Checking approximations

In the previous problems the magnitude of K was such that the extent of reaction was significant, and equilibrium pressures were significantly different to initial pressures.
 

For example, In the problem 200 kPa of PCl₅ were put in, and 27 kPa remained at equilibrium.

For reactions having smaller equilibrium constants, the extent of reaction is less, and the amount of reactants consumed is small.

In these cases, the amount of reactants remaining at equilibrium can be approximated by amount that was put in. Such approximations have the effect of simplifying the equation that must be solved for x as if x is small, expressions like 3.00 -x can be simplified to 3.00.

The validity of such approximations must be always checked at the end of the calculation to assess for example if x is REALLY small in comparison to 3.00. However, this is easy to do. Thus it is always worthwhile to consider making an approximation before trying to solve a complicated equation (like the one in the last two problems).