Question

Write the mathematical expression for the reaction quotient, \({Q_c}\), for each of the following reactions:

(a) \({N_2}(g) + 3{H_2}(g) \rightleftharpoons 2N{H_3}(g)\)

(b) \(4N{H_3}(g) + 5{O_2}(g) \rightleftharpoons 4NO(g) + 6{H_2}O(g)\)

(c) \({N_2}{O_4}(g) \rightleftharpoons 2N{O_2}(g)\)

(d) \(C{O_2}(g) + {H_2}(g) \rightleftharpoons CO(g) + {H_2}O(g)\)

(e) \(N{H_4}Cl(s) \rightleftharpoons N{H_3}(g) + HCl(g)\)

(f) \(2\;Pb{\left( {N{O_3}} \right)_2}(s) \rightleftharpoons 2PbO(s) + 4N{O_2}(g) + {O_2}(g)\)

(g) \(2{H_2}(g) + {O_2}(g) \rightleftharpoons 2{H_2}O(l)\)

(h) \({S_8}(g) \rightleftharpoons 8\;S(g)\)

Short answer

1. The required reaction quotient is \({Q_c} = \frac{{{{\left| {N{H_3}} \right|}^2}}}{{\left( {{{\left. {\;{N_2}||{H_2}} \right|}^3}} \right.}}\)
2. The required reaction quotient is \({Q_c} = \frac{{\left| {N{O^4}} \right|{H_2}O{O^6}}}{{{{\left| {N{H_3}} \right|}^4}{{\left| {{O_2}} \right|}^3}}}\)
3. The required reaction quotient is \({Q_c} = \frac{{\left| {{N_2}{O_4}} \right|}}{{{{\left| {N{O_,}} \right|}^2}}}\)
4. The required reaction quotient is \({Q_c} = \frac{{\left| {C{O^{\\mid {H_2}O}}} \right|}}{{\left| {C{O_2}} \right|\left| {{H_2}} \right|}}\)
5. The required reaction quotient is \({Q_c} = \left( {N{H_3}} \right)(HCl)\)
6. The required reaction quotient is \({Q_c} = {\left( {N{O_2}} \right)^4}\left( {{O_2}} \right)\)
7. The required reaction quotient is \({Q_c} = \frac{1}{{{{\left| {{H_2}} \right|}^2}\left| {{O_2}} \right|}}\)
8. The required reaction quotient is \({Q_c} = \frac{{|S{|^8}}}{{\left| {{S_8}} \right|}}\)

Step-by-step solution

Definition of reaction quotient

• Under non-equilibrium conditions, the reaction quotient 'Q' is defined as the ratio of the product of initial product concentrations to the product of initial reactant concentrations.

Determine the reaction quotient \({Q_c}\) for  \({N_2}(g) + 3{H_2}(g)  \rightleftharpoons  2N{H_3}(g)\)

(a)

In the case of any reversible response,\({Q_c}\), is the product of all the reactants' concentrations increased to the power of their individual reaction coefficients.

For the form's reversible reaction, \(aA + bB \rightleftharpoons cC + dD\)

\({Q_c} = \frac{{\mid C{)^q}|D{|^d}}}{{|A{|^\mid }|B{|^b}}}\)

So the reaction, \({N_2}(\;g) + 3{H_2}(\;g) \rightleftharpoons 2N{H_3}(\;g)\)

The required reaction quotient is

\({Q_c} = \frac{{{{\left| {N{H_3}} \right|}^2}}}{{|\;N|{{\left| {{H_3}} \right|}^3}}}\)

Determine the reaction quotient \({Q_c}\) for \(4N{H_3}(g) + 5{O_2}(g)  \rightleftharpoons 4NO(g) + 6{H_2}O(g)\)

(b)

In the case of any reversible response,\({Q_c}\), is the product of all the reactants' concentrations increased to the power of their individual reaction coefficients.

For the form's reversible reaction,\(aA + bB \rightleftharpoons cC + dD\)

\({Q_c} = \frac{{\mid C{)^c}|D{|^d}}}{{|A{|^\mid }|B{|^b}}}\)

So, the reaction \(4N{H_3}(\;g) + 5{O_2}(\;g)\rightleftharpoons 4NO(g) + 6{H_2}O(g)\)

The required reaction quotient is \({Q_c} = \frac{{\left| {N{O^4}} \right|{H_2}O{O^6}}}{{{{\left| {N{H_3}} \right|}^4}{{\left| {{O_2}} \right|}^3}}}\)

Determine the reaction quotient \({Q_c}\) for \({N_2}{O_4}(g) \rightleftharpoons 2N{O_2}(g)\)

(c)

In the case of any reversible response,\({Q_c}\), is the product of all the reactants' concentrations increased to the power of their individual reaction coefficients.

