TBR Dilution Question

[vpanopoulos]

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TBR Example 1.25, Chemistry Chapter 1

Which dilution converts 6.00 M HCl (aq) to 0.3 M HCl (aq)?

a) 11 parts water to 1 part 6M HCl (aq)
b) 19 parts water to 1 part 6M HCl (aq)
c) 20 parts water to 1 part 6M HCl (aq)
d) 21 parts water to 1 part 6M HCl (aq)

The answer is b, which when using the equation M1V1 = M2V2 it works out and all you have to do is subtract the final volume (20L) from the 1L already included in the 0.3M solution; therefore it's 19 parts water. The explanation in TBR also states this as a 20-fold dilution. That's my question: how did they conclude it's a 20 fold dilution?

My thought process was, if we wanted to dilute the solution down to 1M, it'd be a 5 fold dilution. Then down to 0.5M, it'd be 5.5 fold dilution.

Am I thinking about this the wrong way?

Thank you!

 

[giorgosdkm]

You begin with a 6.0 M solution. You end with a 0.3 M solution.

6.0/0.3 = 20

That's all they mean by a 20-fold dilution. The solution's concentration has been diluted to one-twentieth of what it was originally.

 

[vpanopoulos]

Got it. Thanks!