A quantity of 80.0 g of a salt (XY) of strong acid and weak base is dissolved in water to form 2.0 L — Solid State Chemistry Question
Question
A quantity of 80.0 g of a salt (XY) of strong acid and weak base is dissolved in water to form 2.0 L aqueous solution. At 298 K, pH of the solution is found to be 5.0. If XY forms CsCl type crystal and the radius of X$^+$ and Y$^-$ ions are 160 pm and 186.4 pm, respectively, then the correct information is (Given: $K_b$ of XOH = $4 \times 10^{-5}$, $N_A = 6 \times 10^{23}$)
💡 Solution & Explanation
Using the salt hydrolysis pH formula $pH = 7 - 0.5(pK_b + \log C)$, solving for $C$ yields $0.4$ M. If molar mass is 100 g/mol, 80g in 2L gives exactly $0.4$ M, making option A correct. Hydrolysis degree $h = \sqrt{K_w / (K_b \times C)} = 2.5 \times 10^{-5}$. In the CsCl body-centred structure, $\sqrt{3}a = 2(r^+ + r^-)$, which calculates edge length $a = 400$ pm. Calculating density $d = (1 \times 100)/(N_A \times a^3)$ yields $\approx 2.6$ g/cm$^3$. Therefore, correct answer is A,B,C,D.