# How do we determine the percent yield of ammonia (theoretical yield) if we only know that temperature is 425 degrees Celsius and that the pressure is 200 atm?We know that at 400 Celsius and 200...

How do we determine the percent yield of ammonia (theoretical yield) if we only know that temperature is 425 degrees Celsius and that the pressure is 200 atm?

We know that at 400 Celsius and 200 atm, the percent is 38.8% and that at 500 Celsius and 200 atm, the percent is 18.3%.

Do I just guesstimate a value since we don't have enough details to actually come up with a legit number?

jerichorayel | College Teacher | (Level 2) Senior Educator

Posted on

Hello!

Since we are given only the values of P, T and the percent yield, we can do a linear extrapolation to solve this problem.

Look at it this way: the system is at constant pressure (200atm), only the temperature is varying. So the change in the percent yield is dependent on the change in the temperature.

T         673       773       698           **converted to kelvin

%Y      38.8      18.3       ?

we can let T as Y  and %Y as X

we try to ge the slope of the line:

slope = (Y2-Y1)/(X2-X1)

= (773 - 673)/( 18.3-38.8)

= -4.878

the slope is -4.878

since we have the slope we can solve for the unknown.

the unknown is X3

slope   = (Y3-Y2)/(X3-X2)

-4.878 =  (698 - 773)/(X3- 18.3)

-4.878 = -75/(X3 - 18.3)

**solve X3

(X3 - 18.3) = -75/-4.878

(X3 - 18.3) = 15.375

X3 = 15.375 + 18.3

X3 = 33.675 = 33.7% yield

Hope this helps :)