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