10/19/2017 11:55 PM80.6/100010/19/2017 05:48 PM ore Grade Question 14 of 16 Sapl

Question

10/19/2017 11:55 PM80.6/100010/19/2017 05:48 PM ore Grade Question 14 of 16 Sapling Learning For many weak acid or weak base calculations, you can use a simpitying assumption to quadratic equations. Classify these situations by whether the assumption is valid or the quadratic formula is required. Assumption is valid Quadratic formula is required [HA-0.1 M [HA]-0.001 M K1x10- [HA]-1 M Ka-1x 103 [HAJ-0.01 M Ka-1x10-5 [HAJ 0.01 M K1x 10 There is a hint available! bottom divider bar, Click on the divider bar again to hide the hint. Close

Explanation / Answer

[HA] =0.001 with out quadratic expression, x2=0.001*1*10-5, x=0.0001

With quadratic expression, x2/(0.001-x)=1*10-5,

When solved using excel, x=0.000099 which is not significantly different from x calculated from not considering the quadratic expression. Since Ka is significantly lower than the concentration of weak acid HA, quadratic expression need not be considered.

For the second case, without considering the quadratic expression

, x2= 1.1*10-5*0.01 ,x =0.003162

While accounting the quadratic expression

, x2/(0.01-x)= 1.1*10-5, when solved using excel, x= 0.000328

Not much different from the previous value. Hence

When Ka is very low and concentration of acid is less, the assumption of not considering the quadratic expression is valid.

Ka is 1*10-3M, and [HA]=0.1M, quadratic expression will not have to be considered. This is proved below

Without considering the quadratic expression x2= 1*10-3*0.1, x=10-2 = 0.01

With considering the quadratic expression, x2(0.1-x)= 1*10-3, when solved using excel, x=0.0096, not significantly different

Since the acid is weak, the extent of dissociation is limited and if ka is less, the approximation of not considering the quadratic expression is valid.

When [HA]=1M

Without considering the quadratic expression, x=sqrt(1*10-3)= 0.03162M

When considering the quadratic expression, x2/(1-x)= 1*10-3, x=0.0312M

Here not valid.

when x=0.01M, Ka= 1*10-4

without considering the quadratic expression, x= 0.001

when considering the quadratic expression, x2/(0.01-x)= 1*10-4

when solved using excel, x= 0.000955 ,hence one does not have to consider the quadratic expression.

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