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Consider a sealed rigid bottle containing $CO_{2}$ and $H_{2}O$ at $10$ bar and ambient temperature. Assume that the gas phase in the bottle is pure $CO_{2}$ and follows the ideal gas law. The liquid phase in the bottle contains $CO_{2}$ dissolved in $H_{2}O$ and is an ideal solution. The Henry's constant at the system pressure and temperature is $H_{CO_{2}}=1000$ bar. The equilibrium mole fraction of $CO_{2}$ dissolved in $H_{2}O$ is __________________ (rounded off to three decimal places).
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