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

Verified step by step guidance

1. 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, $K\_w\; =\; 1.0\; \backslash times\; 10^\{-14\}$.
2. Step 2: Rearrange the equation to solve for [H₃O⁺]: $[H₃O⁺]\; =\; \backslash frac\{K\_w\}\{[OH⁻]\}$.
3. Step 3: Substitute the given value of [OH⁻] into the equation. For baking soda, [OH⁻] = $1.0\; \backslash times\; 10^\{-6\}\; \backslash text\{\; M\}$. The equation becomes: $[H₃O⁺]\; =\; \backslash frac\{1.0\; \backslash times\; 10^\{-14\}\}\{1.0\; \backslash times\; 10^\{-6\}\}$.
4. Step 4: Simplify the expression by dividing the values in the numerator and denominator. Use the rules of exponents: $\backslash frac\{10^\{-14\}\}\{10^\{-6\}\}\; =\; 10^\{-14\; +\; 6\}\; =\; 10^\{-8\}$.
5. Step 5: Conclude that the [H₃O⁺] for the solution is $1.0\; \backslash times\; 10^\{-8\}\; \backslash text\{\; M\}$. This indicates the solution is slightly basic, as [H₃O⁺] is less than $1.0\; \backslash times\; 10^\{-7\}\; \backslash text\{\; M\}$.

Key Concepts

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.