Multiple Choice
Which of the following statements correctly describes strong acids and bases in aqueous solution?
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17. Acid and Base Equilibrium
Acids Introduction
Multiple Choice
Given that the concentration of [HX] in the reagent bottle is 1.0 M, the pH is 2.43, and the temperature is 22.1 degrees Celsius, with an equilibrium concentration of [HX] at 0.996 M and [X^-] at 4 x 10^-3 M, what is the equilibrium concentration of [H3O^+]?
A
1.0 x 10^-2 M
B
4.0 x 10^-3 M
C
2.5 x 10^-3 M
D
3.7 x 10^-3 M
Verified step by step guidance1
Start by understanding that the problem involves a weak acid HX dissociating in water to form H3O^+ and X^-. The equilibrium expression for this dissociation is: \( K_a = \frac{[H_3O^+][X^-]}{[HX]} \).
Given the equilibrium concentrations: [HX] = 0.996 M and [X^-] = 4 \(\times\) 10^{-3} M, we need to find the equilibrium concentration of [H3O^+].
Assume that the concentration of [H3O^+] at equilibrium is equal to the concentration of [X^-] because each molecule of HX that dissociates produces one H3O^+ and one X^-. Therefore, [H3O^+] = 4 \(\times\) 10^{-3} M.
Verify this assumption by calculating the pH from the given concentration of [H3O^+]. Use the formula: \( \text{pH} = -\log[H_3O^+] \). Substitute [H3O^+] = 4 \(\times\) 10^{-3} M into the equation to check if it matches the given pH of 2.43.
If the calculated pH matches the given pH, then the assumption is correct, and the equilibrium concentration of [H3O^+] is indeed 4 \(\times\) 10^{-3} M. If not, re-evaluate the assumptions or calculations.
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