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What will be the pressure of the gaseous...

What will be the pressure of the gaseous mixture when 0.5 L of `H_(2)` at 0.8 bar and 2.0 L of dioxygen at 0.7 bar are introduced in a 1L vessel at `27^(@)C`?

Text Solution

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Step I. Calculation of partial pressure of `H_(2)` in `1 L` vessel.
`V_(1) = 0.5 L , V_(2) = 1.0 L`
`P_(1) = 0.8 "bar" , P_(2) = ?`
According to Boyle's Law, `P_(1)V_(1) = P_(2)V_(2)`
`P_(2) = (P_(1)V_(1))/(V_(2)) = ((0.8"bar") xx (0.5 L))/((1.0 L)) = 0.4 "bar"`
Step II. Calculation of partial pressure of `O_(2)` in 1 L vessel .
`V_(1) = 2.0 L , V_(2) = 1.0 L`
`P_(1) = 0.7 "bar"`
According to Boyle's Law, `P_(1)V_(1) = P_(2)V_(2)`
`P_(2) = (P_(1)V_(1))/(V_(2)) = ((0.7 "bar") xx (2.0 L))/((1.0 L)) = 1.4 "bar"`
Step III. Calculation of total pressure of gaseous mixture.
`P = P_(1) + P_(2) = (0.4+1.4) "bar" = 1.8 "bar"`
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