Equilibria chemistry
 

The Equilibrium Law

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Calculation errors

Five students were asked to find Kc for the equilibrium 2HI(g)  H2(g) + I2(g). The information they were given and their calculations are shown below.

Hydrogen iodide was heated in a 4 dm3 sealed container at 440 ºC. At equilibrium, the mixture contained 0.78 moles of HI, 0.11 moles of H2 and 0.11 moles of I2.

Student A

 \inline \dpi{100} \large K_\textup{c} = \frac{(0.78)^{2}}{(0.11)(0.11)}= \frac{0.608}{0.012}= 50.7

Student B

 \inline \dpi{100} \large K_\textup{c} = \frac{(0.11)(0.11)}{(0.78)}= \frac{0.012}{0.78}= 0.154

Student C

 \inline \dpi{100} \large K_\textup{c} = \frac{(0.11)+(0.11)}{(0.78)^{2}}= \frac{0.22}{0.608}= 0.362

Student D

 \inline \dpi{100} \large K_\textup{c} = \frac{(0.11)(0.11)}{(0.78)^{2}}= \frac{0.012}{0.608}= 0.0197

None of the students has calculated a correct value for Kc. What error have all the students made?

All the students have used amounts of each substance in moles rather than their concentrations in mol dm–3.

In addition to this common error, some students have made additional mistakes.

What additional error has student A made?

Student A has put the fraction the wrong way up.

What additional error has student B made?

Student B hasn't included a power of 2 for HI. 

What additional error has student C made?

Student C has added rather than multiplied the H2 and I2 values.

In what way are the answers from students B and C incomplete?

The answers from students B and C would need units. In the answers from students A and D there are the same number of moles at the top and bottom of the fraction so units cancel out.

What is the correct value of Kc?

\inline \dpi{100} \large K_\textup{c} = \frac{(\frac{0.11}{4})(\frac{0.11}{4})}{(\frac{0.78}{4})^{2}}= \frac{(0.0275)(0.0275)}{(0.188)^{2}}= \frac{0.000756}{0.0353}= 0.0214

 
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