What is the hydronium ion $[H_3 O^+]$ concentration for a $6.42 \times 10^{-9} M [OH^-]$ solution?
Answer (2)
The hydronium ion concentration in a solution with a hydroxide ion concentration of 6.42 × 1 0 − 9 M is calculated using the ion product of water. The final concentration is approximately 1.56 × 1 0 − 6 M . This is determined by rearranging the formula for the ion product of water and substituting the known values.
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Use the ion product of water formula: K w = [ H 3 O + ] [ O H − ] = 1.00 × 1 0 − 14 M 2 .
Solve for hydronium ion concentration: [ H 3 O + ] = [ O H − ] K w .
Substitute the given hydroxide ion concentration: [ H 3 O + ] = 6.42 × 1 0 − 9 1.00 × 1 0 − 14 .
Calculate the hydronium ion concentration: [ H 3 O + ] ≈ 1.56 × 1 0 − 6 M .
1.56 × 1 0 − 6 M
Explanation
Problem Analysis and Given Data We are given the hydroxide ion concentration, [ O H − ] = 6.42 × 1 0 − 9 M , and we need to find the hydronium ion concentration, [ H 3 O + ] . We know that the ion product of water, K w , is 1.00 × 1 0 − 14 M 2 at 2 5 ∘ C .
Relevant Formula We can use the following equation to relate the hydronium and hydroxide ion concentrations:
K w = [ H 3 O + ] [ O H − ]
We can rearrange this equation to solve for the hydronium ion concentration:
[ H 3 O + ] = [ O H − ] K w
Substitution Now, we can substitute the given values into the equation:
[ H 3 O + ] = 6.42 × 1 0 − 9 M 1.00 × 1 0 − 14 M 2
Calculation Performing the calculation:
[ H 3 O + ] = 1.5576323987538942 × 1 0 − 6 M
Rounding to three significant figures, we get:
[ H 3 O + ] ≈ 1.56 × 1 0 − 6 M
Final Answer Therefore, the hydronium ion concentration is approximately 1.56 × 1 0 − 6 M .
Examples
Understanding hydronium and hydroxide ion concentrations is crucial in many real-world applications. For example, in environmental science, monitoring the pH levels of water sources helps assess water quality and the impact of pollutants. In medicine, maintaining the correct pH balance in bodily fluids is essential for proper physiological function. In agriculture, soil pH affects nutrient availability for plants, influencing crop yields. By determining the hydronium ion concentration, we can assess the acidity or basicity of a solution, which is vital in these diverse fields.
