Extra Credit 66

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Page ID: 49910

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Q2.74

Assuming there is no heat exchange occurring between a gas system and its surroundings, what will be the final equilibrium temperature of the gas system when Argon atoms in a sealed container start colliding with each starting at an average speed at of $\ 2.74\times10^{4}cm \ s^{-1} ?$ Note that the atoms are allowed to collide with one another until the Maxwell distribution is established.

Q9.13

$\ N_{2}0$ decomposes to $\ N_{2}$ and $\ 0_{2}$ as a first order reaction. The half-life of this reaction at 730°C is 3.58 x 10³ min. Assuming that volume and temperature remain constant, what is the total gas pressure after one half life if the initial pressure of $\ N_{2}0$ is 2.10 atm?

Q10.3

The enzyme acetyl cholinesterase, used to catalyzes the hydrolysis of acetylcholine, has a turnover rate of $\ 25,000 \ s^{ -1}$ . How long will it take for the enzyme to cleave one molecule of acetylcholine?

Q11.3

Calculate the energies for the hydrogen atom Bohr orbitals when n = 2 and n = 3?

Q11.27

An important property of the wave functions of a particle in a one-dimensional box is that they are orthogonal; that is,

$$\int_0^{L} \psi_{n} \psi_{m} dx = \ 0\ \ m \ne n $$
Prove this statement using $\psi_{1} $ and $\psi_{2}$ and Equation $\psi_{n} = \ A\ sin \dfrac {n \pi\ } {L} \ x$

Q12.20

Describe the bonding of a nitrate ion, $\ NO_{3}^{-}$, in terms of delocalized molecular orbitals.

Q14.2

Calculate the wave number and frequency of a photon at a wavelength of 450 nm.

Q14.25

A hemoglobin molecule contains 9272 atoms. Calculate the number of vibrational degrees of freedom for this molecule.

Q2.52

What is the pressure exerted on a $\ 4.0 \ cm ^{2}$ wall when $\ 2.0 \times10^{23} $ argon (Ar) atoms per second strike the wall at a 90° angle while moving at a speed of $\ 45,000 \ cm \ s^{ -1} $? Give your answer in units of atm.

Q2.99

We have 2 moles of each of the following gases: $\ He$ and $\ N_{2} $ . They are both being held at identical and constant temperature and pressure. State which one of the two gases (if any) will have the greater value for: (a) c, (b) $\ C_{rms} $, (c) $\ E_{trans} $, (d) $\ Z_{1} $, (e) $\ Z_{11} $ , (f) density, and (g) mean free path. $\ N_{2} $ has a diameter that is 1. 7 times that of $\ He $.

Answers

S2.74

Suppose there are Ν Argon atoms. Because all the atoms have the same speed, the total translational energy is:

$$ \ E_{trans} = N( \dfrac {1} {2} \ mv^{2} \ ) = N(\ E_{trans} \ ) $$

$$ \ N( \dfrac {1} {2} \ mv^{2} \ ) = N ( \dfrac {3} {2} \ k_{B}{T} \ ) $$

Then T is calculated as follows:

$$ \ T = ( \dfrac {mv^{2} {3k_{B} \ ) = ( \dfrac { 4.003 \times1.661} {3\times1.381} \ ) $$