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

Explanation

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"`