# Find moment of inertia around two axes of sulphur dioxide

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?

• Please take your time and format yuor post with the MathJax syntax so that we have a better idea of what you’re saying.
– Jan
Commented Jun 30, 2016 at 18:10
• First question for you is what is the geometry of sulfur dioxide? Next, how many unique principle axes does it have?
– Zhe
Commented Jan 18, 2017 at 17:45

## 1 Answer

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.)

• 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. Commented Jul 1, 2016 at 18:59
• Could it be I must convert MHz to joules? Commented Jul 1, 2016 at 20:18
• 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! Commented Jul 1, 2016 at 20:56
• please tick and markup if the answer was helpful. Commented Jul 2, 2016 at 6:55
• I appreciaite the answer but it did not help. Fortunately I had the right answer - it was the course grader that malfunctioned. Commented Jul 3, 2016 at 19:55