At $27\,^oC$ temperature in a $2\, L$ closed vessel,$10\, g$ of $H_2$ and $22\, g$ of $CO_2$ gases are filled. Find the partial pressure of each gas and the total pressure of the mixture. (Use $R = 0.08314\, L \cdot bar \cdot K^{-1} \cdot mol^{-1}$ and formula $pV = nRT$)

(N/A) $1$. Calculate moles of each gas:
$n(H_2) = \frac{10\, g}{2\, g/mol} = 5\, mol$
$n(CO_2) = \frac{22\, g}{44\, g/mol} = 0.5\, mol$
$2$. Convert temperature to Kelvin:
$T = 27 + 273 = 300\, K$
$3$. Calculate partial pressures using $p = \frac{nRT}{V}$:
$p(H_2) = \frac{5 \times 0.08314 \times 300}{2} = 62.355\, bar$
$p(CO_2) = \frac{0.5 \times 0.08314 \times 300}{2} = 6.2355\, bar$
$4$. Calculate total pressure:
$P_{total} = p(H_2) + p(CO_2) = 62.355 + 6.2355 = 68.5905\, bar$