Question

1)

A geological sample is found to have a Pb-206/U-238 mass ratio of 0.337/1.00. Assuming there was no Pb-206 present when the sample was formed, how old is it? The half-life of U-238 is 4.5 × 10⁹ years.

A geological sample is found to have a Pb-206/U-238 mass ratio of 0.337/1.00. Assuming there was no Pb-206 present when the sample was formed, how old is it? The half-life of U-238 is 4.5 × 10⁹ years.

	2.1 × 109 years
	1.4 × 1010 years
	2.4 × 1010 years
	7.1 × 109 years
	7.3 × 1011 years 2) A sample initially contains 8.0 moles of a radioactive isotope. How much of the sample remains after five half-lives? Express your answer using two significant figures. 3)The nuclide 6Li reacts with 2H to form two identical particles. Identify the particles 4) Consider a reaction that has a positive ΔH and a positive ΔS. Which of the following statements is TRUE? Consider a reaction that has a positive ΔH and a positive ΔS. Which of the following statements is TRUE? This reaction will be nonspontaneous at all temperatures. This reaction will be nonspontaneous only at high temperatures. This reaction will be spontaneous only at high temperatures. This reaction will be spontaneous at all temperatures. It is not possible to determine without more information. 5) Consider a reaction that has a positive ΔH and a negative ΔS. Which of the following statements is TRUE? Consider a reaction that has a positive ΔH and a negative ΔS. Which of the following statements is TRUE? This reaction will be nonspontaneous only at high temperatures. This reaction will be spontaneous at all temperatures. This reaction will be spontaneous only at high temperatures. This reaction will be nonspontaneous at all temperatures. It is not possible to determine without more information. 6) Consider a reaction that has a negative ΔH and a negative ΔS. Which of the following statements is TRUE? Consider a reaction that has a negative ΔH and a negative ΔS. Which of the following statements is TRUE? This reaction will be nonspontaneous only at high temperatures. This reaction will be spontaneous only at high temperatures. This reaction will be nonspontaneous at all temperatures. This reaction will be spontaneous at all temperatures. It is not possible to determine without more information. 7) For the following example, identify the following. 3O2(g) → 2O3(g) For the following example, identify the following. 3O2(g) → 2O3(g) a negative ΔH and a positive ΔS a positive ΔH and a positive ΔS a positive ΔH and a negative ΔS a negative ΔH and a negative ΔS It is not possible to determine without more information. 8) Which statement is true regarding the sublimation of dry ice (solid CO2)? Which statement is true regarding the sublimation of dry ice (solid )? ΔH is positive, ΔS is positive, and ΔG is positive at low temperature and negative at high temperature. ΔH is negative,ΔS is positive, and ΔG is negative at all temperatures. ΔH is negative, ΔS is negative, and ΔG is negative at low temperature and positive at high temperature. ΔH is positive,ΔS is negative, and ΔG is positive at all temperatures.

Answer 1

Answer 1

Radioactive decay is of first order

t = (2.303/ k) x log (N₀/N)

N₀ is moles of U-235 initially

N is moles of U-235 left

As after time t, mass of Pb : mass of U = 0.337 : 1

Moles of Pb = 0.337/206 = 0.00164 moles

Moles of U = 1.00/238 = 0.0042 moles

As, 1 mole of U on radioactive decay forms 1 mole of Pb

So, initial moles of U = 0.00164 + 0.0042 =  0.00584 moles

t = (2.303/ k) x log (0.00584/0.0042)

t = [2.303 x 4.5 x 10⁹ /0.693] log [(0.00584)/(0.0042)= 2.1 x 10⁹ yrs

t = (14.96 x 10⁹)(0.143)

t = 2.14 x 10⁹ years i.e option A.

Answer 2

After every half life, reactant of first order reaction reduces to half its concentration

So, after n half lives, concentration = Initial concentration/2ⁿ

Now, after five half lives, n = 5, So, Amount of reactant left = 8 moles/2⁵ = 8 moles/32 = 0.25 moles.

Answer 3

Given nucleide is ⁶₃Li reacts with 2 atoms of ¹₁H to form two identical particles

Let these particles have mass number x and atomic number y

So, 6+2 = 2x

x = 4

Also, 3+1 = 2y

y = 2

Hence the particle is ⁴₂He i.e. alpha particle.

Answer 4

As per thermodynamics and spontaniety, ΔG⁰ = ΔH⁰ - TΔS⁰

ΔG⁰ < 0 for spontaneous reaction.

As both ΔH⁰ and ΔS⁰ are positive, So to make  ΔG⁰ < 0, the temperature should be high enough so that TΔS⁰ exceeds the value for  ΔH⁰. Hence, correct answer is option 3

Answer 5

As ΔH⁰ is positive and ΔS⁰ is negative. So,  ΔG⁰ > 0 at all temperatures. Hence, correct answer is option 4

Answer 6

As ΔH⁰ is negative and ΔS⁰ is negative.

So to make  ΔG⁰ < 0, the temperature should be low enough so that TΔS⁰ may not exceed the value for  ΔH⁰

So, correct option is option 1

Answer 7

As the conversion of O2 to O3 is endothermic and decreases entropy.So, correct answer is option 3

Answer 8

Dry ice readily sublimes. For sublimation, heat is absorbed and entropy increases

So, correct answer is option 3