Sig figs and M, rearranging

[jimmyp]

Significant digits count!

Problem:

If PV = [gR(T+273.15)]/M, solve for M when P = 286, V = 0.491, g = 0.929, R = 62.37, and T = 36.


I can thus write:

M = [(0.929)(62.37)(36+273.15)] / (286)(0.419)

M = [(0.929)(62.37)(309)] / (286)(0.419)

M = 17903.99457 / 119.834 = 149.407


I feel a little confused on the sig figs on the last line there... Am I suppose to do the multiplication and division on the second line of the whole thing together and assume the lowest sig fig value for the final answer or do I do the numerator and then demoninator first and apply the sig fig rules to each? Did I do this correctly?


Thanks for reading. :)

[Russ]

Did the value of T in the question get written as 36 or 36.00?

If it's 36 then you have too many significant figures in your answer I think (you can only have an answer that's as accurate as the least accurate piece of information).

That said, significant figures isn't my strong point, I never really learned it properly (my old teacher would kill me for saying that!)

[jimmyp]

It's just written as 36.


I was thinking that as well but then I thought about chain calculations and how you have to write out the sig figs of certain parts of the calculation first and what not.


I'm also worried about how I rewrote the equation to solve for M, did I do this correctly?


Thanks for the reply.

[Russ]

Assuming you were writing the ideal gas law, i've never seen the form: PV = GRT/M

Also, conversion from C to K is +273 not +273.15 (it is right?)

That said, your rearranging was fine since

M = GRT/PV

which is what you wrote (with numbers).

From memory, chain calculations involve doing one calculation (say for number of moles) then putting that into another calculation (say mass of compound). You didn't do that, you just solved for M from the one formula. That's my best guess, hope somebody who knows sig figs well comes along and can help better than this!

[jimmyp]

Assuming you were writing the ideal gas law, i've never seen the form: PV = GRT/M

Also, conversion from C to K is +273 not +273.15 (it is right?)

That said, your rearranging was fine since

M = GRT/PV

which is what you wrote (with numbers).

From memory, chain calculations involve doing one calculation (say for number of moles) then putting that into another calculation (say mass of compound). You didn't do that, you just solved for M from the one formula. That's my best guess, hope somebody who knows sig figs well comes along and can help better than this!
Yeh, I know that the form may be incorrect, this is more of an introductory question to see if one has the skill set of dimensional analysis and can ultilize information they're given. I know the conversion is different for C->K but I'm just going by what I was given. :)


I reworked it for sig figs I BELIEVE I did this correctly (a check would be helpful):

M = (0.929)(62.37)(309) / (286)(0.149)

M = (17912.68583) / 119.834 becomes with sig figs -> M = 17.9 * 10^3 / 120

Thus M = 143



How does this look?