What is the concentration of a solution made by diluting 45 ml of 6.0 M HCl to a final volume of 750 ml?

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The concentration would be 0.76 mol/L.

The most common way to solve this problem is to use the formula

#c_1V_1 = c_2V_2#

In your problem,

#c_1# = 4.2 mol/L; #V_1# = 45.0 mL
#c_2# = ?; #V_2# = 250 mL

#c_2 = c_1 × V_1/V_2# = 4.2 mol/L × #(45.0"mL")/(250"mL")# = 0.76 mol/L

This makes sense. You are increasing the volume by a factor of about 6, so the concentration should be about ¹/₆ of the original (¹/₆ × 4.2 = 0.7).

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