Solubility Question

[Sailor Senshi Dermystify]

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Which one will precipitate first and why? I know the smallest Ksp will precipitate first but in your opinion which one is the smallest




Ksp(Bi2S3) = 1.0 x 10-97

Ksp (Ag2S) = 2.0 x 10-49

Ksp (ZnS) = 1.0 x 10-21

Ksp (CuS) = 9.0 x 10-36

I picked Zn+2 because I thought it was smaller than Bismuth, obviously I am wrong.

This is how I ranked them from largest to smallest CuS > Ag2S > Bi2S3 > ZnS

Clearly, I made a mistake.

Rank from largest to smallest, please. I am too old to NOT understand this simple exponents, lol.

 

[dsoz]

Which one will precipitate first and why? I know the smallest Ksp will precipitate first but in your opinion which one is the smallest




Ksp(Bi2S3) = 1.0 x 10-97 (smallest)

Ksp (Ag2S) = 2.0 x 10-49

Ksp (ZnS) = 1.0 x 10-21 (largest)

Ksp (CuS) = 9.0 x 10-36

I picked Zn+2 because I thought it was smaller than Bismuth, obviously I am wrong.

This is how I ranked them from largest to smallest CuS > Ag2S > Bi2S3 > ZnS

Clearly, I made a mistake.

Rank from largest to smallest, please. I am too old to NOT understand this simple exponents, lol.

with negative exponents, the larger the exponent, the smaller the number

10^-2 is larger than 10^-3

0.01 is bigger than 0.001

so 10^-21 is larger than 10^-97.

The exponent is how many times you move the decimal to the LEFT (if negative) or RIGHT (if positive). So moving the decimal to the left 21 times gives 0.0000000000000000000010 but moving it 97 times would put 0. (*96 zeros*) than 10 a much smaller number.

(*note*) I did not want to hit my zero button 96 times to illustrate it.

dsoz

 

[milski]

Bi < Ag < Cu < Zn

The smaller the exponent, the smaller the absolute value of the number is.

 

[milski]

with negative exponents, the larger the magnitude of the exponent, the smaller the number

10^-2 is larger than 10^-3

-2 is still larger than -3.

 

[Sailor Senshi Dermystify]

with negative exponents, the larger the exponent, the smaller the number

10^-2 is larger than 10^-3

0.01 is bigger than 0.001

so 10^-21 is larger than 10^-97.

The exponent is how many times you move the decimal to the LEFT (if negative) or RIGHT (if positive). So moving the decimal to the left 21 times gives 0.0000000000000000000010 but moving it 97 times would put 0. (*96 zeros*) than 10 a much smaller number.

(*note*) I did not want to hit my zero button 96 times to illustrate it.

dsoz

Bi < Ag < Cu < Zn

The smaller the exponent, the smaller the absolute value of the number is.

-2 is still larger than -3.

Thank you guys for the quick responses. SO, I shouldn't look at the whole numbers then, instead just look at the exponents to see which one is bigger.

How about 3.0 x 10^-3 , 2.0 x 10^-3, and 4.0 x 10^-3 which one will be the largest to smallest in this example? Should I use the whole numbers to differentiate and the larger number will be first or last?

Thanks again because I am reviewing GS 3 and I got this question wrong, 😡

Easy as$ points

 

[milski]

Yes, if the exponent is the same, you have to compare the coefficient in front of it. For positive numbers, the larger number will the be the one with the larger coefficient.

In your case, 2x10^-3 < 3x10^-3 < 4x10^-3

For negative numbers, the large coefficient corresponds to larger magnitude which makes the number smaller. When we take everything we've mentioned so far in account you have this:

-4x10^-3 < -2x10^-3 < -2x10^-5 < 2x10^-5 < 2x10^-3 < 4x10^-3

 

[Sailor Senshi Dermystify]

Yes, if the exponent is the same, you have to compare the coefficient in front of it. For positive numbers, the larger number will the be the one with the larger coefficient.

In your case, 2x10^-3 < 3x10^-3 < 4x10^-3

For negative numbers, the large coefficient corresponds to larger magnitude which makes the number smaller. When we take everything we've mentioned so far in account you have this:

-4x10^-3 < -2x10^-3 < -2x10^-5 < 2x10^-5 < 2x10^-3 < 4x10^-3

Shouldn't -2x10^-5 < -2x10^-3, since 10^-5 is smaller than 10^-3

-2x10^-5 < -4x10^-3 < -2x10^-3 < 2x10^-5 < 2x10^-3 < 4x10^-3

 

[Sailor Senshi Dermystify]

Yes, if the exponent is the same, you have to compare the coefficient in front of it. For positive numbers, the larger number will the be the one with the larger coefficient.

In your case, 2x10^-3 < 3x10^-3 < 4x10^-3

For negative numbers, the large coefficient corresponds to larger magnitude which makes the number smaller. When we take everything we've mentioned so far in account you have this:

-4x10^-3 < -2x10^-3 < -2x10^-5 < 2x10^-5 < 2x10^-3 < 4x10^-3

You're a fricking LIFE Saver! Thanks to you and Dosz 😀

 

[milski]

Shouldn't -2x10^-5 < -2x10^-3, since 10^-5 is smaller than 10^-3

-2x10^-5 < -4x10^-3 < -2x10^-3 < 2x10^-5 < 2x10^-3 < 4x10^-3

No, negative numbers with larger magnitude are actually smaller. The same way -200 < -2.

 

[ridethecliche]

Don't you have to take in molar solubility into account here?

There are different numbers of ions involved in each of the compounds, so there's a difference due to that, no?

