Determine the pH of an HNO₂ solution of each concentration. In which cases can you not make the simplifying assumption that x is small? a. 0.500 M b. 0.100 M c. 0.0100 M

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Start by writing the dissociation equation for HNO_2: \[ \text{HNO}_2 \rightleftharpoons \text{H}^+ + \text{NO}_2^- \].

Write the expression for the acid dissociation constant (K_a) for HNO_2: \[ K_a = \frac{[\text{H}^+][\text{NO}_2^-]}{[\text{HNO}_2]} \].

Assume the initial concentration of HNO_2 is \([\text{HNO}_2]_0\) and the change in concentration due to dissociation is \(x\). Therefore, \([\text{H}^+] = x\), \([\text{NO}_2^-] = x\), and \([\text{HNO}_2] = [\text{HNO}_2]_0 - x\).

Substitute these expressions into the K_a expression: \[ K_a = \frac{x^2}{[\text{HNO}_2]_0 - x} \].

For each concentration, check if \(x\) is small compared to \([\text{HNO}_2]_0\) by assuming \([\text{HNO}_2]_0 - x \approx [\text{HNO}_2]_0\) and solving for \(x\). If \(x\) is not negligible, the assumption is invalid.>

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주요 개념

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pH and Acid Dissociation

pH is a measure of the acidity or basicity of a solution, calculated as the negative logarithm of the hydrogen ion concentration. For weak acids like HNO2, the dissociation in water is not complete, and the pH can be determined using the acid dissociation constant (Ka). The extent of dissociation affects the pH, making it crucial to understand how weak acids behave in solution.

Weak Acid Equilibrium

Weak acids do not fully dissociate in solution, establishing an equilibrium between the undissociated acid and its ions. The equilibrium expression involves the concentration of the products (H+ and the conjugate base) and the undissociated acid. This concept is essential for calculating pH and determining when the simplifying assumption of 'x' being small can be applied.

Assumption of 'x' being small

In weak acid calculations, the assumption that 'x' (the change in concentration due to dissociation) is small simplifies the equilibrium expression. This assumption is valid when the initial concentration of the acid is significantly greater than the dissociated amount. However, at higher concentrations, or when the acid is stronger, this assumption may not hold, necessitating a more precise calculation.

Determine the pH of an HNO2 solution of each concentration. In which cases can you not make the simplifying assumption that x is small? a. 0.500 M b. 0.100 M c. 0.0100 M