# Speed of sound in a gas (sig fig problem)

1. Apr 14, 2010

### darryw

1. The problem statement, all variables and given/known data

Calculate the speed of sound waves in hydrogen gas (M = 2.00 g/mol and γ = 1.40) at T = 300 K.

2. Relevant equations

v = root (γRT/M)

3. The attempt at a solution

I keep getting 1321.4km/s but its not being acccepted (automated homework) so Im pretty sure this is a sig fig error.

I converted M into kg/mo (2/1000) = .002kg/mol

and my answer seems reasonable also.

the least amount of sig figs is M, which is 3

2. Apr 14, 2010

### Staff: Mentor

Seems to me like ALL data is given with three sig figs.

3. Apr 14, 2010

### darryw

R is given as 8.3134
gamma is 1.4
M is 2.00 g/mol
and T given as 300K

4. Apr 14, 2010

### darryw

if gamma is 2 sig digs, even though its dimensionless, should my answer also be only 2 digs?

5. Apr 14, 2010

### darryw

sorry i meant to say 1.32e3 km/s

6. Apr 14, 2010

### Staff: Mentor

You wrote gamma as 1.40, that's 3 sig figs.

--

7. Apr 14, 2010

### darryw

edit: yes youre right. gamma is also 3 sig digs. But site wont accept the answer 1.32e3 km/s. so i dont know what im doing wrong?

8. Apr 14, 2010

### darryw

(tried to delete this extraneous post)

9. Apr 14, 2010

### Staff: Mentor

km/s?

10. Apr 14, 2010

### darryw

ohhhh duh. i was thinking in terms of km/hr and thats why i thought it reasonable answer.
thanks!
but am i right in saying that my answer is only as many digits as the value with least amount of sig figs, and also, if gamma is dimensionless why do use that to determine sig figs in answer?
Also, it accepted "1.3 km/s" --but thats 2 sig digs.. why?

11. Apr 15, 2010

### Staff: Mentor

What dimensionality has to do with sig figs? Sig figs are about accuracy. You can use pi equal to 3.2 or equal to 3.1415927 - and for obvious reasons in the first case accuracy of your result will be much lower. And remember that pi is a dimensionless number...

No idea.

But I would not pay too much attention to that. Sig figs are not used where there is a real need to evaluate accuracy of the results and they are not a really important thing. The only lesson to learn - don't write too many digits as they are just noise, but do the calculations with high precision enough to not loose any of those digits that are important.

--