Solid Ba (NO₃)₂ is gradually dissolved in a 1.0x 10⁻⁴ × Na₂CO₃ solution. At what concentration of Ba²⁺ will a precipitate begin to form?(K_sp for BaCO₃ = 5.1 ×10⁻⁹ )

4.1 x 10^-5 M

5.1 x 10^-5 M

8.1 x 10^-8 M

8.1 x 10^-7 M

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Solution

5.1 x 10^-5 M

Na subscript 2 CO subscript 3 space rightwards arrow with space on top space 2 Na to the power of plus space plus space CO subscript 3 superscript 2 minus end superscript space space space space space space space space space space space space space space space space space space space space space space space space space space space 1 space straight x space 10 to the power of negative 4 end exponent space straight M BaCO subscript 3 space space space space space space space space space space space space space Ba to the power of 2 plus end exponent space plus space CO subscript 3 superscript 2 minus end superscript Ksp space equals space left square bracket Ba to the power of 2 plus end exponent right square bracket left square bracket CO subscript 3 superscript 2 minus end superscript right square bracket 5.1 space straight x space 10 to the power of negative 9 end exponent space equals space left square bracket Ba to the power of 2 plus end exponent right square bracket left square bracket 1 space straight x space 10 to the power of negative 4 end exponent right square bracket left square bracket Ba to the power of 2 plus end exponent right square bracket space equals space fraction numerator 5.1 space straight x space 10 to the power of negative 9 end exponent over denominator 1 space straight x space 10 to the power of negative 4 end exponent end fraction space equals space 5.1 space straight x space 10 to the power of negative 5 end exponent space straight M

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