For the form's reversible reaction, \(aA + bB \rightleftharpoons cC + dD\)

\({Q_c} = \frac{{\mid C{)^c}|D{|^d}}}{{|A{|^\mid }|B{|^b}}}\)

So, the reaction, \({N_2}{O_4}(\;g) \rightleftharpoons 2N{O_2}(\;g)\)

The required reaction quotient is \({Q_c} = \frac{{\left| {{N_2}{O_4}} \right|}}{{{{\left| {N{O_,}} \right|}^2}}}\)

Determine the reaction quotient \({Q_c}\)for \(C{O_2}(g) + {H_2}(g)\rightleftharpoons  CO(g) + {H_2}O(g)\) 

(d) In the case of any reversible response, \({Q_c}\), is the product of all the reactants' concentrations increased to the power of their individual reaction coefficients.

For the form's reversible reaction, \(aA + bB \rightleftharpoons cC + dD\)

\({Q_c} = \frac{{\mid C{)^c}|D{|^d}}}{{|A{|^{a\mid }}|B{|^b}}}\)

So, the reaction, \(C{O_2}(\;g) + {H_2}(\;g) \rightleftharpoons CO(g) + {H_2}O(g)\)

The required reaction quotient is \({Q_c} = \frac{{\left| {C{O^{\mid {H_2}O}}} \right|}}{{\left| {C{O_2}} \right|\left| {{H_2}} \right|}}\)

Determine the reaction quotient \({Q_c}\) for \(N{H_4}Cl(s) \rightleftharpoons N{H_3}(g) + HCl(g)\) 

(e)

In the case of any reversible response,\({Q_c}\), is the product of all the reactants' concentrations increased to the power of their individual reaction coefficients.

For the form's reversible reaction, \(aA + bB \rightleftharpoons cC + dD\)

\({Q_c} = \frac{{\mid C{)^c}|D{|^d}}}{{|A{|^{a\mid }}|B{|^b}}}\)

Furthermore, because the concentration of pure solids and liquids does not fluctuate considerably during the course of a reversible reaction, the concentration term for them is not included in the reaction quotient.

So, the reaction, \(N{H_4}Cl(s) \rightleftharpoons N{H_3}(\;g) + HCl(g)\)

The required reaction quotient is \({Q_c} = \left( {N{H_3}} \right)(HCl)\)

Determine the reaction quotient \({Q_c}\)for \(2\;Pb{\left( {N{O_3}} \right)_2}(s) \rightleftharpoons 2PbO(s) + 4N{O_2}(g) + {O_2}(g)\)

(f)

In the case of any reversible response,\({Q_c}\), is the product of all the reactants' concentrations increased to the power of their individual reaction coefficients.

For the form's reversible reaction, \(aA + bB \rightleftharpoons cC + dD\)

\({Q_c} = \frac{{\mid C{)^c}|D{|^d}}}{{|A{|^{a\mid }}|B{|^b}}}\)

Furthermore, because the concentration of pure solids and liquids does not change much during a reversible reaction, the concentration term for them is not included in the reaction quotient.

So, the reaction, \(2\;Pb{\left( {N{O_3}} \right)_2}(\;s) \rightleftharpoons 2PbO(s) + 4N{O_2}(\;g) + {O_2}(\;g)\)

The required reaction quotient is \({Q_c} = {\left( {N{O_2}} \right)^4}\left( {{O_2}} \right)\)

Determine the reaction quotient \({Q_c}\) for \(2{H_2}(g) + {O_2}(g) \rightleftharpoons 2{H_2}O(l)\)

(g) In the case of any reversible response, \({Q_c}\), is the product of all the reactants' concentrations increased to the power of their individual reaction coefficients.

For the form's reversible reaction, \(aA + bB \rightleftharpoons cC + dD\)

\({Q_c} = \frac{{\mid C{)^c}|D{|^d}}}{{|A{|^{a\mid }}|B{|^b}}}\)

So, the reaction \(2{H_2}(\;g) + {O_2}(\;g) \rightleftharpoons 2{H_2}O(l)\)

Furthermore, because the concentration of pure solids and liquids does not change much during a reversible reaction, the concentration term for them is not included in the reaction quotient.

The required reaction quotient is \({Q_c} = \frac{1}{{{{\left| {{H_2}} \right|}^2}\left| {{O_2}} \right|}}\)

Determine the reaction quotient \({Q_c}\) for \({S_8}(g) \rightleftharpoons  8\;S(g)\)

(h)

In the case of any reversible response,\({Q_c}\), is the product of all the reactants' concentrations increased to the power of their individual reaction coefficients.

For the form's reversible reaction, \(aA + bB \rightleftharpoons cC + dD\)

\({Q_c} = \frac{{\mid C{)^c}|D{|^d}}}{{|A{|^{a\mid }}|B{|^b}}}\)

So, the reaction, \({S_8}(g) \rightleftharpoons 8\;S(g)\)

The required reaction quotient is \({Q_c} = \frac{{|S{|^8}}}{{\left| {{S_8}} \right|}}\)