# You want to produce 579 mL of a 0.440 M solution of NaCl. You have a 1.40 M solution. How many mL of it should you use and dilute with water?

Let's start by assuming that you're not familiar with the formula for dilution calculations, so that you can't just plug in your values and do a quick calculation.

So, the idea with dilution calculations is that the number of moles of solute remains constant when diluting a given sample.

In essence, to dilute a solution you need to decrease the concentration of the solute by keeping the number of moles of solute constant and Increasing the volume.

Use the molarity and volume of the target solution to determine how many moles of solute it must contain

This is exactly how many moles of solute must be present in the sample of stock solution used to prepare the target solution.

This means that you can use the definition of molarity to determine what volume of the stock solution would contain this many moles of sodium chloride

Expressed in milliliters, the answer will be

Alternatively, you can use the formula for dilution calculations, which expresses the exact same concept

In this case, you would get

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Use 221 mL of the 1.40 M solution and dilute it with water to reach the desired volume of 579 mL, resulting in a 0.440 M NaCl solution.

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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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