Question

Activity and pH

Answer 1

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?

Answer 2

Are we going to get the solutions?