# If somehow, #"50.0 mL"# of a stock solution of #"120. M"# #"HCl"# is available, what volume of water should the appropriate amount of #"HCl"# be added to, in order to reduce its concentration to #"4.00 M"#?

I assume you mean the "before/after" formula:

Basically, you have a relationship of concentration to volume:

What you already have are:

Or, to three sig figs:

Remember, that's your FINAL volume, NOT the amount of water you might start with, so you should subtract to get:

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To dilute the stock solution to 4.00 M, add 850 mL of water to the 50.0 mL of 120.0 M HCl.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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