Activity and pH

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The true definition of pH is: \[\Large pH = -\log(a_{\sf H^{+}})\] Where \(a_{\sf H^{+}}\) is the activity of protons in aqueous solution. We usually approximate that equation with the following expression: \[\Large pH = -\log(m_{\sf H^{+}})\] Where \(m_{\sf H^{+}}\) is the molality of protons in the aqueous solution. In question we shall be looking at how good this approximation is by using Debye­-Hückel theory to evaluate the pH of a aqueous solution of hydrochloric acid. a) Using the approximation expression of pH, calculate the pH of a 0.40 molal aqueous solution of hydrochloric acid. b) In the lab I was measuring the pH of a 0.40 molal aqueous solution of hydrochloric acid as accurately I could to 0.52 at 25 \(^{\circ}\)C. Calculate the activity coefficient for \(\sf H^{+} \) HINT: \(\gamma_{H^{+}}=\gamma_{\pm}\) c) Calculate the activity coefficient using the simple Debye­-Hückel equation for a 0.40 molal hydrochloric acid solution. d) Using the measured activity coefficient from b), calculate the \(B\) factor using the extended Debye­-Hückel equation (assume that \(C=0\)) e) Using the \(B\) factor and the extended Debye­-Hückel equation, calculate the pH for a 1.0 molal HCL solution. Did the result fit your expectations and why?
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