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Question: What concentrations of acetic acid are needed to give a hydrogen ion concentration of \[3.5 \times {...

What concentrations of acetic acid are needed to give a hydrogen ion concentration of 3.5×10−4M3.5 \times {10^{ - 4}}M ?
(Ka=1.8×10−5)\left( {{K_a} = 1.8 \times {{10}^{ - 5}}} \right)
a.6.80×10−3M6.80 \times {10^{ - 3}}M
b.3.5×10−4M3.5 \times {10^{ - 4}}M
c.4.2×10−4M4.2 \times {10^{ - 4}}M
d.7.2×10−4M7.2 \times {10^{ - 4}}M

Explanation

Solution

Acid is a compound that can dissociate to give two ions. Out of them, one is hydrogen ion. The hydrogen ion concentration is equal to the concentration of another ion that was produced from acid on dissociation. From these values and the given value of acid dissociation constant, the concentration of acetic acid can be determined.
Formula used:
Ka=[CH3COO−][H+]CH3COOH{K_a} = \dfrac{{\left[ {C{H_3}CO{O^ - }} \right]\left[ {{H^ + }} \right]}}{{C{H_3}COOH}}
Ka{K_a} is acid dissociation constant
[CH3COO−]\left[ {C{H_3}CO{O^ - }} \right] is concentration of acetate ion
[H+]\left[ {{H^ + }} \right] is concentration of hydrogen ion

Complete answer:
Acetic acid is a weak acid that can dissociates into acetate ion and hydrogen ion as follows:
CH3COOH⇌CH3COO−+H+C{H_3}COOH \rightleftharpoons C{H_3}CO{O^ - } + {H^ + }
The concentration of hydrogen ion is given as 3.5×10−4M3.5 \times {10^{ - 4}}M
As the acetic acid is at equilibrium with the acetate ion and hydrogen ion.
Thus, the concentration of acetate ion is also 3.5×10−4M3.5 \times {10^{ - 4}}M
Equilibrium constant is the value that gives the information about how far the reactants were converted into products and it is represented by Ka{K_a}
By substituting these all values in the above formula,
1.8×10−5=[3.5×10−4][3.5×10−4][CH3COOH]1.8 \times {10^{ - 5}} = \dfrac{{\left[ {3.5 \times {{10}^{ - 4}}} \right]\left[ {3.5 \times {{10}^{ - 4}}} \right]}}{{\left[ {C{H_3}COOH} \right]}}
Further simplification gives the value as [CH3COOH]=0.0068M\left[ {C{H_3}COOH} \right] = 0.0068M
It can be written as 6.80×10−3M6.80 \times {10^{ - 3}}M
Thus, the concentrations of acetic acid is needed to give a hydrogen ion concentration of 3.5×10−4M3.5 \times {10^{ - 4}}M will be 6.80×10−3M6.80 \times {10^{ - 3}}M

Option a is the correct one.

Note:
When both the reactants and products are at the same rate, then the equilibrium condition will be established. At this point, there is no change in the concentrations of reactants and products with time. Based on this fact only, the concentrations of acetate ion and hydrogen ion were equal.