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Phosphoric acid dissociates to form hydronium ion and dihydrogen phosphate. Phosphoric acid has a \(K_{\mathrm{a}}\) of \(7.5 \times 10^{-3}\). Write the equation for the reaction and the acid dissociation expression for phosphoric acid.

Short Answer

Expert verified
The reaction is \( \text{H}_3\text{PO}_4 + \text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{H}_2\text{PO}_4^- \), and the acid dissociation expression is \( 7.5 \times 10^{-3} = \frac{[\text{H}_3\text{O}^+][\text{H}_2\text{PO}_4^-]}{[\text{H}_3\text{PO}_4]} \).

Step by step solution

01

Title - Write the chemical equation for the dissociation

Phosphoric acid (H鈧働O鈧) dissociates in water to form a hydronium ion (H鈧僌鈦) and a dihydrogen phosphate ion (H鈧侾O鈧勨伝). The chemical equation for this process is: \[ \text{H}_3\text{PO}_4 (aq) + \text{H}_2\text{O} (l) \rightleftharpoons \text{H}_3\text{O}^+ (aq) + \text{H}_2\text{PO}_4^- (aq) \]
02

Title - Write the expression for the acid dissociation constant (K_{\text{a}})

The acid dissociation constant (K_{\text{a}}) is defined as the ratio of the concentrations of the products to the concentration of the reactants, each raised to the power of their coefficients in the balanced equation. For phosphoric acid, the expression is: \[ K_{\text{a}} = \frac{[\text{H}_3\text{O}^+][\text{H}_2\text{PO}_4^-]}{[\text{H}_3\text{PO}_4]} \]
03

Title - Substitute the given K_{\text{a}} value

Substitute the given value of K_{\text{a}} into the expression: \[ K_{\text{a}} = 7.5 \times 10^{-3} \] Thus, the complete expression with the known K_{\text{a}} value is: \[ 7.5 \times 10^{-3} = \frac{[\text{H}_3\text{O}^+][\text{H}_2\text{PO}_4^-]}{[\text{H}_3\text{PO}_4]} \]

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Key Concepts

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

Acid Dissociation Constant
The acid dissociation constant, often denoted as \(K_{\text{a}}\), is a crucial value in chemistry that helps us understand the strength of an acid in a solution.
It's derived from the equilibrium concentrations of the acids and its dissociated ions in water.
A high \(K_{\text{a}}\) value indicates a strong acid, which dissociates well in water, while a low \(K_{\text{a}}\) value suggests a weak acid.
For example, phosphoric acid (H鈧働O鈧) with a \(K_{\text{a}}\) of \(7.5 \times 10^{-3}\) signifies a moderately strong acid.
The general form of the acid dissociation constant expression is:
  • \ K_{\text{a}} = \frac{ [ \text{H}_3\text{O}^+ ] [ \text{dissociated\text{anion}} ] } { [ \text{original\text{acid}} ] } \
  • This ratio gives us a measure of how much the acid dissociates.
Understanding the \(K_{\text{a}}\) is essential for calculating the pH and various equilibrium concentrations in a solution.
Chemical Equilibrium
Chemical equilibrium is a state in which the concentrations of reactants and products remain constant over time.
This occurs when the forward and reverse reactions proceed at the same rate.
For phosphoric acid dissociation:
\[ \text{H}_3\text{PO}_4 (aq) + \text{H}_2\text{O} (l) \rightleftharpoons \text{H}_3\text{O}^+ (aq) + \text{H}_2\text{PO}_4^- (aq) \]
  • At equilibrium, no net change in the concentrations of H鈧働O鈧, H鈧僌鈦, and H鈧侾O鈧勨伝 occurs.
    This balance is dynamic, meaning that molecules continuously react, but with constant concentrations.
  • The equilibrium position and how much it shifts depend on the reaction conditions like concentration, temperature and pressure.
Knowing the equilibrium point helps chemists predict how a change in conditions will affect the system.
Chemical Reaction Equation
A chemical reaction equation provides a concise format to describe a chemical reaction.
It shows reactants transforming into products using chemical symbols.
For phosphoric acid dissociation:
\[ \text{H}_3\text{PO}_4 (aq) + \text{H}_2\text{O} (l) \rightleftharpoons \text{H}_3\text{O}^+ (aq) + \text{H}_2\text{PO}_4^- (aq)\]
  • The arrow (\(\rightleftharpoons\)) indicates a reversible reaction where both forward and backward reactions can occur.
  • This equation tells us that H鈧働O鈧 dissociates into H鈧僌鈦 and H鈧侾O鈧勨伝 in an aqueous solution.
Writing balanced chemical equations like this is essential for understanding and predicting the results of chemical reactions.
It also forms the basis for calculating the acid dissociation constant, \(K_{\text{a}}\).
Hydronium Ion
Hydronium ions (H鈧僌鈦) are formed when a proton (H鈦) attaches to a water molecule (H鈧侽).
In acidic solutions, these ions are prevalent and play a key role in determining the pH of the solution.
For example, in the dissociation of phosphoric acid:
\[ \text{H}_3\text{PO}_4 + \text{H}_2\text{O} \rightarrow \text{H}_3\text{O}^+ + \text{H}_2\text{PO}_4^- \]
  • Each molecule of H鈧働O鈧 that dissociates forms one H鈧僌鈦 ion.
  • The concentration of H鈧僌鈦 directly reflects the acidity of the solution.
The more hydronium ions present, the lower the pH, and the more acidic the solution.
Dihydrogen Phosphate
Dihydrogen phosphate (H鈧侾O鈧勨伝) is one of the products formed when phosphoric acid dissociates in water.
It's a conjugate base of H鈧働O鈧 and can further dissociate to form hydrogen phosphate (HPO鈧劼测伝) under certain conditions:
\[ \text{H}_2\text{PO}_4^- \rightleftharpoons \text{H}^+ + \text{HPO}_4^{2-} \]
  • The dissociation of H鈧侾O鈧勨伝 is part of a series of equilibria involving phosphoric acid and its ions
  • H鈧働O鈧 \rightarrow H鈧侾O鈧勨伝 \rightarrow HPO鈧劼测伝 \rightarrow PO鈧劼斥伝 .
Understanding dihydrogen phosphate and its behavior is crucial in fields like biochemistry, where phosphate buffering is vital to maintaining pH in biological systems.

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