A ' 2 litre' kettle contains 450 gram of boiler scale CaCO 3 . If total number of times would the kettle have to be completely filled with distilled water to remove all the deposits at 2 5

Question

A ' 2 litre' kettle contains 450 gram of boiler scale $CaCO_{3}$ . If total number of times would the kettle have to be completely filled with distilled water to remove all the deposits at $2 5^{\circ} C$ is $a \times 10^{- b}$ (in scientific notation), then find the value of $[2 (a + b)]$ is

[Given: $K_{s p} (C a C O_{3}) = 8.1 \times 1 0^{- 9}$ at $2 5^{\circ} C$ ]

TestHub · Accepted Answer

CaCO 3 ( s ) ​ ⇌ Ca ( aq ) 2 + ​ + CO 3 ( aq ) 2 − ​ K s p ​ = s 2 s = 81 × 1 0 − 10 ​ = 9 × 1 0 − 5 m o l e / l i t ∴ V solution ​ n CaCO 3 ​ ​ = 9 × 1 0 − 5 ⇒ V solution ​ = 100 450 ​ × 9 × 1 0 − 5 1 ​ = 5 × 1 0 4 l i t V H 2 ​ O ​ required = 5 × 1 0 4 lit ∴ No. of times kettle filled = 2 5 × 1 0 4 ​ = 2.5 × 1 0 4 ∴ a = 2.5 ; b = 4

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