Urgent GC Question

[Muggs]

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The molar solubility of a salt of the formula MX2 is 2.0x10^-6 M. What is the Ksp?

Now I know that Ksp = 4x^3 and x = 2.0x10^-6.

Ksp = 4(2.0x10^-6)^3

However, wouldn't this reduce to 4(2.0x10^-18) and not 4(8.0x10^-18)?
The answer key says the latter, but I thought that according to the rules of exponents...
(x^m)^n = x^mn

I thought just the -6 exponent gets multiplied by 3 and not the 2.0 as well.

 

[Corleon2000]

The molar solubility of a salt of the formula MX2 is 2.0x10^-6 M. What is the Ksp?

Now I know that Ksp = 4x^3 and x = 2.0x10^-6.

Ksp = 4(2.0x10^-6)^3

However, wouldn't this reduce to 4(2.0x10^-18) and not 4(8.0x10^-18)?
The answer key says the latter, but I thought that according to the rules of exponents...
(x^m)^n = x^mn

I thought just the -6 exponent gets multiplied by 3 and not the 2.0 as well.

The -6 gets multiplied by the power of 3, while the 2 gets raised to the power of 3 since its not an exponent. 2x2x2=8.

Hope this helps.

 

[Muggs]

The -6 gets multiplied by the power of 3, while the 2 gets raised to the power of 3 since its not an exponent. 2x2x2=8.

Hope this helps.

But then why does Chad give this example...

Ksp = [Bi][I-]^3
Ksp = (x)(3x)^3 = 27x^4
27(1.32x10^-5)^4 = 27x10^-20 = 2.7x10^-19

He doesn't raise 1.32 to the 4th power and instead just multiples 27 by 1.32...

 

[J777]

But then why does Chad give this example...

Ksp = [Bi][I-]^3
Ksp = (x)(3x)^3 = 27x^4
27(1.32x10^-5)^4 = 27x10^-20 = 2.7x10^-19

He doesn't raise 1.32 to the 4th power and instead just multiples 27 by 1.32...

Chad was just doing a quick approximation. The idea is that we can approximate the value of (1.32 x 10^-5)^4 as being close enough to (1.00 x 10^-5)^4 = 1 x 10^-20. Then, when you multiply by 27, you get 2.7 x 10^-19. This number is low compared to the actual number. However, your answer choices will likely be far enough apart such that our approximation will lead you to the correct answer.

But you are correct, to precisely calculate the value, you would need to raise everything to the 4th power.. The exact computation is (1.32 x 10^-5)^4 = 3.059 x 10-19.

When you multiply that by 27, you get 8.19 x 10^-19. This value is slightly larger than our approximation of 2.7 x 10^-19, but likely much closer than any of the other answer choices that will be provided.

The most important number is the 10^-19, not the 8.19 or 2.7. I hope that helps!

 

[Muggs]

Chad was just doing a quick approximation. The idea is that we can approximate the value of (1.32 x 10^-5)^4 as being close enough to (1.00 x 10^-5)^4 = 1 x 10^-20. Then, when you multiply by 27, you get 2.7 x 10^-19. This number is low compared to the actual number. However, your answer choices will likely be far enough apart such that our approximation will lead you to the correct answer.

But you are correct, to precisely calculate the value, you would need to raise everything to the 4th power.. The exact computation is (1.32 x 10^-5)^4 = 3.059 x 10-19.

When you multiply that by 27, you get 8.19 x 10^-19. This value is slightly larger than our approximation of 2.7 x 10^-19, but likely much closer than any of the other answer choices that will be provided.

The most important number is the 10^-19, not the 8.19 or 2.7. I hope that helps!

Awesome. Thank you!