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# Simultaneuos Equation Help watch

1. Hi there I'm struggling to do this simple process could anyone walk me through it please? The answer is given but not sure how to get there.

θ = 25/Vm at P=10 mbar
θ = 41/Vm at P=18 mbar

and θ = KP/(1+KP)

Thus 25/Vm = 10K/(1+10K) and 41/Vm = 18K/(1+18K)

Rearranging:

1/K = (10Vm - 250)/25
1/K = (18Vm - 738)/41.

Solve simultaneous equations for 1/K  Vm = 205 cm3
2. (Original post by Mitty1990)

Rearranging:

1/K = (10Vm - 250)/25
1/K = (18Vm - 738)/41.

Solve simultaneous equations for 1/K  Vm = 205 cm3
Since 1/K equals both of those, we can cut out the middle man and get:

(10Vm - 250)/25 = (18Vm - 738)/41.

Then it's just a question of multiplying through, collecting terms,...

Does that cover it, or are you concerned about a different part of the process?
3. Thank you but I'm not sure how to get to the 1/K to start with.
4. (Original post by Mitty1990)
Thank you but I'm not sure how to get to the 1/K to start with.
OK. I suspect a full answer might be best in this case, so:

Spoiler:
Show

I''ll use T rather than theta to simplify my typing.

So, T=KP/(1+KP)

Multiplying through we have T(1+KP) = KP

Expanding brackets T+TKP=KP

Collect terms in K together T=KP-TKP

Factor out the K, so K(P-TP)=T

And divide through by K and T, to get:

1/K = (P-TP)/T

At this stage we could substitute in the values given, and on the right we would multiply the top and bottom of the fraction by "Vm" to simplify it and get it in the form given.

OR we could carry on with:

Now theta is given as "something/Vm", I'll call the something H, so theta = H/Vm

Substituting in we have 1/K = (P - PH/Vm)/(H/Vm)

Multiplying the top and bottom of the fraction on the right by Vm, we get:

1/K=(PVm-PH)/H where H is the given numerical part theta.
5. Hey thank you very much for the reply. I'm following your instruction up until the something/vm part.

If I write it out with the numbers, I get:

1/K = 10 - 10 25 vm / 25 vm.

I don't think this is correct though sadly.
6. (Original post by Mitty1990)
Hey thank you very much for the reply. I'm following your instruction up until the something/vm part.

If I write it out with the numbers, I get:

1/K = 10 - 10 25 vm / 25 vm.

I don't think this is correct though sadly.
That should be 1/K = (10 - 10x25/vm) / (25/vm).

Then multiply top and bottom by Vm on the right hand side.
7. (Original post by ghostwalker)
That should be 1/K = (10 - 10x25/vm) / (25/vm).

Then multiply top and bottom by Vm on the right hand side.
Doesn't that just remove vm from the equation?
8. (Original post by Mitty1990)
Doesn't that just remove vm from the equation?
I haven't really been following but you will still have 10vm

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