For which of the following mixtures will Ag2SO4(s)precipitate?150.0 mL of 0.10 M Na2SO4(aq) and 5.0 mL of 0.20 M AgNO3(aq)150.0 mL of 0.10 M Na2SO4(aq) and 5.0 mL of 0.30 M AgNO3(aq)150.0 mL of 0.10 M Na2SO4(aq) and 5.0 mL of 0.40 M AgNO3(aq)150.0 mL of 0.10 M Na2SO4(aq) and 5.0 mL of 0.50 M AgNO3(aq)

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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 asKsp mK_ mspKsp​. The solubility product value relates to the saturated solution and indicates the precipitate level of the compound. The formation precipitation starts when ionic product exceeds the solubility product.

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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 Ag2SO4 mA mg_ m2 mS mO_4Ag2​SO4​

The equilibrium equation for the ionic compound is given below:

Therefore, the solubility product of the ionic compound is

Ksp=2=1.2×10−5eginarrayc\ mK_ msp, m = ,left< mA mg^ m + ight>^ m2left< mSO_4^2 - ight>\\ = 1.2 imes 10^ - 5\endarrayKsp​=2=1.2×10−5​

The balanced equation for the reaction of AgNO3andNa2SO4: mAgN mO_3; mand N ma_ m2 mS mO_ m4:AgNO3​andNa2​SO4​:

The initial concentration of left< mA mg^ + ight> ions in AgNO3 mAgN mO_3AgNO3​is given below:

initial=5.0mL×0.20mmolAgNO3mL×1molAg+1molAgNO3(150.0+5.0)mL=0.00645Meginarrayc\left< mA mg^ + ight>_ minitial = frac5.0 mmL imes frac m0 m.20mmol AgN mO_3 mmL imes frac1 m mol A mg^ + 1 m mol AgN mO_3left( 150.0 + 5.0 ight) mmL\\ = 0.00645 mM\endarrayinitial​=(150.0+5.0)mL5.0mL×mL0.20mmolAgNO3​​×1molAgNO3​1molAg+​​=0.00645M​

The initial concentration of left< mSO_4^2 - ight> ions in Na2SO4 mN ma_ m2 mS mO_ m4Na2​SO4​is given below:

initial=150.0mL×0.10mmolNa2SO4mL×1molSO42−1molNa2SO4(150.0+5.0)mL=0.0968Meginarrayc\left< mSO_ m4^ m2 - ight>_ minitial = frac150.0 mmL imes frac m0 m.10mmol N ma_ m2 mS mO_ m4 mmL imes frac1 m mol SO_4^2 - 1 m mol N ma_ m2 mS mO_ m4left( 150.0 + 5.0 ight) mmL\\ = 0.0968 mM\endarrayinitial​=(150.0+5.0)mL150.0mL×mL0.10mmolNa2​SO4​​×1molNa2​SO4​1molSO42−​​​=0.0968M​

The ionic product of Ag2SO3 mA mg_ m2 mS mO_ m3Ag2​SO3​is given below:

KIP=initial2initial=(0.00645)2(0.0968)=4.0×10−6eginarrayc\ mK_ mIP = left< mA mg^ + ight>_ minitial^2left< mSO_4^2 - ight>_ minitial\\ = left( 0.00645 ight)^2left( 0.0968 ight)\\ = 4.0 imes 10^ - 6\endarrayKIP​=initial2​initial​=(0.00645)2(0.0968)=4.0×10−6​

The ionic product (KIP)left( mK_ mIP ight)(KIP​) is less than the solubility product (Ksp)left( mK_ msp ight)(Ksp​),

KIPKsp⇒precipitationdoesnottakesplace mK_ mIP KIP​Ksp​⇒precipitationdoesnottakesplace

The balanced equation for the reaction of AgNO3andNa2SO4: mAgN mO_3; mand N ma_ m2 mS mO_ m4:AgNO3​andNa2​SO4​:

The initial concentration of left< mA mg^ + ight> ions in AgNO3 mAgN mO_3AgNO3​is given below:

initial=5.0mL×0.30mmolAgNO3mL×1molAg+1molAgNO3(150.0+5.0)mL=0.00968Meginarrayc\left< mA mg^ + ight>_ minitial = frac5.0 mmL imes frac m0 m.30mmol AgN mO_3 mmL imes frac1 m mol A mg^ + 1 m mol AgN mO_3left( 150.0 + 5.0 ight) mmL\\ = 0.00968 mM\endarrayinitial​=(150.0+5.0)mL5.0mL×mL0.30mmolAgNO3​​×1molAgNO3​1molAg+​​=0.00968M​

