What is meant by positive and negative deviations from Raoult's law and how is the sign of mix ∆sol H related to positive and negative deviations from Raoult's law?

What is meant by positive and negative deviations from Raoult's law and how is the sign of mix ∆_sol H related to positive and negative deviations from Raoult's law?

Solution

Solutions showing positive deviations from Raoult's law: Let Take a  binary solution with have components A and B. If the force of attraction between molecular of and A and B in the solution are weaker than that of between  A — A and B — B, then the tendency of escaping of molecules A—B from the solution becomes more than that of pure liquids. The total pressure of the solution will be greater than the corresponding vapour pressure of ideal solution of the same component  A and B. This type of solution shows positive deviation from Raoult's law. The positive deviation  of solution have been shown in figure. Some energy loose when we mix both solutions. This reaction is endothermic reaction. For Endothermic reaction delta H is always positive

 

Solutions showing negative deviations from Raoult's law : Let Take a  binary solution with have components A and B. If the force of attraction between molecular of and A and B in the solution are stronger  than that of between  A — A and B — B, then the tendency of escaping of molecules A—B from the solution becomes less than that of pure liquids. The total pressure of the solution will be lower than the corresponding vapour pressure of ideal solution of the same component  A and B. This type of solution shows negative deviation from Raoult's law. The negative deviation  of solution have been shown in figure. Some energy released when we mix both solutions. This reaction is exothermic reaction. For Exothermic reaction delta H is always negative 

A sample of drinking water was found to be severely contaminated with chloroform (CHCl3) supposed to be a carcinogen. The level of contamination was 15 ppm (by mass): (i) Express this in percent by mass (ii) Determine the molality of chloroform in the water sample.

A sample of drinking water was found to be severely contaminated with chloroform (CHCl3) supposed to be a carcinogen. The level of contamination was 15 ppm (by mass):

(i) Express this in percent by mass

(ii) Determine the molality of chloroform in the water sample.

Solution

(i)

In this problem level is 15 ppm by mass

So   ppm is the part per millions

15 ppm =  mass of solute ×10⁶/mass of solvent                      ...(1)

Mass % = mass of solute × 10² / mass of solvent                     ... (2)

Divide equation second by first we get

Mass %  of CHCl3  =  15 × 10^-4 %

(ii)

                                             ... (3)

Here we have already find the mass % is 15 × 10^-4 

When even mass % is given take total mass of solution = 100 gram

And mass of solute (CHCl3)  will  =  15 × 10^-4  g

Mass of solvent = mass of solution – mass of solute

Here mass of solute is very small as compare to total mass of solution so neglect it and we get

Mass of solvent = mass of solution

Mass of solvent = 100 g

Now we have to find the number of moles of solute

                            … (4)

So we have to calculate the molar mass of solute (CHCl3)

Molar mass of CHCl3               =12 +1+106.5

                                                =119.5

Plug the value in equation (4)

No of moles of chloroform        = 15×10⁴/119.5

                                                =1.25×10^-5

Now plug the value of number of moles and mass of solvent in equation (4)

