91Ó°ÊÓ

To calculate K_p from K_cor vice versa, we will use the following equation:

\({K_p} = {K_c} \cdot {(RT)^{\Delta n}}\)

Where\(R\)is gas constant\(\left( {8.314J{K^{ - 1}}mo{l^{ - 1}}} \right)\)and\(T\)is thermodynamic temperature.\(\Delta n\)can be defined for this hypothetical reaction:

\(aA(g) + bB(g) \to cC(g) + dD(g)\)

\(\Delta n = c + d - (a + b)\)

\((a,b,c,d\)are stoichiometry coefficients but only for the gas reactants or products).

a) Here \(\Delta n\) is:

\(\Delta n = 2 - 1 - 3\)

\(\Delta n = - 2\)

Thermodynamic temperature is calculated like this:

\(T = t + 273.15\)

\(T = (400 + 273.15)K\)

\(T = 673.15K\)

Now we can calculate\({K_p}\):

\({K_p} = 0.5 \times {\left( {673.15\;{\rm{K}} \times 8.314J{K^{ - 1}}\;{\rm{mo}}{{\rm{l}}^{ - 1}}} \right)^{ - 2}}\)

\({K_p} = 0.5 \times 3.2 \times {10^{ - 8}}\)

\({K_p} = 1.6 \times {10^{ - 8}}\)

b) Here \(\Delta n\) is:

\(\Delta n = 2 - 1 - 1\)

\(\Delta n = 0\)

Thermodynamic temperature is:

\(T = t + 273.15\)

\(T = (448 + 273.15)K\)

\(T = 721.15K\)

Now we can calculate\({K_p}\):

\({K_p} = 50.2 \times {\left( {721.15K \times 8.314{J^{ - 1}}\;{\rm{mo}}{{\rm{l}}^{ - 1}}} \right)^0}\)

\({K_p} = 50.2 \times 1\)

\({K_p} = 50.2\)

c)

\(\Delta n = 10 + 0 - 0\)

(Remember only\(\Delta n\)is calculated only for the gas reactants and products)

\(\Delta n = 10\)

Thermodynamic temperature is:

\(T = t + 273.15\)\(\)

\(T = 298.15K\)

Now we can calculate\({K_c}\):

\({K_p} = {K_c} \cdot {(RT)^{\Delta n}}\)

\({K_c} = \frac{{{K_p}}}{{{{(RT)}^{\Delta n}}}}\)

\({K_c} = \frac{{4.08 \times {{10}^{ - 25}}}}{{{{\left( {298.15K \times 8.314{J^{ - 1}}\;{\rm{mo}}{{\rm{l}}^{ - 1}}} \right)}^{10}}}}\)

\({K_c} = \frac{{4.08 \times {{10}^{ - 25}}}}{{8.76 \times {{10}^{33}}}}\)

\({K_c} = 4.7 \times {10^{ - 59}}\)

d)

\(\Delta n = 1 - 0\)

(Remember only\(\Delta n\)is calculated only for the gas reactants and products)

\(\Delta n = 1\)

Thermodynamic temperature is:

\(T = t + 273.15\)

\(T = (60 + 273.15)K\)

\(T = 333.15K\)

Now we can calculate\({K_c}\):

\({K_p} = {K_c} \cdot {(RT)^{\Delta n}}\)

\({K_c} = \frac{{{K_p}}}{{{{(RT)}^{\Delta n}}}}\)

\({K_c} = \frac{{0.196}}{{{{\left( {333.15K \times 8.314J{K^{ - 1}}\;{\rm{mo}}{{\rm{l}}^{ - 1}}} \right)}^1}}}\)

\({K_c} = \frac{{0.196}}{{{{2769.8}^1}}}\)

\({K_c} = 542.9\)