Solubility product computations

[Addallat]

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Q: The value of the solubility product for copper(I) chloride is 1.2*10^-6. Under normal conditions, the maximum concentration of an aqueous CuCl solution will be.


A. Less than 10^-6 M and less than 10^-4 M
B. greater than 10^-6 M and less than 10^-4 M
C. greater than 10^-4 M and less than 10^2 M


I understand that setting the solubility product to molar solubility is the way you go about solving the problem

Cu+ Cl so molar solubility = x*x = x^2

plug this into the solubility product equation:


1.2*10^-6 = x^2

now i realize that you have to take the square root of both sides to find the molar solubility

solving for x = sqrt(1.2*10^-6)

I know the sqrt of 10^-6 is just 10^-3

but I have no clue how to solve for the square root of 1.2 and even if I did the answer choices confuse the heck out of me and make me lose my entire train of thought to the point where I'm not sure what the problem is asking for .... can somebody please pick up from where I left off (if i'm on the right track) and explain where to go from there to arrive at the right answer choice. I don't understand why the answer would be a range. To my understanding molar solubility is the maximum concentration you can place in before seeing a precipitate, so shouldn't the answer be in the form of less than or equal to x



btw answer is C

 

[enervate]

Bump sqrt(1.2 * 10^-6) to sqrt(12 * 10^-7). sqrt(12) falls between 3 and 4 so you're left with 3.? * 10^-3.5.

Invert that number to find the maximum. Remember that 3.? * 10^-3.5 = 3.? / 10^3.5 so the inverse leaves you with 10^3.5 / 3.?. Obviously that number is much greater than zero so you should choose B or C since they're both the same as you've written them.

 

[Addallat]

Bump sqrt(1.2 * 10^-6) to sqrt(12 * 10^-7). sqrt(12) falls between 3 and 4 so you're left with 3.? * 10^-3.5.

Invert that number to find the maximum. Remember that 3.? * 10^-3.5 = 3.? / 10^3.5 so the inverse leaves you with 10^3.5 / 3.?. Obviously that number is much greater than zero so you should choose B or C since they're both the same as you've written them.

Alright so what you're saying is:

i need to know the sqrt of 1.2*10^-6

so i turn it into

sqrt (12 * 10^-7)

since the square root of 12 is between 3 and 4 (probably closer to 3 I'm assuming since 3^2 is 9 and 4^2 is 16), i get the following

3.4 *10^-3.5 <~~~~~ i lost you at this point lol This problem just seems like a lot of math that's tripping me up. I appreciate your response, but does anyone have an easier way to approach this problem? are there any shortcuts?

 

[deh2ase]

Split this problem up into two square roots.
sqrt of 1.2*10^-6 = sqrt(1.2) * sqrt(10^-6)

Since 1.2 is between 1 and 2. sqrt(1) = 1 and sqrt(2) = 1.4

Your answer should be a number slightly greater than 1 * 10^-3 but less than 1.4 * 10^-3

Also your answer choices have B and C being repeated.

 

[Addallat]

Split this problem up into two square roots.
sqrt of 1.2*10^-6 = sqrt(1.2) * sqrt(10^-6)

Since 1.2 is between 1 and 2. sqrt(1) = 1 and sqrt(2) = 1.4

Your answer should be a number slightly greater than 1 * 10^-3 but less than 1.4 * 10^-3

Also your answer choices have B and C being repeated.

ahhhhh great approach thank you makes a lot of sense now

 

[enervate]

Your answer should be a number slightly greater than 1 * 10^-3 but less than 1.4 * 10^-3

How does that correlate with the correct answer that you've edited to be "greater than 10^-4 M and less than 10^2 M?" It accounts for the lower limit but not the upper limit.

 

[Addallat]

How does that correlate with the correct answer that you've edited to be "greater than 10^-4 M and less than 10^2 M?" It accounts for the lower limit but not the upper limit.

I see what you're saying, but going back to the problem you can rule out A and B. While less than 10^2 M isn't the exact range your answer will be found,
1.4 * 10^-3 is less than 10^2 M so it's your best bet out of the other three choices given