Hello -
In this question you need to determine the number of moles of base
needed to neutralize a given number of moles of acid. The first step
is determining the number of moles of acid.
HCl is a strong acid which dissociates rapidly into H+ and Cl- ions.
H+ ions are what contribute to the acidity of a substance. By the
formula, we can see that each HCl molecule will contribute a single H+
ion. Therefore, there is a 1:1 relation between the concentration of
the HCl (0.5M) and the number of H+ ions which will be produced.
Thus, our concentration of H+ ions is also 0.5M. Molarity is defined
as the number of moles divided by the number of liters. Therefore, to
determine the number of moles of acid which we have we need to
multiply our molar concentration by the volume which we have:
0.5 moles H+
0.5 M H+ -> ------------- * 0.03 L = 0.015 moles of H+
1 L
NaOH rapidly dissociates into Na+ and OH- ions. OH- ions rapidly
combine with H+ ions to form water, removing the acid from the
solution (if there is an excess of OH- ions, a solution is basic). We
now know that we need 0.015 moles of OH- ion to neutralize the 0.015
moles of H+ ion generated by the HCl and the question gives us that
the concentration of NaOH is 0.20M. As there is one OH moiety in
NaOH, the concentration of OH- is also 0.20M. To calculate the volume
needed, we need to divide the number of moles desired by the
concentration (or in this case, multiply by the inverse for simpler
representation):
0.015 moles 1 L
--------------- * --------------- = 0.075 L = 75 mL
1 0.2 moles H+
This relation can be expressed by the formula:
V1 * C1 = V2 * C2
where V1 = volume of the first solution
C1 = concentration of the first solution
V2 = volume of the second solution
C2 = concentration of the second solution
solving for V2, as the question asks:
V1 * C1 0.030 * 0.5 M
V2 = --------- = -------------- = 0.075 L = 75 mL
C2 0.2 M
Reference:
http://genchem.rutgers.edu/acid.html
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