2
$\begingroup$

Problem:

Find the moment of inertia for 2 axes of $\ce{SO2}$. The rotational constants are given in $\pu{MHz}$. The answer is required to be $10^{-46}\rm~ kg\cdot m^2$, 7 digit accuracy.

I used $$I = \frac{h}{8\times\pi^2\times B}$$ but the answer is marked wrong. I do not understand what I am doing incorrectly. I thought maybe that $\ce{SO2}$ is asymmetric so that formula will not work.

This is an online course that has minimal discussion assistance. I have scrounged on Google & physical chemistry textbook to see what the alternative could be. Did not see another formula. Where did I go wrong?

$\endgroup$
  • $\begingroup$ Please take your time and format yuor post with the MathJax syntax so that we have a better idea of what you’re saying. $\endgroup$ – Jan Jun 30 '16 at 18:10
  • 1
    $\begingroup$ First question for you is what is the geometry of sulfur dioxide? Next, how many unique principle axes does it have? $\endgroup$ – Zhe Jan 18 '17 at 17:45
1
$\begingroup$

Without explaining some more its hard to help, but the most likely error is in using the wrong units. The rotational constant is usually given in wavenumber units (cm$^{-1}$), e.g. 2.02736 cm$^{-1}$. In a linear molecule the equilibrium value is

$B_e = \frac{h}{(8\pi^2cI)}$

with $B_e$ in wavenumbers and c is the speed of light in cm/sec. In your case since the SO$_2$ is not linear (its planar bent at the S atom, C$_{2v}$ point group) there are three rotational constants usually called A$_0$, B$_0$, C$_0$.
(You can check the units by converting Joules in to base units, m, kg, s etc . The moment of inertia is in kg m$^2$ and $10^{-46}$ is of the correct order of magnitude. Seven decimal places seems too many as the rotational constants are not usually known to more than 5 places.)

$\endgroup$
  • $\begingroup$ Thank you. But I am back at square 1. I can't use the formula B = h/(8(pi^2)I)? I thought that Ia = h/(8(pi^2)Ba). And the same for Bb. The problem requires 7 digit accuracy. *For the vibrational ground state, the rotational constants, A and B, are 60778.79 MHz and 10318.10 MHz, respectively. Calculate Ia and Ib (Unit: 10^−46 kg m2, 7-digit accuracy). ** The moments of inertia around the principal axes Ia=(2mOmS/M)*r^2*cos^2⁡(θ/2) Ib=2mO*(r^2)sin^2(⁡θ/2) Ic=Ia+Ib mO and mS are the masses for oxygen and sulfur, respectively. M≡mS+2mO is the mass of SO2. $\endgroup$ – hindishe Lee Jul 1 '16 at 18:59
  • $\begingroup$ Could it be I must convert MHz to joules? $\endgroup$ – hindishe Lee Jul 1 '16 at 20:18
  • $\begingroup$ I thought I was going koo-koo. I was going over & over what I was doing wrong for this problem. I am REALLY sure I put in the same answer that I did just now - i did the SAME CACULATION. Now I got the green check - for this problem. What happened before? Who knows with MOOC graders! Thank you for the response to help! $\endgroup$ – hindishe Lee Jul 1 '16 at 20:56
  • $\begingroup$ please tick and markup if the answer was helpful. $\endgroup$ – porphyrin Jul 2 '16 at 6:55
  • $\begingroup$ I appreciaite the answer but it did not help. Fortunately I had the right answer - it was the course grader that malfunctioned. $\endgroup$ – hindishe Lee Jul 3 '16 at 19:55

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.