A first-order chemical reaction is observed to have a constant of 26 min^-1. Wha

Question

A first-order chemical reaction is observed to have a constant of 26 min^-1. What is the corresponding rate half life for the reaction? 1.6 s 1.6 min 37.2 s 2.3 s 38 min What is the pH of a solution prepared by dissolving 0.194 g of NaOH(s) in 7.00 L of water? 10.841 3.159 11.686 2.314 7.000 For a second-order reaction, what are the possible units of the rate constant s L mol^-1 s^-1 mol L^-1 mol L^-1 s^-1 L^-1 s^-1 The rate constants for decomposition of a compound are 5.75 times 10^-4 s^-1 at 42 degree C and 1.82 times 10^-3 s^-1 at 63 degree C. What is the value of the activation energy for this reaction? (R = 8.314 J/(mol K)) 0.524 kJ/mol 21 kJ/mol 1.21 kJ/mol 0456 kJ/mol 48.3 KJ/mol What is the molarity of a 40.0% by mass hydrochloric acid solution? The density solution is of the 1.1980 g/mL 0.0479 M 18.3 M 13.9 M 1301 M 0.400 M

Explanation / Answer

Solution:- (1) For first order reaction the relationship between rate constant, k and half life, t1/2 is as follows...

t1/2 = 0.693/k

k is given as 26 min-1. So...

t1/2 = 0.693/26 min-1 = 0.0267 min

none of the choices match with this so let's convert it to second and see which is the right choice.

0.0267 min x (60 s/min) = 1.6 s

choice A is the right one.

(2) 0.194 g of NaOH are dissolved in 7.00 L water.

First of we will convert the grams into moles and then divide the moles by liters to get the molarity of NaOH solution.

moles = grams/molar mass

molar mass of NaOH is 40 g/mol

0.194 g x (1mol/40g) = 0.00485 mol

now we will calculate the molarity.

0.00485 mol/7.00L = 6.93 x 10-4 M

NaOH is a strong base and dissociate completely to give the ions.

so, [OH-] concentration would exactly be same as the molarity of NaOH.

[OH-] = 6.93 x 10-4 M

pOH = - log [OH-] = - log 6.93 x 10-4 = 3.159

pH = 14 - 3.159

pH = 10.841

choice A is correct.

(3) rate law for second order is written as..

rate = k[A]2

where [A] stands for the concentration of the reactant. rate is change in concentration per unit time. If change in concentration is represented by dx and change in time as dt then...

dx/dt = k[A]2

mostly the time is taken in second and concentration is mol/L. mol/L could also be written as mol.L-1.

let's put mol.L-1 in place of dx and s in place of dt. Also, mol.L-1 in place of [A].

k = (dx/dt)/[A]2

k = mol.L-1.s-1/mol2.L-2

k = mol.L-1.s-1 x mol-2.L2

k = mol-1.L.s-1

choice B is the correct one.

(4) to calculate the activation energy we would use the integrated arrhenius equation..

ln(K2/K1) = (Ea/R)(1/T1 - 1/T2)

given data is...

K1 = 5.75 x 10-4 s-1, K2 = 1.82 x 10-3 s-1

T1 = 42 + 273 = 315 K

T2 = 63 + 273 = 336 K

R is the universal gas constant and in terms of energy is it is 8.314 J.K-1.mol-1

Ea is activation energy and we have to find it out. Let's plug in the values in the equation...

ln(1.82 x 10-3 s-1/5.75 x 10-4 s-1) =(Ea/8.314 J.K-1.mol-1)(1/315 - 1/336)

1.15 = (Ea/8.314 J.K-1.mol-1) (1.98 x 10-4 K)

1.15 = Ea(2.38 x 10-5 J-1.mol)

Ea = 1.15/(2.38 x 10-5 J-1.mol)

Ea = 4.83 x 104 J.mol-1 OR 48.3 kJ/mol

choice E is the correct one.

(5) 40.0 % by mass hydrochloric acid means 40.0 g of HCl present in 100 g solution.

molar mass of HCl is 36.46 g/mol. we will divide the grams by molar mass to get the moles.

40.0 g x (1mol/36.46 g) = 1.097 mol

mass of solution is 100 g and density is 1.1980 g/mL

volume = mass/density

100 g x 1mL/1.1980 g = 83.47 mL = 0.08347 L

molarity of HCl = 1.097 mol/0.08347 L = 13.1 M

choice D is the right one.

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