Question

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the hydronium ion concentration of an aqueous solution of 0.413 m acetylsalicylic acid (aspirin), hc9h7o4, (ka = 3.00×10^-4) is
h3o+ = m.
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Explanation:

Step1: Write the dissociation equation

Acetylsalicylic acid (\(HC_9H_7O_6\)) dissociates as \(HC_9H_7O_6 + H_2O
ightleftharpoons H_3O^++C_9H_7O_6^-\). Let \([H_3O^+]=x\). Then \([C_9H_7O_6^-]=x\) and \([HC_9H_7O_6]=0.413 - x\).

Step2: Apply the \(K_a\) formula

\(K_a=\frac{[H_3O^+][C_9H_7O_6^-]}{[HC_9H_7O_6]}\). Substituting the values, \(3.30\times10^{-4}=\frac{x\times x}{0.413 - x}\). Since \(K_a\) is small, \(0.413 - x\approx0.413\). So \(3.30\times10^{-4}=\frac{x^{2}}{0.413}\).

Step3: Solve for \(x\)

\(x^{2}=3.30\times10^{-4}\times0.413\). \(x^{2}=1.3629\times10^{-4}\). \(x=\sqrt{1.3629\times10^{-4}}\). \(x = 0.0117\)

Answer:

\(0.0117\)