The initial concentration of left< mSO_4^2 - ight> ions in Na2SO4 mN ma_ m2 mS mO_ m4Na2​SO4​is given below:

initial=150.0mL×0.10mmolNa2SO4mL×1molSO42−1molNa2SO4(150.0+5.0)mL=0.0968Meginarrayc\left< mSO_ m4^ m2 - ight>_ minitial = frac150.0 mmL imes frac m0 m.10mmol N ma_ m2 mS mO_ m4 mmL imes frac1 m mol SO_4^2 - 1 m mol N ma_ m2 mS mO_ m4left( 150.0 + 5.0 ight) mmL\\ = 0.0968 mM\endarrayinitial​=(150.0+5.0)mL150.0mL×mL0.10mmolNa2​SO4​​×1molNa2​SO4​1molSO42−​​​=0.0968M​

The ionic product of Ag2SO3 mA mg_ m2 mS mO_ m3Ag2​SO3​is given below:

KIP=initial2initial=(0.00968)2(0.0968)=9.1×10−6eginarrayc\ mK_ mIP = left< mA mg^ + ight>_ minitial^2left< mSO_4^2 - ight>_ minitial\\ = left( 0.00968 ight)^2left( 0.0968 ight)\\ = 9.1 imes 10^ - 6\endarrayKIP​=initial2​initial​=(0.00968)2(0.0968)=9.1×10−6​

The ionic product (KIP)left( mK_ mIP ight)(KIP​) is less than the solubility product(Ksp)left( mK_ msp ight)(Ksp​),

KIPKsp⇒precipitationdoesnottakesplace mK_ mIP KIP​Ksp​⇒precipitationdoesnottakesplace

The balanced equation for the reaction of AgNO3andNa2SO4: mAgN mO_3; mand N ma_ m2 mS mO_ m4:AgNO3​andNa2​SO4​:

The initial concentration of left< mA mg^ + ight> ions in AgNO3 mAgN mO_3AgNO3​is given below:

initial=5.0mL×0.40mmolAgNO3mL×1molAg+1molAgNO3(150.0+5.0)mL=0.0129Meginarrayc\left< mA mg^ + ight>_ minitial = frac5.0 mmL imes frac m0 m.40mmol AgN mO_3 mmL imes frac1 m mol A mg^ + 1 m mol AgN mO_3left( 150.0 + 5.0 ight) mmL\\ = 0.0129 mM\endarrayinitial​=(150.0+5.0)mL5.0mL×mL0.40mmolAgNO3​​×1molAgNO3​1molAg+​​=0.0129M​

The initial concentration of left< mSO_4^2 - ight> ions in Na2SO4 mN ma_ m2 mS mO_ m4Na2​SO4​is given below:

initial=150.0mL×0.10mmolNa2SO4mL×1molSO42−1molNa2SO4(150.0+5.0)mL=0.0968Meginarrayc\left< mSO_ m4^ m2 - ight>_ minitial = frac150.0 mmL imes frac m0 m.10mmol N ma_ m2 mS mO_ m4 mmL imes frac1 m mol SO_4^2 - 1 m mol N ma_ m2 mS mO_ m4left( 150.0 + 5.0 ight) mmL\\ = 0.0968 mM\endarrayinitial​=(150.0+5.0)mL150.0mL×mL0.10mmolNa2​SO4​​×1molNa2​SO4​1molSO42−​​​=0.0968M​

The ionic product of Ag2SO3 mA mg_ m2 mS mO_ m3Ag2​SO3​is given below:

KIP=initial2initial=(0.0129)2(0.0968)=1.6×10−5eginarrayc\ mK_ mIP = left< mA mg^ + ight>_ minitial^2left< mSO_4^2 - ight>_ minitial\\ = left( 0.0129 ight)^2left( 0.0968 ight)\\ = 1.6 imes 10^ - 5\endarrayKIP​=initial2​initial​=(0.0129)2(0.0968)=1.6×10−5​

The ionic product (KIP)left( mK_ mIP ight)(KIP​) is greater than the solubility product (Ksp)left( mK_ msp ight)(Ksp​),

KIP>Ksp⇒precipitationtakesplace mK_ mIP > mK_ msp Rightarrow mprecipitation takes placeKIP​>Ksp​⇒precipitationtakesplace

