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A solution is \(0.030 \mathrm{M} \mathrm{HNO}_{3}\) (nitric acid). What is the hydronium-ion concentration at \(25^{\circ} \mathrm{C} ?\) What is the hydroxide-ion concentration at \(25^{\circ} \mathrm{C} ?\)

Short Answer

Expert verified
[H鈧僌鈦篯 = 0.030 M, [OH鈦籡 = 3.33 x 10鈦宦孤 M.

Step by step solution

01

Understanding Molarity of HNO鈧

The given solution is 0.030 M HNO鈧, which means that the concentration of HNO鈧 is 0.030 moles per liter. Since HNO鈧 is a strong acid, it dissociates completely in solution.
02

Hydronium Ion Concentration

Upon dissociation, each mole of HNO鈧 produces one mole of hydronium ions (H鈧僌鈦). Therefore, the concentration of hydronium ions, [H鈧僌鈦篯, is the same as the concentration of the HNO鈧 solution, which is 0.030 M.
03

Relation Between Hydronium and Hydroxide Ions

At 25掳C, water has an ionic product constant, Kw, of 1.0 x 10鈦宦光伌. We can use the equation: \[ \text{[H}_3\text{O}^+\text{] [OH}^-\text{]} = K_w = 1.0 \times 10^{-14} \] We already know [H鈧僌鈦篯 = 0.030 M from the previous step.
04

Calculate Hydroxide Ion Concentration

Rearrange the equation to solve for [OH鈦籡: \[ \text{[OH}^-\text{]} = \frac{K_w}{\text{[H}_3\text{O}^+\text{]}} = \frac{1.0 \times 10^{-14}}{0.030} \] By performing the division: \[ \text{[OH}^-\text{]} = 3.33 \times 10^{-13} \text{ M} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molarity
Molarity is a fundamental concept that defines the concentration of a solution. It is expressed as the number of moles of solute per liter of solution. In simpler terms, it tells us how much of a substance is present in a given amount of liquid. For example, a 0.030 M solution of nitric acid (HNO鈧) means there are 0.030 moles of HNO鈧 dissolved in every liter of solution.
Nitric acid, being a strong acid, dissociates completely in water. This characteristic is important because it means the molarity of the acid directly represents the concentration of hydrogen ions it generates in solution. Understanding molarity is crucial when predicting how solutions will behave in chemical reactions, such as those involving acid-base equilibria.
  • Molarity is measured in moles per liter (mol/L).
  • Strong acids dissociate completely, affecting the molarity of ions in solution.
Hydronium Ions
Hydronium ions, denoted as H鈧僌鈦, are a key player in acid-base chemistry. They form when an acid dissociates and releases hydrogen ions (H鈦), which then associate with water molecules. For instance, in the dissociation of nitric acid (HNO鈧), each molecule of HNO鈧 releases one hydrogen ion, resulting in the formation of hydronium ions. Consequently, for a 0.030 M solution of HNO鈧, the concentration of hydronium ions is also 0.030 M.
The concentration of hydronium ions is vital as it directly correlates to the acidity of a solution. More hydronium ions indicate a stronger acidic environment.
Here are some interesting points about hydronium ions:
  • The symbol [H鈧僌鈦篯 represents the concentration of hydronium ions.
  • The strength of an acid correlates with how many hydrogen ions it releases, forming hydronium ions upon interacting with water.
Hydroxide Ions
Hydroxide ions, expressed as OH鈦, are fundamental in understanding the base side of the acid-base equilibrium. When a solution is more basic, it has a higher concentration of hydroxide ions, and therefore, lower acidity. In a neutral water solution at 25掳C, the concentration of both hydronium and hydroxide ions is balanced at 1.0 x 10鈦烩伔 M.
When working with acidic solutions like our example of 0.030 M HNO鈧, determining the hydroxide ion concentration involves using the ionic product of water. The hydroxide ion concentration is inversely related to the hydronium ion concentration. This inverse relationship helps us find the concentration of hydroxide ions when we know the hydronium ion concentration.
Remember:
  • [OH鈦籡 serves as the notation for hydroxide ion concentration.
  • The relationship between [H鈧僌鈦篯 and [OH鈦籡 is critical in calculating the pH and pOH of solutions.
Ionic Product of Water
The ionic product of water (Kw) is a constant value crucial for understanding aqueous solutions' properties, particularly acid and base behavior. At 25掳C, this constant is 1.0 x 10鈦宦光伌, defining the relationship between hydronium [H鈧僌鈦篯 and hydroxide [OH鈦籡 ions in water. This equilibrium equation shows that the product of their concentrations remains constant regardless of whether the solution is acidic or basic, allowing us to derive either ion's concentration when the other is known.
In our example, by knowing the concentration of hydronium ions ([H鈧僌鈦篯 = 0.030 M), we can calculate the hydroxide ion concentration by rearranging the Kw formula: [OH鈦籡 = Kw / [H鈧僌鈦篯.
Key points:
  • Kw is dependent on temperature, known to be 1.0 x 10鈦宦光伌 at 25掳C.
  • Understanding Kw is essential for solving problems involving acid-base equilibria.

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