish Ingale
Description: . Construct four MOLS of order 5 .

Key Concepts

Latin Square

A Latin square of order n is an n×n array filled with n distinct symbols, each occurring exactly once in each row and column. This structure is fundamental in combinatorial design and provides the groundwork for studying arrangements and scheduling problems where repetition within a row or column is forbidden.

Mutually Orthogonal Latin Squares (MOLS)

MOLS are a set of Latin squares of the same order in which every pair of squares is orthogonal. Two Latin squares are orthogonal if, when one is superimposed on the other, each ordered pair of symbols (one from each square) appears exactly once. This property is critical for applications in experimental design and error-correcting codes.

Order of a Latin Square

The order of a Latin square refers to the number of rows (and columns) in the square, corresponding to the number of distinct symbols used. In the context of constructing MOLS, ensuring the correct order is essential because the existence and number of MOLS depend heavily on this value, especially when using algebraic structures like finite fields.

Construction Using Finite Fields

For orders corresponding to a prime number or a prime power, finite fields provide an effective algebraic structure to construct MOLS. By defining operations in a finite field (e.g., GF(5) for order 5) and using these operations to systematically generate Latin squares, one can ensure the orthogonality condition is met. This method is widely used due to its ability to produce maximum sets of MOLS.

Transcript

0:00 Hi everyone.

00:01 So in this question they asked to determine molar mass till four significant figures of water, iron chloride, potassium bromide, ammonium nitrate and sodium hydroxide.

00:14 So you know molar mass determination of the following following till four significant figures.

00:45 Figures so first one is molar mass of water molar mass of water you know water has formula h2 and therefore molar mass of water that is equal to 1 plus 16 into 1 that is equal to 2 plus 16 that is equal to 18 but they asked to calculate in four significant figures so we'll take mass of hydrogen in detail so it is 1 .007 into 2 plus mass of oxygen 15 point 2 2 2 2 plus mass of oxygen 15 point triple 94 into 1 and that is equal to 2 .014 plus 15 .994 and therefore molar mass of water that is equal to 18 .0134 gram and that is equal to 18 .0134 gram and that is equal to 18.

02:55 1 gram.

03:14 The next second one is second molar mass of iron 3 chloride.

03:30 Molar mass of iron 3 chloride in bracket f e .cl 3 cl3.

04:02 So that is equal to you know iron atomic mass is 55 .8.

04:12 47 into 1 plus chlorine 35 .45 into 3.

04:26 So that is equal to 55 .847 plus 106 .35.

04:39 That is equal to 162 .162.

04:57 Point 197 gram and that is equal to four significant figures 162 .2 gram.

05:10 So therefore molar mass of fecl3, fecl3, that is equal to 162 .2 gram per mole.

05:38 The next third, molar mass of kbr, kbr, kbr, so that is equal to you know atomic mass operation is 39 .098 into 1 plus bromine 79 .916 into 1 and that is equal to 39 .098 plus bromine 70 .916 .6.

06:39 So that is equal to 119 .0 gram and therefore molar mass of kbr potassium bromide that is equal to 1190 gram.

07:27 The next fourth we can say molar mass of 4th, molar mass of ammonium nitrate.

07:54 Ammonium nitrate in bracket an h4 no3 and h4 no3 so an h4 no3 now so molar mass is equal to now there are two nitroations that is we can say r n2h 4 o 3...

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