For 2:2 electrolyte (\(\text{MgSO}_{4}\)), the slope in Debye-Hückel plot is:
(a) 0.51
(b) 2.04
(c) 1.02
(d) 0.255
Step 1: Identify the formula and constant
The Debye-Hückel limiting law for the mean ionic activity coefficient (\(\gamma _{\pm }\)) in a dilute aqueous solution at 298 K is given by the equation:
\(\log _{10}(\gamma _{\pm })=-A|z_{+}z_{-}|\sqrt{I}\)
where \(A\) is the Debye-Hückel constant (approximately \(0.509\text{\ mol}^{-1/2}\text{kg}^{1/2}\) in water),
\(z_{+}\) and \(z_{-}\) are the charges of the cation and anion, respectively,
\(I\) is the ionic strength.
The slope of the plot of \(\log _{10}(\gamma _{\pm })\) versus \(\sqrt{I}\) is therefore \(-A|z_{+}z_{-}|\)
Step 2: Calculate the slope for \(\text{MgSO}_{4}\)
For a 2:2 electrolyte like \(\text{MgSO}_{4}\),
the charges are \(z_{+}=+2\) and \(z_{-}=-2\).
The absolute product of the charges is \(|z_{+}z_{-}|=|(2)(-2)|=4\).
Using the standard value for \(A\approx 0.51\):\(\text{Slope\ Magnitude}=A|z_{+}z_{-}|\approx 0.51\times 4=2.04\)
The slope in the Debye-Hückel plot (magnitude of the coefficient) for a 2:2 electrolyte like \(\text{MgSO}_{4}\) is 2.04.