Or does that only matter when you're looking for the amount of a particular ion or common ion?

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Figured it out.

Molar solubility does matter, but it does for the same reason as it does here. The 'x' for the smallest molar solubility is the smallest for the bismuth, meaning that a smaller amount is necessary for precipitation.

Got it!

 

[Morsetlis]

You should not look at whole numbers, unless they are of different significance. That is, the exponent is a power of 10, so as long as your whole numbers are within 10 units of each other, the power matters more.

Example:

2.0 x 10^4 > 2.0 x 10^3 > 2.0 x 10^-3
A power of 4th is greater than a power is 3rd is greater than a power of -3rd.

2.0 x 10^4 > 8.0 x 10^3 > 9.0 x 10^-3
In this case, even though the second term has a greater "significant" digit, the exponent is smaller. Likewise, even though the third term has a greater "significant" digit, the exponent is negative.

1.0 x 10^-2 > 5.0 x 10^-3 > 9.0 x 10^-11
In this case, even though the terms have increasingly greater "significant" digits, the exponents are getting progressively more negative, i.e. smaller, and getting closer to 0! Note that these are all positive numbers between 1 and 0.

-1.0 x 10^-2 < -5.0 x 10^-3 < -9.0 x 10^-11
In this case, the numbers have the same absolute values as the last example, but since the significant digits are negative, the third term is closest is 0 on the negative side, the first term is farthest away from 0 on the negative side, and thus the signs are reversed! You can think of this as -1000 < -50 < -9, etc.

2.34 x 10^3 = 23.4 x 10^2
Now the significant digits have different significance! Realize how 23.4 is 10 times greater than 2.34, and thus it takes 1 less order of magnitude on the exponent to reach the same value.

2.34 x 10^3 < 23.5 x 10^2
Now, usually a power of 3rd will be greater than a power of 2nd, but since the difference in the significant digits are greater than 10 (the base power of the exponent is 10), you cannot evaluate the expression using solely the magnitude of the power! 23.5 - 2.34 = 21.16. When written out, 2.34 x 10^3 = 2340, and 23.5 x 10^2 = 2350. To make the comparison easier, make the decimal point at the same significance for both digits, and then compare powers or significant digits.
2.34 x 10^3 < 2.35 x 10^3

 

[Sailor Senshi Dermystify]

Don't you have to take in molar solubility into account here?

There are different numbers of ions involved in each of the compounds, so there's a difference due to that, no?

Or does that only matter when you're looking for the amount of a particular ion or common ion?

------
Figured it out.

Molar solubility does matter, but it does for the same reason as it does here. The 'x' for the smallest molar solubility is the smallest for the bismuth, meaning that a smaller amount is necessary for precipitation.

Got it!

You should not look at whole numbers, unless they are of different significance. That is, the exponent is a power of 10, so as long as your whole numbers are within 10 units of each other, the power matters more.

Example:

2.0 x 10^4 > 2.0 x 10^3 > 2.0 x 10^-3
A power of 4th is greater than a power is 3rd is greater than a power of -3rd.

2.0 x 10^4 > 8.0 x 10^3 > 9.0 x 10^-3
In this case, even though the second term has a greater "significant" digit, the exponent is smaller. Likewise, even though the third term has a greater "significant" digit, the exponent is negative.

1.0 x 10^-2 > 5.0 x 10^-3 > 9.0 x 10^-11
In this case, even though the terms have increasingly greater "significant" digits, the exponents are getting progressively more negative, i.e. smaller, and getting closer to 0! Note that these are all positive numbers between 1 and 0.

-1.0 x 10^-2 < -5.0 x 10^-3 < -9.0 x 10^-11
In this case, the numbers have the same absolute values as the last example, but since the significant digits are negative, the third term is closest is 0 on the negative side, the first term is farthest away from 0 on the negative side, and thus the signs are reversed! You can think of this as -1000 < -50 < -9, etc.

2.34 x 10^3 = 23.4 x 10^2
Now the significant digits have different significance! Realize how 23.4 is 10 times greater than 2.34, and thus it takes 1 less order of magnitude on the exponent to reach the same value.

2.34 x 10^3 < 23.5 x 10^2
Now, usually a power of 3rd will be greater than a power of 2nd, but since the difference in the significant digits are greater than 10 (the base power of the exponent is 10), you cannot evaluate the expression using solely the magnitude of the power! 23.5 - 2.34 = 21.16. When written out, 2.34 x 10^3 = 2340, and 23.5 x 10^2 = 2350. To make the comparison easier, make the decimal point at the same significance for both digits, and then compare powers or significant digits.
2.34 x 10^3 < 2.35 x 10^3

OMG! Thanks for the intense scientific crash course 😀. I need to brush up on scientific notations and decimals, especially dividing decimals. The simple math slows me down in my PS section, ALL the time. I get simple questions wrong because of this.
Thanks again 😀. I am still a little bit confuse with the negative significant and the negative exponent.
It's the one that is the smallest (or that's closet to zero) that will be the greatest then.

 

[ridethecliche]

Ksp is essentially a product of the molar solubilities, hence solubility product.

When comparing relative solubilities, you need to compare the 'x' values because the units are different otherwise making the values meaningless.

These are hypotheticals but:

If Ag2S03 has a ksp of 1x10^-100 (M^3)
and Mg2(OH)3 has a ksp also 1x10^-100 (M^5)

then Ag2SO3 actually precipitates first because the molar solubility is 1x10^-33 vs 1x10^-20 for Mg2 (OH)3. I.e. M values.

The units are different for the ksp's so it's useless to compare them.

 

[ridethecliche]

Someone correct me if I'm wrong.