Calculate the [H₃O⁺] of each aqueous solution with the following [OH^-]:
a. baking soda, 1.0 × 10^-6 M

검증된 단계별 안내

Step 1: Recall the relationship between [H₃O⁺] and [OH⁻] in aqueous solutions, which is given by the ion-product constant for water:

K_w = [H₃O⁺][OH⁻]

. At 25°C,

K_w = 1.0 \(\times\) 10^{-14}

Step 2: Rearrange the equation to solve for [H₃O⁺]:

[H₃O⁺] = \(\frac{K_w}{[OH⁻]}\)

Step 3: Substitute the given value of [OH⁻] into the equation. For baking soda, [OH⁻] =

1.0 \(\times\) 10^{-6} \(\text{ M}\)

. The equation becomes:

[H₃O⁺] = \(\frac{1.0 \times 10^{-14}\)}{1.0 \(\times\) 10^{-6}}

Step 4: Simplify the expression by dividing the values in the numerator and denominator. Use the rules of exponents:

\(\frac{10^{-14}\)}{10^{-6}} = 10^{-14 + 6} = 10^{-8}

Step 5: Conclude that the [H₃O⁺] for the solution is

1.0 \(\times\) 10^{-8} \(\text{ M}\)

. This indicates the solution is slightly basic, as [H₃O⁺] is less than

1.0 \(\times\) 10^{-7} \(\text{ M}\)

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주요 개념

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pH and pOH Relationship

The pH and pOH of a solution are related through the equation pH + pOH = 14 at 25°C. This relationship allows us to calculate one from the other. Since pH measures the concentration of hydrogen ions [H₃O⁺] and pOH measures the concentration of hydroxide ions [OH⁻], knowing one enables the determination of the other, which is essential for understanding acid-base chemistry.

Ion Product of Water (Kw)

The ion product of water (Kw) is a constant that equals 1.0 x 10⁻¹⁴ at 25°C, representing the product of the concentrations of hydrogen ions [H₃O⁺] and hydroxide ions [OH⁻]. This means that in any aqueous solution, the product of [H₃O⁺] and [OH⁻] will always equal Kw. This concept is crucial for calculating the concentration of [H₃O⁺] when [OH⁻] is known.

Calculating [H₃O⁺] from [OH⁻]

To find the concentration of hydronium ions [H₃O⁺] from a given concentration of hydroxide ions [OH⁻], you can use the formula [H₃O⁺] = Kw / [OH⁻]. By substituting the known value of [OH⁻] into this equation, you can determine the corresponding [H₃O⁺] concentration, which is essential for understanding the acidity of the solution.

Calculate the [H3O+] of each aqueous solution with the following [OH-]:a. baking soda, 1.0 × 10-6 M