The balanced equation for the reaction of AgNO3andNa2SO4: mAgN mO_3; mand N ma_ m2 mS mO_ m4:AgNO3​andNa2​SO4​:

The initial concentration of left< mA mg^ + ight> ions in AgNO3 mAgN mO_3AgNO3​is given below:

initial=5.0mL×0.50mmolAgNO3mL×1molAg+1molAgNO3(150.0+5.0)mL=0.0161Meginarrayc\left< mA mg^ + ight>_ minitial = frac5.0 mmL imes frac m0 m.50mmol AgN mO_3 mmL imes frac1 m mol A mg^ + 1 m mol AgN mO_3left( 150.0 + 5.0 ight) mmL\\ = 0.0161 mM\endarrayinitial​=(150.0+5.0)mL5.0mL×mL0.50mmolAgNO3​​×1molAgNO3​1molAg+​​=0.0161M​

The initial concentration of left< mSO_4^2 - ight> ions in Na2SO4 mN ma_ m2 mS mO_ m4Na2​SO4​is given below:

initial=150.0mL×0.10mmolNa2SO4mL×1molSO42−1molNa2SO4(150.0+5.0)mL=0.0968Meginarrayc\left< mSO_ m4^ m2 - ight>_ minitial = frac150.0 mmL imes frac m0 m.10mmol N ma_ m2 mS mO_ m4 mmL imes frac1 m mol SO_4^2 - 1 m mol N ma_ m2 mS mO_ m4left( 150.0 + 5.0 ight) mmL\\ = 0.0968 mM\endarrayinitial​=(150.0+5.0)mL150.0mL×mL0.10mmolNa2​SO4​​×1molNa2​SO4​1molSO42−​​​=0.0968M​

The ionic product of Ag2SO3 mA mg_ m2 mS mO_ m3Ag2​SO3​is given below:

KIP=initial2initial=(0.0161)2(0.0968)=2.5×10−5eginarrayc\ mK_ mIP = left< mA mg^ + ight>_ minitial^2left< mSO_4^2 - ight>_ minitial\\ = left( 0.0161 ight)^2left( 0.0968 ight)\\ = 2.5 imes 10^ - 5\endarrayKIP​=initial2​initial​=(0.0161)2(0.0968)=2.5×10−5​

The ionic product (KIP)left( mK_ mIP ight)(KIP​) is greater than the solubility product(Ksp)left( mK_ msp ight)(Ksp​),

KIP>Ksp⇒precipitationtakesplace mK_ mIP > mK_ msp Rightarrow mprecipitation takes placeKIP​>Ksp​⇒precipitationtakesplace

Ans:

For the mixture, 150.0mLof0.10MNa2SO4(aq)and5.0mLof0.20MAgNO3(aq) m150 m.0mL of 0 m.10 M N ma_ m2 mS mO_ m4left( maq ight) m and 5 m.0 mL of 0 m.20 M AgN mO_ m3left( maq ight)150.0mLof0.10MNa2​SO4​(aq)and5.0mLof0.20MAgNO3​(aq) precipitation does not take place.

For the mixture, 150.0mLof0.10MNa2SO4(aq)and5.0mLof0.30MAgNO3(aq) m150 m.0mL of 0 m.10 M N ma_ m2 mS mO_ m4left( maq ight) m and 5 m.0 mL of 0 m.30 M AgN mO_ m3left( maq ight)150.0mLof0.10MNa2​SO4​(aq)and5.0mLof0.30MAgNO3​(aq) precipitation does not take place.

For the mixture, 150.0mLof0.10MNa2SO4(aq)and5.0mLof0.40MAgNO3(aq) m150 m.0mL of 0 m.10 M N ma_ m2 mS mO_ m4left( maq ight) m and 5 m.0 mL of 0 m.40 M AgN mO_ m3left( maq ight)150.0mLof0.10MNa2​SO4​(aq)and5.0mLof0.40MAgNO3​(aq) precipitation takes place.

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For the mixture, 150.0mLof0.10MNa2SO4(aq)and5.0mLof0.50MAgNO3(aq) m150 m.0mL of 0 m.10 M N ma_ m2 mS mO_ m4left( maq ight) m and 5 m.0 mL of 0 m.50 M AgN mO_ m3left( maq ight)150.0mLof0.10MNa2​SO4​(aq)and5.0mLof0.50MAgNO3​(aq) precipitation takes place.