Question

Write a balanced equation for the proton-transfer reaction between a hydrogen phosphate ion and a hydroxide ion. Identify each conjugate acid-base pair, and determine in which direction the equilibrium is favored.

Short answer

The reaction forms \(PO_4^{3-}\) and \(H_2O\); equilibrium favors the right.

Step-by-step solution

Write the Chemical Equation

Identify the reactants and products in the proton-transfer reaction. The reactants are hydrogen phosphate ion (\(HPO_4^{2-}\)) and hydroxide ion (\(OH^-\)). The products formed when \(OH^-\) accepts a proton from \(HPO_4^{2-}\) are phosphate ion (\(PO_4^{3-}\)) and water (\(H_2O\)). The balanced chemical equation is:\[HPO_4^{2-} + OH^- \rightarrow PO_4^{3-} + H_2O\]

Identify Conjugate Acid-Base Pairs

In the reaction, hydrogen phosphate ion (\(HPO_4^{2-}\)) donates a proton to form phosphate ion (\(PO_4^{3-}\)), and hydroxide ion (\(OH^-\)) accepts a proton to form water (\(H_2O\)). Thus, the conjugate acid-base pairs are: - \(HPO_4^{2-}\) and \(PO_4^{3-}\) - \(OH^-\) and \(H_2O\)

Determine the Direction of Equilibrium

Compare the strengths of the acids and bases involved. \(OH^-\) is a stronger base than \(PO_4^{3-}\), and \(H_2O\) is a weaker acid than \(HPO_4^{2-}\). Thus, the equilibrium will be favored in the direction that forms the weaker acid and weaker base, which is the forward direction to form \(PO_4^{3-}\) and \(H_2O\).

Key concepts

Conjugate Acid-Base Pairs

In a proton-transfer reaction, we often deal with pairs of substances that can act as acids and bases. A conjugate acid-base pair consists of two species that transform into each other by gaining or losing a proton. This is key to understanding how substances can both donate and accept protons under different conditions.
For example, consider the proton-transfer reaction in our exercise:

• Hydrogen phosphate ion, \(HPO_4^{2-}\), acts as an acid because it donates a proton.
• Phosphate ion, \(PO_4^{3-}\), is the conjugate base that results after \(HPO_4^{2-}\) loses a proton.
• Hydroxide ion, \(OH^-\), is a base as it accepts a proton to transform into water.
• Water, \(H_2O\), becomes the conjugate acid of \(OH^-\).

These pairs are fundamental to predicting reactions and deciding the direction in which reactions favorably proceed.

Chemical Equilibrium

Chemical equilibrium occurs when a chemical reaction proceeds at such a rate that the concentrations of reactants and products remain constant over time. It is a state of balance where no net change in the concentration of substances occurs, even though the reactions continue to take place.
In a reversible reaction like a proton-transfer reaction, the equilibrium can be affected by:

• The strength of acids and bases: Stronger acids and bases react more completely, pushing the equilibrium towards weaker acids and bases.
• Temperature: Higher temperatures can shift equilibrium positions depending on the reaction being endothermic or exothermic.

In the example reaction, equilibrium is favored towards the formation of \(PO_4^{3-}\) and \(H_2O\), as they are weaker acid and base, respectively. Understanding equilibrium helps us to manipulate and predict reaction behaviors under various conditions.

Chemical Equation Balancing

Balancing chemical equations is a vital skill in chemistry that ensures the law of conservation of mass is obeyed. This means the number of atoms for each element must be the same on both sides of a chemical reaction equation.
Consider a chemical reaction equation like \(HPO_4^{2-} + OH^- \rightarrow PO_4^{3-} + H_2O\). To successfully balance it:

• Count the number of atoms of each element present in the reactants and products.
• Adjust coefficients, not subscripts, to obtain equal numbers of atoms for each element on both sides of the equation.
• Ensure that the charges are balanced if the equation involves ions.

Balancing the equation correctly helps in determining the exact stoichiometry of a reaction, which is crucial for understanding how much of each substance is needed or produced.