 We get

Here mass of solvent = 100 g

Convert it in Kg we divide by 100 we get

Mass of solvent = 0.1Kg 

Molality of            = 1.25×10^-5/0.1

                             = 1.25×10^-4m

DETERMINANTS questions

S.No.	DETERMINANTS
	EXERCISE 4.1
1-2	Evaluate the determinants in Exercises 1 and 2.
3	If A = ,then show that | 2A | = 4 | A |
4	If A = then show that | 3 A | = 27 | A |
5	Evaluate the determinants
6	If A =find | A |
7	Find values of x, if
8	If, then x is equal to (A) 6 (B) ± 6 (C) – 6 (D) 0
	EXERCISE 4.2
1-7	Using the property of determinants and without expanding in Exercises 1 to 7, provethat: Answer 1- 4  Answer 4- 7
8-14	By using properties of determinants, in Exercises 8 to 14, show that: Answer 8 - 10  Answer 11 - 12 Answer 13- 14
15	Let A be a square matrix of order 3 × 3, then | kA| is equal to (A) k| A| (B) k2 | A| (C) k3 | A| (D) 3k | A |
16	Which of the following is correct(A) Determinant is a square matrix.(B) Determinant is a number associated to a matrix.(C) Determinant is a number associated to a square matrix.(D) None of these
	EXERCISE 4.3
1	Find area of the triangle with vertices at the point given in each of the following : (i) (1, 0), (6, 0), (4, 3) (ii) (2, 7), (1, 1), (10, 8)(iii) (–2, –3), (3, 2), (–1, –8)
2	Show that pointsA (a, b + c), B (b, c + a), C (c, a + b) are collinear.
3	Find values of k if area of triangle is 4 sq. units and vertices are (i) (k, 0), (4, 0), (0, 2) (ii) (–2, 0), (0, 4), (0, k)
4	(i) Find equation of line joining (1, 2) and (3, 6) using determinants. (ii) Find equation of line joining (3, 1) and (9, 3) using determinants.
5	If area of triangle is 35 sq units with vertices (2, – 6), (5, 4) and (k, 4). Then k is (A) 12 (B) –2 (C) –12, –2 (D) 12, –2
	EXERCISE 4.4
1-2	Write Minors and Cofactors of the elements of following determinants:
3	Using Cofactors of elements of second row, evaluate Δ =
4	Using Cofactors of elements of third column, evaluate Δ
5	If Δ =and Aij is Cofactors of aij, then value of Δ is given by (A) a11 A31+ a12 A32 + a13 A33 (B) a11 A11+ a12 A21 + a13 A31 (C) a21 A11+ a22 A12 + a23 A13 (D) a11 A11+ a21 A21 + a31 A31
	EXERCISE 4.5
1-2	Find adjoint of each of the matrices in Exercises 1 and 2.
3-4	Verify A (adj A) = (adj A) A = |A| I in Exercises 3 and 4
5-11	Find the inverse of each of the matrices (if it exists) given in Exercises 5 to 11.
12	Let A = and B = Verify that (AB)–1 = B–1 A–1.
13	If A =, show that A2 – 5A + 7I = O. Hence find A–1.
14	For the matrix A =, find the numbers a and b such that A2 + aA + bI = O.
15	For the matrix A = Show that A3– 6A2 + 5A + 11 I = O. Hence, find A–1.
16	If A =Verify that A3 – 6A2 + 9A – 4I = O and hence find A–1
17	Let A be a nonsingular square matrix of order 3 × 3. Then |adj A| is equal to (A) |A| (B) |A|2 (C) |A|3 (D) 3|A|
18	If A is an invertible matrix of order 2, then det (A–1) is equal to (A) det (A) (B) 1/ det (A) (C) 1 (D) 0
	EXERCISE 4.6
1-6	Examine the consistency of the system of equations in Exercises 1 to 6.
7-14	Solve system of linear equations, using matrix method, in Exercises 7 to 14. Question 7                    Question 8                         Question 9  Question 10                  Question 11                       Question 12  Question 13                  Question 14
15	If A =find A–1. Using A–1 solve the system of equations 2x – 3y + 5z = 11, 3x + 2y – 4z = – 5, x + y – 2z = – 3
16	The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs 70. Find cost of each item per kg by matrix method.
	Miscellaneous Exercises on Chapter 4
1	Prove that the determinant is independent of θ.
2	Without expanding the determinant, prove that
3	Evaluate
4	If a, b and c are real numbers, and Δ = Show that either a + b + c = 0 or a = b = c.
5	Solve the equation
6	Prove that
7	If A–1 =and Bfind AB -1
8	Verify that (i) [adj A]–1 = adj (A–1) (ii) (A–1)–1 = A
11-15	Using properties of determinants in Exercises 11 to 15, prove that:
16	Solve the system of equations
17	If a, b, c, are in A.P, then the determinant
18	If x, y, z are nonzero real numbers, then the inverse of matrix
19	Let A = , where 0 ≤ θ ≤ 2π. Then

Construct a 3×4 matrix whose elements are given by:

Construct a 3 × 4 matrix, whose elements are given by: