Concepts and reason
The solubility product for the reaction is equilibrium constant where the solid ionic compound dissociates into its ions in a solution. The solubility product is denoted asK s p {{\rm{K}}_{{\rm{sp}}}} K s p
Fundamentals
The solubility product value of the compound depends on the concentrations of its ions in a solution.
Example: AB is a solid ionic compound.
Precipitation: If the solubility product value is lesser than the concentration of the ions present in the solution, the compound precipitates in the solution.
The given solid ionic compound is A g 2 S O 4 {\rm{A}}{{\rm{g}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_4} A g 2 S O 4
The equilibrium equation for the ionic compound is given below:
Therefore, the solubility product of the ionic compound is
K s p = [ A g + ] 2 [ S O 4 2 − ] = 1 . 2 × 1 0 − 5 \begin{array}{c}\\{{\rm{K}}_{{\rm{sp}}}}\,{\rm{ = }}\,{\left[ {{\rm{A}}{{\rm{g}}^{\rm{ + }}}} \right]^{\rm{2}}}\left[ {{\rm{SO}}_4^{2 - }} \right]\\\\ = 1.2 \times {10^{ - 5}}\\\end{array} K s p = [ A g + ] 2 [ S O 4 2 − ] = 1 . 2 × 1 0 − 5
The balanced equation for the reaction of A g N O 3 a n d N a 2 S O 4 : {\rm{AgN}}{{\rm{O}}_3}\;{\rm{and N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}: A g N O 3 a n d N a 2 S O 4 :
The initial concentration of [ A g + ] \left[ {{\rm{A}}{{\rm{g}}^ + }} \right] [ A g + ] A g N O 3 {\rm{AgN}}{{\rm{O}}_3} A g N O 3
[ A g + ] i n i t i a l = 5 . 0 m L × 0 . 2 0 m m o l A g N O 3 m L × 1 m o l A g + 1 m o l A g N O 3 ( 1 5 0 . 0 + 5 . 0 ) m L = 0 . 0 0 6 4 5 M \begin{array}{c}\\{\left[ {{\rm{A}}{{\rm{g}}^ + }} \right]_{{\rm{initial}}}} = \frac{{5.0{\rm{mL}} \times \frac{{{\rm{0}}{\rm{.20mmol AgN}}{{\rm{O}}_3}}}{{{\rm{mL}}}} \times \frac{{1{\rm{ mol A}}{{\rm{g}}^ + }}}{{1{\rm{ mol AgN}}{{\rm{O}}_3}}}}}{{\left( {150.0 + 5.0} \right){\rm{mL}}}}\\\\ = 0.00645{\rm{M}}\\\end{array} [ A g + ] i n i t i a l = ( 1 5 0 . 0 + 5 . 0 ) m L 5 . 0 m L × m L 0 . 2 0 m m o l A g N O 3 × 1 m o l A g N O 3 1 m o l A g + = 0 . 0 0 6 4 5 M
The initial concentration of [ S O 4 2 − ] \left[ {{\rm{SO}}_4^{2 - }} \right] [ S O 4 2 − ] N a 2 S O 4 {\rm{N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}} N a 2 S O 4
[ S O 4 2 − ] i n i t i a l = 1 5 0 . 0 m L × 0 . 1 0 m m o l N a 2 S O 4 m L × 1 m o l S O 4 2 − 1 m o l N a 2 S O 4 ( 1 5 0 . 0 + 5 . 0 ) m L = 0 . 0 9 6 8 M \begin{array}{c}\\{\left[ {{\rm{SO}}_{\rm{4}}^{{\rm{2 - }}}} \right]_{{\rm{initial}}}} = \frac{{150.0{\rm{mL}} \times \frac{{{\rm{0}}{\rm{.10mmol N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}}}{{{\rm{mL}}}} \times \frac{{1{\rm{ mol }}SO_4^{2 - }}}{{1{\rm{ mol N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}}}}}{{\left( {150.0 + 5.0} \right){\rm{mL}}}}\\\\ = 0.0968{\rm{M}}\\\end{array} [ S O 4 2 − ] i n i t i a l = ( 1 5 0 . 0 + 5 . 0 ) m L 1 5 0 . 0 m L × m L 0 . 1 0 m m o l N a 2 S O 4 × 1 m o l N a 2 S O 4 1 m o l S O 4 2 − = 0 . 0 9 6 8 M
The ionic product of A g 2 S O 3 {\rm{A}}{{\rm{g}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{3}}} A g 2 S O 3
K I P = [ A g + ] i n i t i a l 2 [ S O 4 2 − ] i n i t i a l = ( 0 . 0 0 6 4 5 ) 2 ( 0 . 0 9 6 8 ) = 4 . 0 × 1 0 − 6 \begin{array}{c}\\{{\rm{K}}_{{\rm{IP}}}} = \left[ {{\rm{A}}{{\rm{g}}^ + }} \right]_{{\rm{initial}}}^2{\left[ {{\rm{SO}}_4^{2 - }} \right]_{{\rm{initial}}}}\\\\ = {\left( {0.00645} \right)^2}\left( {0.0968} \right)\\\\ = 4.0 \times {10^{ - 6}}\\\end{array} K I P = [ A g + ] i n i t i a l 2 [ S O 4 2 − ] i n i t i a l = ( 0 . 0 0 6 4 5 ) 2 ( 0 . 0 9 6 8 ) = 4 . 0 × 1 0 − 6
The ionic product ( K I P ) \left( {{{\rm{K}}_{{\rm{IP}}}}} \right) ( K I P ) ( K s p ) \left( {{{\rm{K}}_{{\rm{sp}}}}} \right) ( K s p )
K I P < K s p ⇒ p r e c i p i t a t i o n d o e s n o t t a k e s p l a c e {{\rm{K}}_{{\rm{IP}}}} < {{\rm{K}}_{{\rm{sp}}}} \Rightarrow {\rm{precipitation does not takes place}} K I P < K s p ⇒ p r e c i p i t a t i o n d o e s n o t t a k e s p l a c e
The balanced equation for the reaction of A g N O 3 a n d N a 2 S O 4 : {\rm{AgN}}{{\rm{O}}_3}\;{\rm{and N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}: A g N O 3 a n d N a 2 S O 4 :
The initial concentration of [ A g + ] \left[ {{\rm{A}}{{\rm{g}}^ + }} \right] [ A g + ] A g N O 3 {\rm{AgN}}{{\rm{O}}_3} A g N O 3
[ A g + ] i n i t i a l = 5 . 0 m L × 0 . 3 0 m m o l A g N O 3 m L × 1 m o l A g + 1 m o l A g N O 3 ( 1 5 0 . 0 + 5 . 0 ) m L = 0 . 0 0 9 6 8 M \begin{array}{c}\\{\left[ {{\rm{A}}{{\rm{g}}^ + }} \right]_{{\rm{initial}}}} = \frac{{5.0{\rm{mL}} \times \frac{{{\rm{0}}{\rm{.30mmol AgN}}{{\rm{O}}_3}}}{{{\rm{mL}}}} \times \frac{{1{\rm{ mol A}}{{\rm{g}}^ + }}}{{1{\rm{ mol AgN}}{{\rm{O}}_3}}}}}{{\left( {150.0 + 5.0} \right){\rm{mL}}}}\\\\ = 0.00968{\rm{M}}\\\end{array} [ A g + ] i n i t i a l = ( 1 5 0 . 0 + 5 . 0 ) m L 5 . 0 m L × m L 0 . 3 0 m m o l A g N O 3 × 1 m o l A g N O 3 1 m o l A g + = 0 . 0 0 9 6 8 M
The initial concentration of [ S O 4 2 − ] \left[ {{\rm{SO}}_4^{2 - }} \right] [ S O 4 2 − ] N a 2 S O 4 {\rm{N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}} N a 2 S O 4
[ S O 4 2 − ] i n i t i a l = 1 5 0 . 0 m L × 0 . 1 0 m m o l N a 2 S O 4 m L × 1 m o l S O 4 2 − 1 m o l N a 2 S O 4 ( 1 5 0 . 0 + 5 . 0 ) m L = 0 . 0 9 6 8 M \begin{array}{c}\\{\left[ {{\rm{SO}}_{\rm{4}}^{{\rm{2 - }}}} \right]_{{\rm{initial}}}} = \frac{{150.0{\rm{mL}} \times \frac{{{\rm{0}}{\rm{.10mmol N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}}}{{{\rm{mL}}}} \times \frac{{1{\rm{ mol }}SO_4^{2 - }}}{{1{\rm{ mol N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}}}}}{{\left( {150.0 + 5.0} \right){\rm{mL}}}}\\\\ = 0.0968{\rm{M}}\\\end{array} [ S O 4 2 − ] i n i t i a l = ( 1 5 0 . 0 + 5 . 0 ) m L 1 5 0 . 0 m L × m L 0 . 1 0 m m o l N a 2 S O 4 × 1 m o l N a 2 S O 4 1 m o l S O 4 2 − = 0 . 0 9 6 8 M
The ionic product of A g 2 S O 3 {\rm{A}}{{\rm{g}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{3}}} A g 2 S O 3
K I P = [ A g + ] i n i t i a l 2 [ S O 4 2 − ] i n i t i a l = ( 0 . 0 0 9 6 8 ) 2 ( 0 . 0 9 6 8 ) = 9 . 1 × 1 0 − 6 \begin{array}{c}\\{{\rm{K}}_{{\rm{IP}}}} = \left[ {{\rm{A}}{{\rm{g}}^ + }} \right]_{{\rm{initial}}}^2{\left[ {{\rm{SO}}_4^{2 - }} \right]_{{\rm{initial}}}}\\\\ = {\left( {0.00968} \right)^2}\left( {0.0968} \right)\\\\ = 9.1 \times {10^{ - 6}}\\\end{array} K I P = [ A g + ] i n i t i a l 2 [ S O 4 2 − ] i n i t i a l = ( 0 . 0 0 9 6 8 ) 2 ( 0 . 0 9 6 8 ) = 9 . 1 × 1 0 − 6
The ionic product ( K I P ) \left( {{{\rm{K}}_{{\rm{IP}}}}} \right) ( K I P ) ( K s p ) \left( {{{\rm{K}}_{{\rm{sp}}}}} \right) ( K s p )
K I P < K s p ⇒ p r e c i p i t a t i o n d o e s n o t t a k e s p l a c e {{\rm{K}}_{{\rm{IP}}}} < {{\rm{K}}_{{\rm{sp}}}} \Rightarrow {\rm{precipitation does not takes place}} K I P < K s p ⇒ p r e c i p i t a t i o n d o e s n o t t a k e s p l a c e
The balanced equation for the reaction of A g N O 3 a n d N a 2 S O 4 : {\rm{AgN}}{{\rm{O}}_3}\;{\rm{and N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}: A g N O 3 a n d N a 2 S O 4 :
The initial concentration of [ A g + ] \left[ {{\rm{A}}{{\rm{g}}^ + }} \right] [ A g + ] A g N O 3 {\rm{AgN}}{{\rm{O}}_3} A g N O 3
[ A g + ] i n i t i a l = 5 . 0 m L × 0 . 4 0 m m o l A g N O 3 m L × 1 m o l A g + 1 m o l A g N O 3 ( 1 5 0 . 0 + 5 . 0 ) m L = 0 . 0 1 2 9 M \begin{array}{c}\\{\left[ {{\rm{A}}{{\rm{g}}^ + }} \right]_{{\rm{initial}}}} = \frac{{5.0{\rm{mL}} \times \frac{{{\rm{0}}{\rm{.40mmol AgN}}{{\rm{O}}_3}}}{{{\rm{mL}}}} \times \frac{{1{\rm{ mol A}}{{\rm{g}}^ + }}}{{1{\rm{ mol AgN}}{{\rm{O}}_3}}}}}{{\left( {150.0 + 5.0} \right){\rm{mL}}}}\\\\ = 0.0129{\rm{M}}\\\end{array} [ A g + ] i n i t i a l = ( 1 5 0 . 0 + 5 . 0 ) m L 5 . 0 m L × m L 0 . 4 0 m m o l A g N O 3 × 1 m o l A g N O 3 1 m o l A g + = 0 . 0 1 2 9 M
The initial concentration of [ S O 4 2 − ] \left[ {{\rm{SO}}_4^{2 - }} \right] [ S O 4 2 − ] N a 2 S O 4 {\rm{N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}} N a 2 S O 4
[ S O 4 2 − ] i n i t i a l = 1 5 0 . 0 m L × 0 . 1 0 m m o l N a 2 S O 4 m L × 1 m o l S O 4 2 − 1 m o l N a 2 S O 4 ( 1 5 0 . 0 + 5 . 0 ) m L = 0 . 0 9 6 8 M \begin{array}{c}\\{\left[ {{\rm{SO}}_{\rm{4}}^{{\rm{2 - }}}} \right]_{{\rm{initial}}}} = \frac{{150.0{\rm{mL}} \times \frac{{{\rm{0}}{\rm{.10mmol N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}}}{{{\rm{mL}}}} \times \frac{{1{\rm{ mol }}SO_4^{2 - }}}{{1{\rm{ mol N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}}}}}{{\left( {150.0 + 5.0} \right){\rm{mL}}}}\\\\ = 0.0968{\rm{M}}\\\end{array} [ S O 4 2 − ] i n i t i a l = ( 1 5 0 . 0 + 5 . 0 ) m L 1 5 0 . 0 m L × m L 0 . 1 0 m m o l N a 2 S O 4 × 1 m o l N a 2 S O 4 1 m o l S O 4 2 − = 0 . 0 9 6 8 M
The ionic product of A g 2 S O 3 {\rm{A}}{{\rm{g}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{3}}} A g 2 S O 3
K I P = [ A g + ] i n i t i a l 2 [ S O 4 2 − ] i n i t i a l = ( 0 . 0 1 2 9 ) 2 ( 0 . 0 9 6 8 ) = 1 . 6 × 1 0 − 5 \begin{array}{c}\\{{\rm{K}}_{{\rm{IP}}}} = \left[ {{\rm{A}}{{\rm{g}}^ + }} \right]_{{\rm{initial}}}^2{\left[ {{\rm{SO}}_4^{2 - }} \right]_{{\rm{initial}}}}\\\\ = {\left( {0.0129} \right)^2}\left( {0.0968} \right)\\\\ = 1.6 \times {10^{ - 5}}\\\end{array} K I P = [ A g + ] i n i t i a l 2 [ S O 4 2 − ] i n i t i a l = ( 0 . 0 1 2 9 ) 2 ( 0 . 0 9 6 8 ) = 1 . 6 × 1 0 − 5
The ionic product ( K I P ) \left( {{{\rm{K}}_{{\rm{IP}}}}} \right) ( K I P ) ( K s p ) \left( {{{\rm{K}}_{{\rm{sp}}}}} \right) ( K s p )
K I P > K s p ⇒ p r e c i p i t a t i o n t a k e s p l a c e {{\rm{K}}_{{\rm{IP}}}} > {{\rm{K}}_{{\rm{sp}}}} \Rightarrow {\rm{precipitation takes place}} K I P > K s p ⇒ p r e c i p i t a t i o n t a k e s p l a c e
The balanced equation for the reaction of A g N O 3 a n d N a 2 S O 4 : {\rm{AgN}}{{\rm{O}}_3}\;{\rm{and N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}: A g N O 3 a n d N a 2 S O 4 :
The initial concentration of [ A g + ] \left[ {{\rm{A}}{{\rm{g}}^ + }} \right] [ A g + ] A g N O 3 {\rm{AgN}}{{\rm{O}}_3} A g N O 3
[ A g + ] i n i t i a l = 5 . 0 m L × 0 . 5 0 m m o l A g N O 3 m L × 1 m o l A g + 1 m o l A g N O 3 ( 1 5 0 . 0 + 5 . 0 ) m L = 0 . 0 1 6 1 M \begin{array}{c}\\{\left[ {{\rm{A}}{{\rm{g}}^ + }} \right]_{{\rm{initial}}}} = \frac{{5.0{\rm{mL}} \times \frac{{{\rm{0}}{\rm{.50mmol AgN}}{{\rm{O}}_3}}}{{{\rm{mL}}}} \times \frac{{1{\rm{ mol A}}{{\rm{g}}^ + }}}{{1{\rm{ mol AgN}}{{\rm{O}}_3}}}}}{{\left( {150.0 + 5.0} \right){\rm{mL}}}}\\\\ = 0.0161{\rm{M}}\\\end{array} [ A g + ] i n i t i a l = ( 1 5 0 . 0 + 5 . 0 ) m L 5 . 0 m L × m L 0 . 5 0 m m o l A g N O 3 × 1 m o l A g N O 3 1 m o l A g + = 0 . 0 1 6 1 M
The initial concentration of [ S O 4 2 − ] \left[ {{\rm{SO}}_4^{2 - }} \right] [ S O 4 2 − ] N a 2 S O 4 {\rm{N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}} N a 2 S O 4
[ S O 4 2 − ] i n i t i a l = 1 5 0 . 0 m L × 0 . 1 0 m m o l N a 2 S O 4 m L × 1 m o l S O 4 2 − 1 m o l N a 2 S O 4 ( 1 5 0 . 0 + 5 . 0 ) m L = 0 . 0 9 6 8 M \begin{array}{c}\\{\left[ {{\rm{SO}}_{\rm{4}}^{{\rm{2 - }}}} \right]_{{\rm{initial}}}} = \frac{{150.0{\rm{mL}} \times \frac{{{\rm{0}}{\rm{.10mmol N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}}}{{{\rm{mL}}}} \times \frac{{1{\rm{ mol }}SO_4^{2 - }}}{{1{\rm{ mol N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}}}}}{{\left( {150.0 + 5.0} \right){\rm{mL}}}}\\\\ = 0.0968{\rm{M}}\\\end{array} [ S O 4 2 − ] i n i t i a l = ( 1 5 0 . 0 + 5 . 0 ) m L 1 5 0 . 0 m L × m L 0 . 1 0 m m o l N a 2 S O 4 × 1 m o l N a 2 S O 4 1 m o l S O 4 2 − = 0 . 0 9 6 8 M
The ionic product of A g 2 S O 3 {\rm{A}}{{\rm{g}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{3}}} A g 2 S O 3
K I P = [ A g + ] i n i t i a l 2 [ S O 4 2 − ] i n i t i a l = ( 0 . 0 1 6 1 ) 2 ( 0 . 0 9 6 8 ) = 2 . 5 × 1 0 − 5 \begin{array}{c}\\{{\rm{K}}_{{\rm{IP}}}} = \left[ {{\rm{A}}{{\rm{g}}^ + }} \right]_{{\rm{initial}}}^2{\left[ {{\rm{SO}}_4^{2 - }} \right]_{{\rm{initial}}}}\\\\ = {\left( {0.0161} \right)^2}\left( {0.0968} \right)\\\\ = 2.5 \times {10^{ - 5}}\\\end{array} K I P = [ A g + ] i n i t i a l 2 [ S O 4 2 − ] i n i t i a l = ( 0 . 0 1 6 1 ) 2 ( 0 . 0 9 6 8 ) = 2 . 5 × 1 0 − 5
The ionic product ( K I P ) \left( {{{\rm{K}}_{{\rm{IP}}}}} \right) ( K I P ) ( K s p ) \left( {{{\rm{K}}_{{\rm{sp}}}}} \right) ( K s p )
K I P > K s p ⇒ p r e c i p i t a t i o n t a k e s p l a c e {{\rm{K}}_{{\rm{IP}}}} > {{\rm{K}}_{{\rm{sp}}}} \Rightarrow {\rm{precipitation takes place}} K I P > K s p ⇒ p r e c i p i t a t i o n t a k e s p l a c e
Ans:
For the mixture, 1 5 0 . 0 m L o f 0 . 1 0 M N a 2 S O 4 ( a q ) a n d 5 . 0 m L o f 0 . 2 0 M A g N O 3 ( a q ) {\rm{150}}{\rm{.0mL of 0}}{\rm{.10 M N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}\left( {{\rm{aq}}} \right){\rm{ and 5}}{\rm{.0 mL of 0}}{\rm{.20 M AgN}}{{\rm{O}}_{\rm{3}}}\left( {{\rm{aq}}} \right) 1 5 0 . 0 m L o f 0 . 1 0 M N a 2 S O 4 ( a q ) a n d 5 . 0 m L o f 0 . 2 0 M A g N O 3 ( a q )
For the mixture, 1 5 0 . 0 m L o f 0 . 1 0 M N a 2 S O 4 ( a q ) a n d 5 . 0 m L o f 0 . 3 0 M A g N O 3 ( a q ) {\rm{150}}{\rm{.0mL of 0}}{\rm{.10 M N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}\left( {{\rm{aq}}} \right){\rm{ and 5}}{\rm{.0 mL of 0}}{\rm{.30 M AgN}}{{\rm{O}}_{\rm{3}}}\left( {{\rm{aq}}} \right) 1 5 0 . 0 m L o f 0 . 1 0 M N a 2 S O 4 ( a q ) a n d 5 . 0 m L o f 0 . 3 0 M A g N O 3 ( a q )
For the mixture, 1 5 0 . 0 m L o f 0 . 1 0 M N a 2 S O 4 ( a q ) a n d 5 . 0 m L o f 0 . 4 0 M A g N O 3 ( a q ) {\rm{150}}{\rm{.0mL of 0}}{\rm{.10 M N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}\left( {{\rm{aq}}} \right){\rm{ and 5}}{\rm{.0 mL of 0}}{\rm{.40 M AgN}}{{\rm{O}}_{\rm{3}}}\left( {{\rm{aq}}} \right) 1 5 0 . 0 m L o f 0 . 1 0 M N a 2 S O 4 ( a q ) a n d 5 . 0 m L o f 0 . 4 0 M A g N O 3 ( a q )
For the mixture, 1 5 0 . 0 m L o f 0 . 1 0 M N a 2 S O 4 ( a q ) a n d 5 . 0 m L o f 0 . 5 0 M A g N O 3 ( a q ) {\rm{150}}{\rm{.0mL of 0}}{\rm{.10 M N}}{{\rm{a}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}\left( {{\rm{aq}}} \right){\rm{ and 5}}{\rm{.0 mL of 0}}{\rm{.50 M AgN}}{{\rm{O}}_{\rm{3}}}\left( {{\rm{aq}}} \right) 1 5 0 . 0 m L o f 0 . 1 0 M N a 2 S O 4 ( a q ) a n d 5 . 0 m L o f 0 . 5 0 M A g N O 3 ( a q )
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