Extra Credit 53

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Q2.56

The C_rmsof 500 ms^-1. What is the temperature of the gas?

S2.56

3RT/M= C²_rms

_T=(C²_rmsM)/3R

=[(500²⁾X(16.04X10^-3)] / 3(8.314)

=160.77K

Q 2.102

A sample of neon gas is heated from 200K to 300K. Calculate the percent increase in its kinetic energy.

S 2.102

K_B = 1.380658X10^-23 JK^-1

3/2 K_B(300K) / 3/2 K_B(200K) =1.5

It means that percent increase 50% in its kinetic energy.

Q 9.24

S 9.24

Q 10.22

Derive Equation: v₀=[V_max/(1+[I]/K_I)][S] / [K_M/(1+[I]/K_I)] +[S]

S 10.22

Q11.4

The He⁺ ion contains only one electron and is therefore a hydrogenlike ion. Calculate the wavelengths in increasing order, of the first 3 in the Balmer series of the He⁺ion. Compare these wavelengths with the same transitions in a H atom. Comment on the differences.

S 11.4

we need to convert the Rydberg constant for He⁺first.

R_H=8.72x 10^-18J / hc= 8.72x 10^-18J / [(6.626X10^-34 J s)(3X 10⁸m s^-1)]=4.387X 10⁵cm^-1

Wave numbers=R_H|(1/n₁²-1/2²)|

Wavelengths= 1 / Wave numbers

Use Constant R_H=109737 cm^-1for H. 4.387X10⁵cm^-1for He⁺

We can get, n=3,4,5 Wavelengths for He⁺=164,122,109 Wavelengths for H =656, 486,434,410

He⁺ are in the ultraviolet region for compare H are all in the visible region.

Wavelengths He⁺ is shorter than H because the factor of Z ²in R_H expression.

Q. 14.12

A single NMR scan of a dilute sample exhibits a signal-to-noise (S/N) ratio of 1.3. If each scan takes 6 mins, calculate the minimum time required to generate a spectrum with a S/N ratio of 13

S. 14.12

=√ 13/1.3=10

n=110

110X6min=663.8 min/ 60=11.8h

Q 12.5

Why the resonance concept is sometimes descried by analogy to a mule, which is a cross between a horse and a donkey. Compare this analogy with the description of a rhinoceros as a cross between a griffin and a unicorn. which description is more appropriate?

S 12.5

The description involving a griffin and a unicorn is more appropriate. Both mule and donkey are real animals whereas resonance structures are nonexistent.

Q 13.9

Calculate the induced dipole moment of I₂ due to a Na⁺ ion that is 3.0 A away from the center of the I₂ molecule. The polarizability of I₂ is 10 x 10^-30 m³.

S 13.9

E=kq / r²

9x10⁹x1.6x10^-19/ ( 5x10-10)² =5.76x10⁹N/c

P induced=polarizability xE=5.76x10⁹N/c X 10 x 10^-30 m³=5.76x10^-20 C.m

Q 2.80

In 3 min, 30mL of He effuse through a small hole. Under the same condition of temperature and pressure, 5mL of a mixture of CO and Co₂ effuse through the hole in the same amount of time. Calculate the percent composition by volume of the mixture.

r_He=30/3=10

r_mix=5/3=1.67

M_mix=(10/1.67)x4.003 g mol^-1= 23.97 g mol^-1

CO(28.01 g mol^-1) +(1-CO)(44.01g mol^-1)=23.97 g mol^-1

16CO=20.04

CO=1.25

CO=125%

% of CO₂by volume = 1-CO=-25%

Q 9.22

The following data were collected for the reaction between hydrogen and nitric oxide at 700^.C

2H₂(g) +2NO(g）--- 2H₂O（g）+N₂(g)

Experiment H₂/M NO/M Initial rate/M s^-1

1 0.020 0.05 4.8x10^-6

2 0.01 0.05 2.4x10^-6

3 0.020 0.025 1.2x10^-6

(A) what is the rate law for the reaction? (B) calculate the rate constant for the reaction. (C)suggest a plausible reaction mechanism that is consistent with the rate law. (D) more careful studies of the reaction show that the rate law over a wide rarange of concentrations of reactants should be

Rate=K₁[NO]²[H₂] / 1+k₂[H₂]

S 9.22

(A) rate= k[NO]²[H₂]

(B) k= rate /NO]²[H₂]= 4.8x10^-6/(0.020² x 0.05)=0.24 M^-2s^-1

O+H₂---- H₂O Fast

(D) At high H concentration rate= (k1/k2)[NO]²

At low H concentration, rate=k1[NO]²[H₂]