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Q.

If equal volumes of BaCl₂ and NaF solutions are mixed, which of these combinations will not give a precipitate?
Substance = BaF₂ k_sp = 1.7 × 10^-7

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a

0.004 M BaCl₂ and 0.02 M NaF

b

0.010 M BaCl₂ and 0.015 M NaF

c

0.1 M BaCl₂ and 0.01 M NaF

d

0.020 M BaCl₂ and 0.002 M NaF

answer is D.

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Detailed Solution

For precipitation, K_IP $\geqslant$ K_sp

$1)K_{IP}=\left[ {B{a^{ + 2}}} \right]{\left[ {{F^ - }} \right]^2}$

$K_{IP}=\frac{4\times10^{-3}}{2}\times\left ( \frac{2\times{10^{-2}}}{2} \right )^2=2\times10^{-7}$

$\therefore$ Precipitation will occur.

$2)K_{IP}=\left ( \frac{10^{-2}}{2} \right )\times\left ( \frac{1.5\times10^{-2}}{2} \right )^2$

${K_{IP}} = 0.28 \times {10^{ - 6}} = 2.8 \times {10^{ - 7}}$

precipitation will occur.

$3)K_{IP}=\left ( \frac{0.1}{2} \right )\times\left ( \frac{0.1}{2} \right )^2$

${K_{IP}} = 2.5 \times {10^{ - 6}}$

precipitation will occur.

$4)K_{IP}=\left ( \frac{0.020}{2} \right )\times\left ( \frac{0.002}{2} \right )^2$

${K_{IP}} = {10^{ - 8}}$

K_IP < K_sp ⇒ No precipitation will occur.

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