A gas mixture at a total pressure of \(150 \mathrm{kPa}\) and \(295 \mathrm{~K}\) contains \(20 \% \mathrm{H}_{2}, 40 \%\) \(\mathrm{O}_{2}\), and \(40 \% \mathrm{H}_{2} \mathrm{O}\) by volume. The absolute velocities of each species are \(-10 \mathrm{~m} / \mathrm{s}\), \(-2 \mathrm{~m} / \mathrm{s}\), and \(12 \mathrm{~m} / \mathrm{s}\), respectively, all in the direction of the \(z\)-axis.

(a) Determine the mass average velocity, \(\mathbf{v}\), and the molar average velocity, \(\mathbf{V}\), for the mixture.

(b) Evaluate the four fluxes: \(\mathrm{jo}_{\mathrm{O} 2}, \mathrm{n}_{\mathrm{O} 2}, \mathrm{~J}_{\mathrm{O} 2}, \mathbf{N}_{\mathrm{O} 2}\).