A 251 ml sample of 0.45M HCl is added to 455 mL of distilled water. What is the molarity of the final solution?

We are given:

251 mL sample of 0.45M HCl added to 455 mL distilled water

Whack a mole! (finding the number of moles):

We know that in order to find molarity, we use the formula:

Molarity = number of moles / Volume (in L)

so, number of moles is:

Number of moles = Molarity * Volume(in L)

now let's plug the values for the HCl solution to find the number of moles

Number of moles = 0.45M * 0.251 L

Number of moles = 0.113 moles

Time to concentrate (finding the final concentration):

Total final volume = 251 mL + 455 mL = 706 mL = 0.706 L

Number of moles of HCl = 0.113 moles

Molarity = Number of moles / Volume (in L)

Molarity = 0.113 / 0.706

Molarity = 0.16 M

BONUS METHOD TIME!!!

We know the relation:

M1 * V1 = M2 * V2

where M1 and M2 are the initial and final molarities and V1 and V2 are initial and final volumes respectively

notice that I didn't mention that the volume has to be in Liters, that's because of the units being concerned with both sides of the equation, say I have the volume in mL and want to convert both these volumes to L, I would divide both sides by 1000, which would NOT change the overall value

Now, plugging values in this equation

(0.45) * (251) = (251 + 455)* (M2)

112.95 = (706)(M2)

M2 = 112.97/706                                [dividing both sides by 706]

M2 = 0.16 Molar